Unit 1 • Problem of the Day Trent’s class followed the story of the astronaut who “ran” a marathon while she was in space.

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The length of a modern-day marathon is about 138,435 feet. How should 138,435 be written in word form?

Pose the following problem to students.

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Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.7 m wide.

© Harcourt

Rewrite the width as a decimal measurement to the hundredths place. Next, write an inequality using a less than symbol (,) and the measures from the problem.

Grade 6

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Unit 1 • Problem of the Day Trent’s class followed the story of the astronaut who “ran” a marathon while she was in space.

1

The length of a modern-day marathon is about 138,435 feet. How should 138,435 be written in word form? one hundred thirty-eight thousand, four hundred thirty-five

Pose the following problem to students.

2

Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.7 m wide.

© Harcourt

Rewrite the width as a decimal measurement to the hundredths place. Next, write an inequality using a less than symbol (,) and the measures from the problem. 1.70 m, 1.35 m , 1.70 m.

Grade 6

Daily Transparency DT • Unit 1

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a marathon is usually measured in miles or kilometers. Measured in feet, a marathon is about 138,435 feet. How would you write 138,435 in expanded form?

Spiral Review 1. Write three hundred thousand, four hundred seventeen in standard form. 2. Write 1,170,007 in word form.

Lesson Quiz Compare the numbers and use , or . for each d. 1. 5,289,200 d 5,279,200 2. 4,795,614 d 2,999,999,000 3. 12 trillion d 152 billion © Harcourt

4. one hundred thirty four thousand, one hundred twelve d. two hundred fifty three 5. In 2005 the U.S. census stated that San Antonio, Texas had a population of 1,256,509. San Diego, that same year, had a population of one million, two hundred fifty five thousand, five hundred and forty. Which city had the largest population?

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a marathon is usually measured in miles or kilometers. Measured in feet, a marathon is about 138,435 feet. How would you write 138,435 in expanded form? (1 3 100,000) 1 (3 3 10,000) 1 (8 3 1,000) 1 (4 3 100) 1 (3 3 10) 1 (5 3 1)

Spiral Review 1. Write three hundred thousand, four hundred seventeen in standard form. 300,417 2. Write 1,170,007 in word form. one million, one hundred seventy thousand, seven

Lesson Quiz Compare the numbers and use , or . for each d. 1. 5,289,200 d 5,279,200 . 2. 4,795,614 d 2,999,999,000 , 3. 12 trillion d 152 billion . © Harcourt

4. one hundred thirty four thousand, one hundred twelve d. two hundred fifty . three 5. In 2005 the U.S. census stated that San Antonio, Texas had a population of 1,256,509. San Diego, that same year, had a population of one million, two hundred fifty five thousand, five hundred and forty. Which city had the largest population? San Antonio, Texas Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was 34.5 kilometers long, which converts to about 113,189 feet in customary measure. Estimate the difference, in feet, between the lengths of a modern-day marathon and the original marathon.

Spiral Review Compare, using ,, ., or 5. 1.

3,050,556 d 3,006,889

2.

7,009,889 d 7,010,889

Lesson Quiz Use an estimate to solve the problems. 1. 5,287 5 4,592 5 2. 7,394,002 2 4,709,287 5

© Harcourt

3. 453 3 605 5 4. 378qw 15,782 5 5. Max has a goal this year to save at least $400 for his college fund. He makes $4.50 for each hour he works. About how many hours would he need to work to save that much money? Should you underestimate or overestimate if he wants to be sure to make his goal?

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was 34.5 kilometers long, which converts to about 113,189 feet in customary measure. Estimate the difference, in feet, between the lengths of a modern-day marathon and the original marathon. Possible estimate: about 30,000 ft

Spiral Review Compare, using ,, ., or 5. 1.

3,050,556 d 3,006,889 3,006,889 , 3,050,556

2.

7,009,889 d 7,010,889 7,010,889 . 7,009,889

Lesson Quiz Use an estimate to solve the problems. Possible answers given 1. 5,287 5 4,592 5 10,000 2. 7,394,002 2 4,709,287 5 2,600,000

© Harcourt

3. 453 3 605 5 300,000 4. 378qw 15,782 5 40 5. Max has a goal this year to save at least $400 for his college fund. He makes $4.50 for each hour he works. About how many hours would he need to work to save that much money? Should you underestimate or overestimate if he wants to be sure to make his goal? About 100 hours; 400 ÷ 4 = 100 I should overestimate. If I underestimate he might not make his goal. I can do that by rounding his pay down to $4 before I divide. Grade 6

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Problem of the Day Trent's class followed the story of an astronaut who "ran" a marathon while she was in space. The length of a modern-day marathon is a little more than 42.195 kilometers, or about 42,195 meters. In ancient Greece, the original race was about 34.5 kilometers, or 34,500 meters, long. Explain whether 7,695 meters is a reasonable answer for the difference between the length of a modern-day marathon and the original marathon.

Spiral Review 1. 2.

Estimate by rounding addends: 1,278 1 176. Use compatible numbers to estimate 1,549 4 29.

Lesson Quiz 1. Meg said that a car traveling 55 miles per hour, would take about 4,345 hours to travel the distance from the moon to Earth, which is 238,900 miles sway. Is this a reasonable answer? © Harcourt

2. In 2005, Pakistan, with a land area of 796,095 square kilometers, had a population of 157,935,100 people. Population density can be found by dividing the number of people by the area of the land they occupy. Is 1,984 people per square kilometer a reasonable number for the density?

Grade 6

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Problem of the Day Trent's class followed the story of an astronaut who "ran" a marathon while she was in space. The length of a modern-day marathon is a little more than 42.195 kilometers, or about 42,195 meters. In ancient Greece, the original race was about 34.5 kilometers, or 34,500 meters, long. Explain whether 7,695 meters is a reasonable answer for the difference between the length of a modern-day marathon and the original marathon. Possible answer: it is a reasonable answer because it is close to my estimate of 7,000 meters (42,000 2 35,000).

Spiral Review 1. 2.

Estimate by rounding addends: 1,278 1 176. Possible answer: 1,500 Use compatible numbers to estimate 1,549 4 29. Possible answer: 50

Lesson Quiz 1. Meg said that a car traveling 55 miles per hour, would take about 4,345 hours to travel the distance from the moon to Earth, which is 238,900 miles sway. Is this a reasonable answer? Possible answer: Yes, because 240,000 4 60 5 4,000 © Harcourt

2. In 2005, Pakistan, with a land area of 796,095 square kilometers, had a population of 157,935,100 people. Population density can be found by dividing the number of people by the area of the land they occupy. Is 1,984 people per square kilometer a reasonable number for the density? No, the population is about 160,000,000 and the area about 800,000. 160,000,000 4 800,000 5 200 so 1,984 is not reasonable. Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was about 34.5 kilometers long, which converts to about 113,189 ft in customary measure. What is the difference, in feet, between the lengths of a modern-day marathon and the original marathon?

Spiral Review 1. 2.

Estimate by rounding the factors: 378 3 19. Why is 56 not a reasonable quotient for 6,899 4 67?

Lesson Quiz

© Harcourt

Find the sum or the difference. 1. 32 1 78 1 93 1 47 5

3. 4,499 1 298 5

2. 7,863 2 3,246 5

4. 647 2 228 5

5. The difference between the area of two parks is 23 square miles. If the smaller park is 370 square miles, what is the area of the bigger park? Explain how you found the answer.

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was about 34.5 kilometers long, which converts to about 113,189 ft in customary measure. What is the difference, in feet, between the lengths of a modern-day marathon and the original marathon? Possible answer: about 25,246 ft

Spiral Review 1. 2.

Estimate by rounding the factors: 378 3 19. Possible answer: 8,000 Why is 56 not a reasonable quotient for 6,899 4 67? Possible answer: It is not close enough to my estimate, about 100 (7000 4 70).

Lesson Quiz

© Harcourt

Find the sum or the difference. 1. 32 1 78 1 93 1 47 5 250

3. 4,499 1 298 5 4,797

2. 7,863 2 3,246 5 4,617

4. 647 2 228 5 419

5. The difference between the area of two parks is 23 square miles. If the smaller park is 370 square miles, what is the area of the bigger park? Explain how you found the answer. 393 sq miles: Addition is the inverse operation for subtraction. 23 1 370 5 393 Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 138,435 feet long. A runner covers the equivalent of a marathon in five days by running an equal distance each day. About how many feet does the runner travel each day?

Spiral Review 1. 2.

Subtract 6,899 from 34,500. Use an inverse operation to explain why 3,000 2 489 is not 2,521.

Lesson Quiz Find the product or quotient, then estimate to check. 1. 413 3 87 5 35,931; © Harcourt

2. 5,279 4 43 5 122 r33; 3. 547 3 698 5 381,806; 4. 7qw 556 5. The parking lot where Fred works pays him $0.75 for every car he parks. Each customer usually tips him $2.00 when he returns their car. If he parks 37 cars on Friday, how much will he make?

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 138,435 feet long. A runner covers the equivalent of a marathon in five days by running an equal distance each day. About how many feet does the runner travel each day? about 27,687 ft each day

Spiral Review 1. 2.

Subtract 6,899 from 34,500. 27,601 Use an inverse operation to explain why 3,000 2 489 is not 2,521. Possible answer: When 2,521 is added to 489, the sum is 3,010 instead of 3,000.

Lesson Quiz Find the product or quotient, then estimate to check. 1. 413 3 87 5 35,931; 400 3 90 5 36,000 © Harcourt

2. 5,279 4 43 5 122 r33; 5200 4 40 5 130 3. 547 3 698 5 381,806; 500 3 700 5 350,000 4. 7qw 556 79 r3; 560 4 7 5 80 5. The parking lot where Fred works pays him $0.75 for every car he parks. Each customer usually tips him $2.00 when he returns their car. If he parks 37 cars on Friday, how much will he make? (37 3 $0.75) 1 ( 37 3 $2.00) or 37 3 $2.75 5 $101.75 Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Trent divided 42,195 by 6 find out the number of meters his uncle ran each day for 6 days. What does the remainder to his division problem represent?

Spiral Review 1. Find the product of 478 and 15. 2. Use an inverse operation to explain why 4,272 4 48 is not 79.

Lesson Quiz © Harcourt

1. There are 52 pieces of candy in a bag. If Petra wants to give each of her 11 friends the same number of pieces of candy, how many pieces will each get and how many pieces will she have left over? 2. Each bus holds 32 students. How many buses will it take to get 102 students to the museum for a field trip? Every student must have a seat.

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Trent divided 42,195 by 6 find out the number of meters his uncle ran each day for 6 days. What does the remainder to his division problem represent? Possible answer: The remainder could represent the number of meters more his uncle needed to run a marathon.

Spiral Review 1. Find the product of 478 and 15. 7,170 2. Use an inverse operation to explain why 4,272 4 48 is not 79. Possible answer: When 79 is multiplied by 48, the product is 3,792 instead of 4,272.

Lesson Quiz © Harcourt

1. There are 52 pieces of candy in a bag. If Petra wants to give each of her 11 friends the same number of pieces of candy, how many pieces will each get and how many pieces will she have left over? 52 4 11 5 4 r8: Each will get 4 pieces and she will have 8 left over. 2. Each bus holds 32 students. How many buses will it take to get 102 students to the museum for a field trip? Every student must have a seat. 102 4 32 5 3 r6: They will need 4 buses. Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Write its length in expanded form with exponents in powers of 10.

Spiral Review 1.

What is the remainder of 3,789 4 23?

2.

What is the remainder of 789 4 23?

3.

What is the remainder of 6,423 4 23?

Lesson Quiz 1. Write 4,872 in expanded form using powers of 10 and exponents.

2. Write (5 3 104) 1 (7 3 103) 1 (8 3 102) 1 (4 3 100) in standard notation. © Harcourt

3. What is the exponent n needed to make this true; 7n 5 2,401 ? 4. Is 542,007 , or . 5 3 105 ? 5. Mercury is about 6 3 107 km from the sun, while Pluto is about 6 3 109 km from the sun. Write each distance in standard notation. Which planet is farther from the sun? How much farther?

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Write its length in expanded form with exponents in powers of 10. (4 3 104) 1 (2 3 103) 1 (1 3 102) 1 (9 3 101) 1 (5 3 100)

Spiral Review 1.

What is the remainder of 3,789 4 23? r 5 17

2.

What is the remainder of 789 4 23? r5 7 What is the remainder of 6,423 4 23? r5 6

3.

Lesson Quiz

© Harcourt

1. Write 4,872 in expanded form using powers of 10 and exponents. (4 3 1,000) 1 (8 3 100) 1 (7 3 10) 1 (2 3 1) 5 (4 3 103) 1 (8 3 102) 1 (7 3 101) 1 (2 3 100) 2. Write (5 3 104) 1 (7 3 103) 1 (8 3 102) 1 (4 3 100) in standard notation. 57,804 3. What is the exponent n needed to make this true; 7n 5 2,401 ? n5 4 4. Is 542,007 , or . 5 3 105 ? . 5. Mercury is about 6 3 107 km from the sun, while Pluto is about 6 3 109 km from the sun. Write each distance in standard notation. Which planet is farther from the sun? How much farther? 60,000,000; 6,000,000,000; Pluto is farther by 5,940,000,000 km.

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 42 kilometers. Fill in the correct number in the numerical expression so that its value is 42: 18 4 j 3 3 1 42 1 52 2 23.

Spiral Review Write 63 find the 2. Write 25 find the 3. Write 33 find the

1.

as a product of factors. Then value. as a product of factors. Then value. as a product of factors. Then value.

Lesson Quiz © Harcourt

Evaluate the expression. 1. 42 2 3 3 2 5

3. 29 2 22 3 7 5

2. (42 2 3) 3 2 5

4. 42 4 7 3 3 5

5. There are 25 buses. Each bus will seat 32 students. 15 of the buses each have 3 empty seats, the rest have only 1 empty seat each. What is the total number of students on the buses? Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 42 kilometers. Fill in the correct number in the numerical expression so that its value is 42: 18 4 j 3 3 1 42 1 52 2 23. 6

Spiral Review 1. 2. 3.

Write 63 find the Write 25 find the Write 33 find the

as a product of factors. Then value. 6 3 6 3 6 5 216 as a product of factors. Then value. 2 3 2 3 2 3 2 3 2 5 32 as a product of factors. Then value. 3 3 3 3 3 5 27

Lesson Quiz

© Harcourt

Evaluate the expression. 1. 42 2 3 3 2 5 10

3. 29 2 22 3 7 5 1

2. (42 2 3) 3 2 5 26

4. 42 4 7 3 3 5 18

5. There are 25 buses. Each bus will seat 32 students. 15 of the buses each have 3 empty seats, the rest have only 1 empty seat each. What is the total number of students on the buses? 15 3 (32 2 3) 1 10 3 (32 2 1) 5 745 Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 26 miles. A runner ran the equivalent of seven marathon races last year during practice runs. Rewrite the expression 7 3 26 to show how the Distributive Property can help you multiply mentally.

Spiral Review 1. 12 1 2 3 33 4 9

2. 12 1 62 4 2 3 9

Lesson Quiz Find the value of n and name the property used. 1. n 1 23 5 23 1 72 2. 7(n 1 4) 5 (7 3 3) 1 (7 3 4) © Harcourt

3. 8 3 (9 × 4) 5 (8 3 n) 3 4 4. (42 3 92) 3 0 5 n 5. What property could you use to make the problem (7 3 87) 1 (7 3 13) easier to calculate? Explain.

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 26 miles. A runner ran the equivalent of seven marathon races last year during practice runs. Rewrite the expression 7 3 26 to show how the Distributive Property can help you multiply mentally. 7 3 26 5 7 3 (20 1 6) 5 (7 3 20) 1 (7 3 6) 5 140 1 42 5 182

Spiral Review 1. 12 1 2 3 33 4 9 12 1 2 3 27 4 9 5 12 1 54 4 9 5 12 1 6 5 18

2. 12 1 62 4 2 3 9 12 1 36 4 2 3 9 5 12 1 18 3 9 5 12 1 162 5 174

Lesson Quiz Find the value of n and name the property used. 1. n 1 23 5 23 1 72 n 5 72, Commutative Property of addition 2. 7(n 1 4) 5 (7 3 3) 1 (7 3 4) n 5 3 Distributive Property © Harcourt

3. 8 3 (9 × 4) 5 (8 3 n) 3 4 n 5 9 Associative Property 4. (42 3 92) 3 0 5 n n 5 0 Zero Property of multiplication 5. What property could you use to make the problem (7 3 87) 1 (7 3 13) easier to calculate? Explain. The Distributive Property says that the expression is equivalent to 7 3 ( 87 1 13) 5 7 3 100. Grade 6

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Problem of the Day

1.10

Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is about 42,195 meters. In ancient Greece, the length of the original race was about 34,500 meters. Show how compensation can help you find the difference, in meters, between the length of a modern-day marathon and the original marathon.

Spiral Review 1. What property is illustrated by 3 3 (7 1 8) 5 (3 3 7) 1 (3 3 8)? 2. What property is illustrated by (8 1 7) 1 3 5 8 1 (7 1 3)

Lesson Quiz Name the property or strategy used to find the value. 1. 15 3 13 5 15 3 (10 1 3) 5 (15 3 10) 1 (15 3 3) 5 195 2. 25 3 15 3 4 5 25 3 4 3 15 5 1,500

3. Mary wrote out the following steps to solve the problem, 4 3 (23 3 2). Write the name of the property that justifies each step which is followed by a blank. © Harcourt

4 3 (23 3 2) 5 4 3 (2 3 23) ______________________ 5 (4 3 2) 3 23 _____________________ 5 8 3 23 5 8 3 (20 1 3) 5 (8 3 20) 1 (8 3 3) ____________________ 5 160 1 24 5 184

Grade 6

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1.10

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is about 42,195 meters. In ancient Greece, the length of the original race was about 34,500 meters. Show how compensation can help you find the difference, in meters, between the length of a modern-day marathon and the original marathon. Possible answer: (42,195 1 500) 2 (34,500 1 500) 5 42,695 2 35,000 5 7,695

Spiral Review 1. What property is illustrated by 3 3 (7 1 8) 5 (3 3 7) 1 (3 3 8)? Distributive Property 2. What property is illustrated by (8 1 7) 1 3 5 8 1 (7 1 3) Associative Property

Lesson Quiz Name the property or strategy used to find the value. 1. 15 3 13 5 15 3 (10 1 3) 5 (15 3 10) 1 (15 3 3) 5 195 Distributive Property 2. 25 3 15 3 4 5 25 3 4 3 15 5 1,500 Commutative Property

3. Mary wrote out the following steps to solve the problem, 4 3 (23 3 2). Write the name of the property that justifies each step which is followed by a blank. Commutative Property 4 3 (23 3 2) 5 4 3 (2 3 23) ______________________ © Harcourt

Associative Property 5 (4 3 2) 3 23 _____________________

5 8 3 23 5 8 3 (20 1 3) Distributive Property 5 (8 3 20) 1 (8 3 3) ____________________

5 160 1 24 5 184

Grade 6

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Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. Write each decimal in word form and expanded form. Which is greater, the height or the width?

Spiral Review Write in exponent form then simplify. 1. 5 3 5 3 5 2. 4 3 4 3. 3 3 3 3 3 3 3

Lesson Quiz 1. Write 1.628 in expanded form and in word form. 2. Compare these two numbers. Write ,, ., or 5 . 5.467 ___ 5.471 © Harcourt

3. Order from least to greatest: 86.541, 86.54, 86.411, 86.514 4. Order from greatest to least: 0.079, 0.81, 0.709, 0.081 5. For a game, David needs to find three decimals that are between 3.88 and 3.90. What could these three numbers be? List them in order from least to greatest.

Grade 6

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Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. Write each decimal in word form and expanded form. Which is greater, the height or the width? one and thirty-five hundredths; 1 1 0.3 1 0.05; one and seventy hundredths; 1 1 0.7 1 0.00; The width is greater.

Spiral Review Write in exponent form then simplify. 1. 5 3 5 3 5 53; 125 2. 4 3 4 42; 16 3. 3 3 3 3 3 3 3 34; 81

© Harcourt

Lesson Quiz 1. Write 1.628 in expanded form and in word form. 1 1 0.6 1 0.02 1 0.008; one and six hundred twenty-eight thousandths 2. Compare these two numbers. Write ,, ., or 5 . 5.467 ___ 5.471 , 3. Order from least to greatest: 86.541, 86.54, 86.411, 86.514 86.411, 86.514, 86.54, 86.541 4. Order from greatest to least: 0.079, 0.81, 0.709, 0.081 0.81, 0.709, 0.081, 0.079 5. For a game, David needs to find three decimals that are between 3.88 and 3.90. What could these three numbers be? List them in order from least to greatest. Possible Answer: 3.89, 3.891, 3.898 Grade 6

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Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. She wants to put a frame around it. Estimate the distance around the chalkboard.

Spiral Review 1. Write as a decimal number: twelve and twelve thousandths. 2. Write as a decimal number: one hundred five and five hundredths. 3. Write in words: 104.004.

Lesson Quiz Estimate and indicate your method of estimation. 1. 6.65 1 8.9 1 3.4

© Harcourt

2. 92.45 3 29.71 3. 236.8 ∏ 75.2 4. 88.12 2 71.3 5. Dylan is buying milk. A gallon of milk costs $2.89. Estimate the number of gallons of milk Dylan can buy if he has $15.25. Grade 6

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Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. She wants to put a frame around it. Estimate the distance around the chalkboard. 6 m

Spiral Review 1. Write as a decimal number: twelve and twelve thousandths. 12.012 2. Write as a decimal number: one hundred five and five hundredths. 105.05 3. Write in words: 104.004. one hundred four and four thousandths

Lesson Quiz Estimate and indicate your method of estimation. Sample answers are provided. 1. 6.65 1 8.9 1 3.4 19; rounded to the nearest ones place

© Harcourt

2. 92.45 3 29.71 2,700; used compatible numbers 3. 236.8 ∏ 75.2 3; used compatible numbers 4. 88.12 2 71.317; rounded to the nearest ones place 5. Dylan is buying milk. A gallon of milk costs $2.89. Estimate the number of gallons of milk Dylan can buy if he has $15.25.5 gallons; used compatible numbers Grade 6

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Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. How much longer is the height of the chalkboard than the width?

Spiral Review Find the whole-number overestimation of the following sums: 1. $2.35 1 $3.90 5 about ____ 3. $1.76 1 $3.34 1 $4.45 5 about ____

2. $3.49 1 $12.75 5 about ____ 4. $2.76 1 $4.34 1 $5.45 5 about ____

Lesson Quiz Estimate. Then find the sum or difference.

© Harcourt

1. 4.8 2. 93.84 112 2 7.258 __ 0.61 86.582 __ 17.41

3. 21.06 0.273 1 9.2 __ 30.533

4. 13.059 2 0.92 __ 12.139

5. Jeremy bought 2.38 pounds of bananas and 0.907 pounds of cherries. How many more pounds of bananas did he buy than cherries?

Grade 6

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2.3

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. How much longer is the height of the chalkboard than the width? 0.35 m

Spiral Review Find the whole-number overestimation of the following sums: 1. $2.35 1 $3.90 $7 5 about ____ 3. $1.76 1 $3.34 1 $4.45 5 about $11 ____

2. $3.49 1 $12.75 $17 5 about ____ 4. $2.76 1 $4.34 1 $5.45 5 about $14 ____

Lesson Quiz Estimate. Then find the sum or difference.

© Harcourt

1. 4.8 2. 93.84 3. 21.06 4. 13.059 112 0.273 2 7.258 2 0.92 __ __ 0.61 1 9.2 86.582 12.139 __ __ 87 17.41 12 30.533 18 30 5. Jeremy bought 2.38 pounds of bananas and 0.907 pounds of cherries. How many more pounds of bananas did he buy than cherries? 1 pound; 1.473 pounds Grade 6

Daily Transparency DT2.3

2.4

Problem of the Day Sarah is painting a chalkboard on her wall using chalkboard paint. The chalkboard will be 1.35 m tall and 1.70 m wide. What is the area of the chalkboard?

Spiral Review 1. 4.8 1 0.5 5 j

2. 4.8 1 5 5 j

3. 4.8 1 0.15 5 j

4. 4.8 1 1.5 5 j

Estimate. Then tell whether the given product is reasonable. 1. 0.821 3 19.3 5 1584.53

© Harcourt

2. 32.564 3 6.15 5 200.26860 Estimate. Then find the product. 3. 2.9 3 6.64

4. 0.67 3 3.29

5. Sharon worked 35.8 hours one week. If she makes $11.75 an hour, how much did she earn that week?

Grade 6

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2.4

Problem of the Day Sarah is painting a chalkboard on her wall using chalkboard paint. The chalkboard will be 1.35 m tall and 1.70 m wide. What is the area of the chalkboard? 2.995 m2

Spiral Review 1. 4.8 1 0.5 5 j 5.3

2. 4.8 1 5 5 j 9.8

3. 4.8 1 0.15 5 j 4.95 4. 4.8 1 1.5 5 j 6.3

Lesson Quiz Estimate. Then tell whether the given product is reasonable.

© Harcourt

1. 0.821 3 19.3 5 1584.53 19; no, it is not reasonable, the correct answer is 15.8453 2. 32.564 3 6.15 5 200.26860 180; yes it is reasonable Estimate. Then find the product. 3. 2.9 3 6.64 21; 19.256

4. 0.67 3 3.29 3; 2.2043

5. Sharon worked 35.8 hours one week. If she makes $11.75 an hour, how much did she earn that week? Possible estimate: $400; $420.65

Grade 6

Daily Transparency DT2.4

2.5

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. She wants to buy color chalk for her chalkboard. A box of 6 pieces costs $1.25, a box of 10 pieces costs $1.60, and a box of 12 pieces costs $1.75. If she has $5.00 and wants to buy only one kind of box, what is the greatest number of boxes of each kind that she can buy?

Spiral Review Multiply. 1. 1.11 3 0.2

2. 0.05 3 0.255

3. $3.45 3 5

4. 1.7 3 1.7

Lesson Quiz Make a table to solve. A juice stand sells apple, cranberry, and orange juices. Apple juice costs $1.50, cranberry juice costs $2.00, and orange juice costs $1.75.

© Harcourt

1. Edward has $7.50. If he wants to buy only one type of juice, what is the greatest number of each type that he can buy?

2. Sam wants to buy orange or cranberry juice. He wants to buy as many juices as he can with $10.00. Will he be able to buy more cranberry or orange juices for $10.00? Explain.

Grade 6

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8/30/07 1:28:36 PM

2.5

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. She wants to buy color chalk for her chalkboard. A box of 6 pieces costs $1.25, a box of 10 pieces costs $1.60, and a box of 12 pieces costs $1.75. If she has $5.00 and wants to buy only one kind of box, what is the greatest number of boxes of each kind that she can buy? 4 boxes of 6 pieces or 3 boxes of 10 pieces or 2 boxes of 12 pieces

Spiral Review Multiply. 1. 1.11 3 0.2 0.222

2. 0.05 3 0.255 0.01275

3. $3.45 3 5 $17.25

4. 1.7 3 1.7 2.89

Lesson Quiz Make a table to solve. A juice stand sells apple, cranberry, and orange juices. Apple juice costs $1.50, cranberry juice costs $2.00, and orange juice costs $1.75. 1. Edward has $7.50. If he wants to buy only one type of juice, what is the greatest number of each type that he can buy? Juice Stand

© Harcourt

Number Apple Cranberry Orange 1 $1.50 $2.00 $1.75 2 $3.00 $4.00 $3.50 3 $4.50 $6.00 $5.25 4 $6.00 $8.00 $7.00 5 $7.50 $10.00 $8.75 5 apple juices, 3 strawberry juices, 4 orange juices

2. Sam wants to buy orange or cranberry juice. He wants to buy as many juices as he can with $10.00. Will he be able to buy more cranberry or orange juices for $10.00? Explain. He will be able to buy the same number of cranberry and orange juices for $10.00. Five cranberry juices cost exactly $10. Even though 5 orange juices cost $8.75, less than $10, he cannot buy 6 orange juices because that would cost more than $10.00. Grade 6

Daily Transparency DT2.5

2.6

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she divides the chalkboard into two equal sections, how wide will each section be?

Spiral Review Order the decimals from greatest to least. 1. 0.17, 0.071, 0.07, 0.007, 1.01 2. 0.45, 0.095, 0.4, 0.05, 0.5

Lesson Quiz

© Harcourt

Estimate. Then correctly place the decimal point in the quotient. 635 2009 50.8 28.126 1. 8qw 2. 14qw Estimate. Then find the quotient. 3. $234.16 ∏ 4

4. 15qw 4.005

5. Derek earned $99.45 for 13 hours of work. What was the average amount he earned per hour?

Grade 6

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2.6

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she divides the chalkboard into two equal sections, how wide will each section be? 0.85 m

Spiral Review Order the decimals from greatest to least. 1. 0.17, 0.071, 0.07, 0.007, 1.01 1.01, 0.17, 0.071, 0.07, 0.007 2. 0.45, 0.095, 0.4, 0.05, 0.5 0.5, 0.45, 0.4, 0.095, 0.05

Lesson Quiz

© Harcourt

Estimate. Then correctly place the decimal point in the quotient. Possible answers are given. 635 2009 50.8 6; 6.35 28.126 2; 2.009 1. 8qw 2. 14qw Estimate. Then find the quotient. Possible answers are given. 3. $234.16 ∏ 4 $60; $58.54

4. 15qw 4.005

0.3; 0.267

5. Derek earned $99.45 for 13 hours of work. What was the average amount he earned per hour? Estimate $10; exact answer $7.65 per hour Grade 6

Daily Transparency DT2.6

2.7

Problem of the Day Sarah painted a chalkboard on her wall. She spent a total of 5.25 hours working on the chalkboard. If she spent 1.75 hours painting the chalkboard each day, how many days did it take her?

Spiral Review 1. 22.8 4 3 5 j 3. 37.6 4 4 5 j

2. 57.26 4 7 5 j 4. 156.6 4 9 5 j

Lesson Quiz

© Harcourt

Use decimal squares to find the quotient. 1. 4.8 4 1.2

2. 1.68 4 0.56

3. 0.98 4 0.14

4. 5.16 4 0.86

5. A farmer sells peanuts in containers that hold 0.75 lb. How many containers are needed for 4.5 lb of peanuts?

Grade 6

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8/30/07 1:28:41 PM

2.7

Problem of the Day Sarah painted a chalkboard on her wall. She spent a total of 5.25 hours working on the chalkboard. If she spent 1.75 hours painting the chalkboard each day, how many days did it take her? 3 days

Spiral Review 1. 22.8 4 3 5 j 7.6 2. 57.26 4 7 5 j 8.18 3. 37.6 4 4 5 j 9.4 4. 156.6 4 9 5 j 17.4

Lesson Quiz

© Harcourt

Use decimal squares to find the quotient. 1. 4.8 4 1.2 4

2. 1.68 4 0.56 3

3. 0.98 4 0.14 7

4. 5.16 4 0.86 6

5. A farmer sells peanuts in containers that hold 0.75 lb. How many containers are needed for 4.5 lb of peanuts? 6

Grade 6

Daily Transparency DT2.7

2.8

Problem of the Day Sarah painted a chalkboard on her wall. The chalkboard is 1.35 m tall and 1.70 m wide. She added a wood frame when it was finished. The total area of the frame and chalkboard is 2.52 m2. If the chalkboard and frame together are 1.8 m wide, what is their height?

Spiral Review 1. 3.2 4 0.8 5 j

2. 5.4 4 0.3 5 j

3. 4.5 4 0.3 5 j

4. 0.52 4 0.26 5 j

Lesson Quiz Place the decimal point in the quotient. 1. 14.78 4 0.5 = 2956 2. 3.048 4 6.35 = 48 © Harcourt

Find the quotient. 3. 6.8qw 2.04 4. 21.32 4 8.2 5. How long will it take a car traveling 67.8 miles

per hour to drive 162.72 miles? Grade 6

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8/30/07 1:28:44 PM

2.8

Problem of the Day Sarah painted a chalkboard on her wall. The chalkboard is 1.35 m tall and 1.70 m wide. She added a wood frame when it was finished. The total area of the frame and chalkboard is 2.52 m2. If the chalkboard and frame together are 1.8 m wide, what is their height? 1.4 m

Spiral Review 1. 3.2 4 0.8 5 j 4

2. 5.4 4 0.3 5 j 18

3. 4.5 4 0.3 5 j 15

4. 0.52 4 0.26 5 j 2

Lesson Quiz Place the decimal point in the quotient. 1. 14.78 4 0.5 = 2956 29.56 2. 3.048 4 6.35 = 48

0.48

© Harcourt

Find the quotient. 3. 6.8qw 2.04 0.3 4. 21.32 4 8.2 2.6 5. How long will it take a car traveling 67.8 miles

per hour to drive 162.72 miles? 2.4 hours Grade 6

Daily Transparency DT2.8

2.9

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If the can of paint will cover 5 m2, does she have enough paint? Explain.

Spiral Review Place the decimal point in the quotient. 1. 13.78 4 0.4 5 3445 2. 42.64 4 4.1 5 104

Lesson Quiz Determine whether an exact answer or an estimate is needed and solve.

© Harcourt

1. Alex runs marathons at about 4.8 miles per hour. About how many miles will he have run after 3 hours? 2. Talia cuts a piece of fabric that is 50 cm long into 4 smaller pieces. The lengths of 3 of the pieces are: 22.5 cm, 10.7 cm, and 6.7 cm. How long is the fourth piece? Grade 6

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DT2.9

8/30/07 1:28:46 PM

2.9

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If the can of paint will cover 5 m2, does she have enough paint? Explain. Yes; the area of the chalkboard is 2.295 m2, which is less than 5 m2.

Spiral Review Place the decimal point in the quotient. 1. 13.78 4 0.4 5 3445 34.45 2. 42.64 4 4.1 5 104 10.4

Lesson Quiz Determine whether an exact answer or an estimate is needed and solve.

© Harcourt

1. Alex runs marathons at about 4.8 miles per hour. About how many miles will he have run after 3 hours? Estimate; about 15 miles 2. Talia cuts a piece of fabric that is 50 cm long into 4 smaller pieces. The lengths of 3 of the pieces are: 22.5 cm, 10.7 cm, and 6.7 cm. How long is the fourth piece? Exact answer; 10.1 cm Grade 6

Daily Transparency DT2.9

Problem of the Day

2.10

Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she paid $15.00 for 0.5 gallon of paint, how much does 1 gallon of paint cost?

Spiral Review Is an estimate or an exact answer needed? 1. Arlina cut 3 kite strings each 3.8 m long from a 12 m piece of string. How much string does she have left over?

Lesson Quiz Solve using mental math, pencil and paper, or a calculator. 1. 25 3 8 3 10 © Harcourt

2. 12.5 2 1.25 3. 22.46 1 21.39 4. 0.8 4 0.32 5. Anna buys 3.25 yards of ribbon. The fabric costs $0.88 per yard. How much does Anna’s fabric cost?

Grade 6

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DT2.10

8/30/07 1:28:48 PM

2.10

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she paid $15.00 for 0.5 gallon of paint, how much does 1 gallon of paint cost? $30.00

Spiral Review Is an estimate or an exact answer needed? 1. Arlina cut 3 kite strings each 3.8 m long from a 12 m piece of string. How much string does she have left over? exact answer

Lesson Quiz Solve using mental math, pencil and paper, or a calculator. 1. 25 3 8 3 10 2,000 © Harcourt

2. 12.5 2 1.25 11.25 3. 22.46 1 21.39 43.85 4. 0.8 4 0.32 2.5 5. Anna buys 3.25 yards of ribbon. The fabric costs $0.88 per yard. How much does Anna’s fabric cost? $2.86 Grade 6

Daily Transparency DT2.10

Unit 2 • Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged.

3

© Harcourt

A mantid egg case may contain as many as 400 eggs. Name 7 pairs of whole number factors of 400.

Sam is making bread. He will need to use 3 _ teaspoon of salt. Sam measured out the salt but 4 spilled 1_2 teaspoon of it. Draw a number line marked with 0 and 1 and place a point on the number line to indicate how much salt Sam has left.

4

The Delgados are fencing in a pasture on their farm. If the western and eastern borders are 1 7_8 mi long and southern and northern borders are 3_4 mi long. How many miles of fencing do they need? 1 7_8 1 1 7_8 1 3_4 1 3_4 5 5 1_4 miles.

5

Manny is preparing a dinner for his friends. He has 3 2_3 ice cream rolls and wants to be sure he has enough for everyone to receive 1_6 of a roll. He decides to express 3 2_3 as a fraction before he divides by 1_6 . What fraction can Manny use that is equivalent to 3 2_3 ?

6

Grade 6

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DT • Unit 2

8/30/07 2:42:58 PM

Unit 2 • Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged.

3

© Harcourt

A mantid egg case may contain as many as 400 eggs. Name 7 pairs of whole number factors of 400. Possible answer: 1 3 400, 2 3 200, 4 3 100, 5 3 80, 8 3 50, 10 3 40, 20 3 20

Sam is making bread. He will need to use 3 _ teaspoon of salt. Sam measured out the salt but 4 spilled 1_2 teaspoon of it. Draw a number line marked with 0 and 1 and place a point on the number line to indicate how much salt Sam has left. Check students’ number lines: 0 on left end; 1 on the right; line segment divided into fourths; point on 1_4 .

4

The Delgados are fencing in a pasture on their farm. If the western and eastern borders are 1 7_8 mi long and southern and northern borders are 3_4 mi long. How many miles of fencing do they need? 1 7_8 1 1 7_8 1 3_4 1 3_4 5 5 1_4 miles.

5

Manny is preparing a dinner for his friends. He has 3 2_3 ice cream rolls and wants to be sure he has enough for everyone to receive 1_6 of a roll. He decides to express 3 2_3 as a fraction before he divides by 1_6 . What fraction can Manny use that is equivalent __ to 3 2_3 ? 11 3

6

Grade 6

Daily Transparency DT • Unit 2

3.1

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The number 252 is divisible by which of the following: 2, 3, 4, 5, 6, 9, 10?

Spiral Review 1. 13.4 1 4.35 5 3. 3.3 3 0.2 5 5. 0.344 4 8 5

2. 3.4 2 2 5 4. 0.66 4 0.02 5 6. 0.03 3 0.02 5

Lesson Quiz

© Harcourt

Tell whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 or none of these. 1. 78

2. 288

3. 521

4. 745

5. A three-digit number is greater than 310, less than 370, a multiple of 7, and divisible by 2, 5, and 10. What is the number? Grade 6

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8/30/07 1:32:21 PM

3.1

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The number 252 is divisible by which of the following: 2, 3, 4, 5, 6, 9, 10? 2, 3, 4, 6, 9

Spiral Review 1. 13.4 1 4.35 5 17.75 2. 3.4 2 2 5 1.4 3. 3.3 3 0.2 5 0.66 4. 0.66 4 0.02 5 33 5. 0.344 4 8 5 0.043 6. 0.03 3 0.02 5 0.0006

Lesson Quiz

© Harcourt

Tell whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 or none of these. 1. 78 2, 3, 6

2. 288 2, 3, 4, 6, 8, 9

3. 521 none

4. 745 5

5. A three-digit number is greater than 310, less than 370, a multiple of 7, and divisible by 2, 5, and 10. What is the number? 350 Grade 6

Daily Transparency DT3.1

3.2

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. Is 252 a prime number, a composite number, or neither?

Spiral Review 1. How do the divisibility rules help you know that 1,484 is divisible by 4?

2. How do the divisibility rules help you know that 918 is divisible by 3?

Lesson Quiz

© Harcourt

Tell whether each number is prime, composite, or neither. 1. 37

2. 88

3. 1

4. 67

5. Of the numbers 29, 39, and 49, which one is not composite? Why?

Grade 6

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DT3.2

8/30/07 1:32:25 PM

3.2

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. Is 252 a prime number, a composite number, or neither? composite number

Spiral Review 1. How do the divisibility rules help you know that 1,484 is divisible by 4? The last two digits form the number 84 which is divisible by 4 (84 4 4 5 21). 2. How do the divisibility rules help you know that 918 is divisible by 3? The sum of the digits is divisible by 3 (9 1 1 1 8 5 18 and 1 1 8 5 9; 9 is divisible by 3.)

Lesson Quiz

© Harcourt

Tell whether each number is prime, composite, or neither. 1. 37 prime

2. 88 composite

3. 1 neither

4. 67 prime

5. Of the numbers 29, 39, and 49, which one is not composite? Why? 29 is the only prime number. Its only factors are 1 and 29. Grade 6

Daily Transparency DT3.2

3.3

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The product of which five prime numbers equals 252?

Spiral Review Tell whether each number is prime or composite. Then list the factors of the number. 1. 9 2. 17

Lesson Quiz © Harcourt

Write the prime factorization in exponent form. 1. 90

2. 75

3. 236

4. 588

5. What number has the prime factorization 2 x 3 x 5 x 72?

Grade 6

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8/30/07 1:32:27 PM

3.3

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The product of which five prime numbers equals 252? 2, 2, 3, 3, 7

Spiral Review Tell whether each number is prime or composite. Then list the factors of the number. 1. 9 composite; 1, 3, 9 2. 17 prime; 1, 17

Lesson Quiz © Harcourt

Write the prime factorization in exponent form. 1. 90 2 x 32 x 5

2. 75 3 x 52

3. 236 22 x 59

4. 588 22 x 3 x 72

5. What number has the prime factorization 2 x 3 x 5 x 72? 1,470

Grade 6

Daily Transparency DT3.3

3.4

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. If another egg case hatched and 180 insects emerged, what is the greatest common factor of 252 and 180?

Spiral Review Write the prime factorization of each number, using exponents when possible. 1. 56 3. 51

2. 36 4. 100

Lesson Quiz Find the LCM.

© Harcourt

1. 10, 35

2. 6, 9, 27

Find the GCF. 3. 10, 45, 5

4. 14, 56, 112

5. The LCM of two numbers is 180. The GCF of the numbers is 9. What are the numbers?

Grade 6

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8/30/07 1:32:30 PM

3.4

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. If another egg case hatched and 180 insects emerged, what is the greatest common factor of 252 and 180? 36

Spiral Review Write the prime factorization of each number, using exponents when possible. 1. 56 23 3 7 3. 51 3 3 17

2. 36 22 3 32 4. 100 22 3 52

Lesson Quiz Find the LCM.

© Harcourt

1. 10, 35 70

2. 6, 9, 27 54

Find the GCF. 3. 10, 45, 5 5

4. 14, 56, 112 14

5. The LCM of two numbers is 180. The GCF of the numbers is 9. What are the numbers? Possible answers are 36 and 45. Grade 6

Daily Transparency DT3.4

3.5

Problem of the Day Amanda’s class is raising insects called mantids. The original number of eggs was a factor of 120. What might have been the original number of eggs?

Spiral Review Find the GCF and LCM of each set of numbers. 1. 6, 8, 18 2. 12, 20 GCF 5 __ GCF 5 __ LCM 5 __ LCM 5 __ 3. 7, 14, 56 4. 3, 6, 8 GCF 5 __ GCF 5 __ LCM 5 __ LCM 5 __

© Harcourt

Lesson Quiz 1. When Tyler was born, his grandfather gave him 15 classic baseball cards. For each birthday, his grandfather gave him 20 more cards. At what birthday did Tyler have more than 75 baseball cards? 2. Betty has 40¢ in collectible coins. None of the coins are pennies. How many different groups of coins totaling 40¢ can Betty have?

Grade 6

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DT3.5

8/30/07 1:32:33 PM

3.5

Problem of the Day Amanda’s class is raising insects called mantids. The original number of eggs was a factor of 120. What might have been the original number of eggs? 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Spiral Review Find the GCF and LCM of each set of numbers. 1. 6, 8, 18 2. 12, 20 2 4 GCF 5 __ GCF 5 __ 72 LCM 5 __ LCM 5 60 __ 3. 7, 14, 56 4. 3, 6, 8 7 1 GCF 5 __ GCF 5 __ 56 LCM 5 __ LCM 5 24 __

© Harcourt

Lesson Quiz 1. When Tyler was born, his grandfather gave him 15 classic baseball cards. For each birthday, his grandfather gave him 20 more cards. At what birthday did Tyler have more than 75 baseball cards? third 2. Betty has 40¢ in collectible coins. None of the coins are pennies. How many different groups of coins totaling 40¢ can Betty have? 7

Grade 6

Daily Transparency DT3.5

4.1

Problem of the Day Sam is making bread. He will need to use 3_4 teaspoon of salt. How could you represent 3_4 using a number line from 0 to 1? Draw a number line marked with 0 and 1.

Spiral Review Find the LCM and GCF for the following numbers: 1. 12, 6, 10 LCM 5 j

GCF 5 j

2. 6, 12, 18 LCM 5 j

GCF 5 j

Lesson Quiz

© Harcourt

Draw a model to represent the fraction. 1. 1_5

5 2. __ 10

3. _49

4. 68_

5. At an archaeological dig, 2_5 of the workers are volunteers and the remaining workers are professionals. What fraction of the workers are professionals?

Grade 6

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8/30/07 1:43:43 PM

4.1

Problem of the Day Sam is making bread. He will need to use 3_4 teaspoon of salt. How could you represent 3_4 using a number line from 0 to 1? Draw a number line marked with 0 and 1. 0

3 4

1

Spiral Review Find the LCM and GCF for the following numbers: 1. 12, 6, 10 LCM 5 j 60 GCF 5 j 2 2. 6, 12, 18 LCM 5 j 36 GCF 5 j 6

Lesson Quiz Draw a model to represent the fraction. Answers may vary. 5 2. __ 1. 1_5 10 © Harcourt

3. _49

4. _68

5. At an archaeological dig, 2_5 of the workers are volunteers and the remaining workers are professionals. What fraction of the workers are professionals? 3_5 Grade 6

Daily Transparency DT4.1

4.2

Problem of the Day Sam is making bread. Sam needs 2 _ teaspoon ground cinnamon. Sam 4 has a 1_4 teaspoon measure and a 1 _ teaspoon measure. How could he 2 use either measuring spoon?

Spiral Review 1. Is 27 prime or composite? 2. Is 53 prime or composite? 3. Is 51 prime or composite?

Lesson Quiz Complete. 4 28 __ 1. __ j 5 49

j 3 __ 2. ___ 160 5 20

© Harcourt

Write the fraction in simplest form. __ 3. 18 27

__ 4. 45 65

5. Tran has 6 heirloom tomato plants, 5 cherry tomato plants, and 7 yellow tomato plants. What fraction of his tomato plants are heirloom tomato plants? Write your answer in simplest form.

Grade 6

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DT4.2

8/30/07 1:43:47 PM

4.2

Problem of the Day Sam is making bread. Sam needs 2 _ teaspoon ground cinnamon. Sam 4 has a 1_4 teaspoon measure and a 1 _ teaspoon measure. How could he 2 use either measuring spoon? Two scoops with the 1_4 teaspoon measure or one scoop with the 21_ teaspoon measure because 2_4 5 21_ .

Spiral Review 1. Is 27 prime or composite? composite 2. Is 53 prime or composite? prime 3. Is 51 prime or composite? composite

Lesson Quiz Complete. 4 28 __ 1. __ j 5 49 7

j 3 __ 2. ___ 160 5 20 24

© Harcourt

Write the fraction in simplest form. 2 18 _ 3. __ 27 3

9 45 __ 4. __ 65 13

5. Tran has 6 heirloom tomato plants, 5 cherry tomato plants, and 7 yellow tomato plants. What fraction of his tomato plants are heirloom tomato plants? Write your answer in simplest form. 1_3 Grade 6

Daily Transparency DT4.2

4.3

Problem of the Day Sam is making bread. Sam will need 5_2 pounds of whole wheat flour. What is 52_ written as a mixed number?

Spiral Review Write the fraction in simplest form. __ 1. 21 27

__ 2. 35 14

16 3. __ 48

40 4. __ 16

Lesson Quiz Write the mixed number as a fraction. 1. 3 1_5

2. 2 7_8

© Harcourt

Write the fraction as a mixed number in simplest form. 21 3. __ 4

22 4. __ 6

5. A cheese wedge weighs 25 ounces. Write the weight in pounds as a fraction and as a mixed number. Note that 1 pound 5 16 ounces. Grade 6

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Problem of the Day Sam is making bread. Sam will need 5_2 pounds of whole wheat flour. What is 5_2 written as a mixed number? 2 1_2

Spiral Review Write the fraction in simplest form. 21 __ 1. 27

7 _ 9

35 __ 2 1_ 2. 14 2

16 __ 3. 48

1 _ 3

40 __ 2 1_ 4. 16 2

Lesson Quiz Write the mixed number as a fraction. 16 1. 3 1_5 __ 5

23 2. 2 78_ __ 8

© Harcourt

Write the fraction as a mixed number in simplest form. __ 5 1_ 3. 21 4 4

__ 3 2_ 4. 22 3 6

5. A cheese wedge weighs 25 ounces. Write the weight in pounds as a fraction and as a mixed 9 __ ; 1 __ number. Note that 1 pound 5 16 ounces. 25 16 16 Grade 6

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4.4

Problem of the Day Sam is baking bread. He needs 3 _ pound of bread flour. Sam's 4 scale expresses weight in decimals. Rename the weight of the flour as a decimal.

Spiral Review Write each fraction as a mixed number in simplest form: 1. twenty-three fourths 2. thirty-two sixths

Lesson Quiz Write as a fraction or mixed number in simplest form. 1. 1.4

2. 0.675

Write as a decimal. Tell whether the decimal terminates or repeats.

© Harcourt

2 3. __ 11

5. During basketball practice, Francie made a basket on 0.6 of her free throws. Charmian made a 7 basket on __ 12 of her free throws. Which girl was more successful in making free throws? Explain.

Grade 6

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4.4

Problem of the Day Sam is baking bread. He needs 3 _ pound of bread flour. Sam's 4 scale expresses weight in decimals. Rename the weight of the flour as a decimal. 0.75

Spiral Review Write each fraction as a mixed number in simplest form: 1. twenty-three fourths 5 3_4 2. thirty-two sixths 5 1_3

Lesson Quiz Write as a fraction or mixed number in simplest form. 1. 1.4 1 2_5

2. 0.675 _58

Write as a decimal. Tell whether the decimal terminates or repeats. 3. repeats 4. terminates

© Harcourt

2 3. __ 11 0.18181818…

9 0.225 4. __ 40

5. During basketball practice, Francie made a basket on 0.6 of her free throws. Charmian made a 7 basket on __ 12 of her free throws. Which girl was more successful in making free throws? Explain. 7 Francie; Charmian made __ 12 or about 0.583 of her free throws. 0.6 . 0.583 Grade 6

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4.5

Problem of the Day Sam is making bread. He has decided to give away 25% of the bread he makes. What is 25% written as a fraction?

Spiral Review Write each fraction as a terminating or repeating decimal. Does it terminate or repeat? 1. _78

2. _79

Lesson Quiz 1. Copy and complete the table. Write each fraction in simplest form.

© Harcourt

Fraction

Decimal 0.6

Percent

7 __ 50

2. Twelve percent of the students have more than one middle name. What fraction of students have more than one middle name?

Grade 6

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4.5

Problem of the Day Sam is making bread. He has decided to give away 25% of the bread he makes. What is 25% written as a ? 5 ___ 25 1 ___ _ fraction? 25% 5 100 100 5 4

Spiral Review Write each fraction as a terminating or repeating decimal. Does it terminate or repeat? 1. 7_8 0.875; terminates 2. 7_9 0.7; repeats

Lesson Quiz 1. Copy and complete the table. Write each fraction in simplest form. Fraction © Harcourt

_3 5 7 __ 50

Decimal 0.6

Percent 60%

0.14

14%

2. Twelve percent of the students have more than one middle name. What fraction of students 3 have more than one middle name? __ 25 Grade 6

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4.6

Problem of the Day Sam is making bread. Which ingredient amount is greater, 3 _ teaspoon cinnamon or 0.5 4 teaspoon ground cloves? Locate the two amounts on the number line labeled 0 to 1. 0

1

Spiral Review Compare. Use ., ,, or 5. 1. 0.4 ____ 7%

2. 0.89 ____ 1

3. 20% ____ _15

4. 3_4 ____ _57

Lesson Quiz Compare. Write , or = for each ___. 1. 5_6 __ 85%

8 _2 2. __ 20 __ 5

Order from least to greatest. 1 3. 16%, __ 10 , 0.09

© Harcourt

Find all possible whole number values for x that make the statement true. __ 4. 8_x 5 16 36

5. Two farmers both plan to grow 100 acres of sunflowers. Farmer A has planted 80% of his 100 acres. Farmer B has __ of his 100 acres. Which farmer has planted planted 19 20 more acres? Show the comparison using symbols.

Grade 6

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4.6

Problem of the Day Sam is making bread. Which ingredient amount is greater, 3 _ teaspoon cinnamon or 0.5 4 teaspoon ground cloves? 3_4 teaspoon Locate the two amounts on the number line labeled 0 to 1. 0.5

0

3 4

1

Spiral Review Compare. Use ., ,, or 5. 1. 0.4 ____ 7% .

2. 0.89 ____ 1 ,

3. 20% ____ 15_ 5

4. 3_4 ____ 5_7 .

Lesson Quiz Compare. Write , or = for each ___. 1. 5_6 __ 85% ,

8 2 _ 2. __ 20 __ 5 5

Order from least to greatest. 1 , 0.09 1 , 16% __ __ 3. 16%, 10 0.09, 10

© Harcourt

Find all possible whole number values for x that make the statement true. __ x 5 18 4. 8_x 5 16 36

5. Two farmers both plan to grow 100 acres of sunflowers. Farmer A has planted 80% of his 100 acres. Farmer B has __ of his 100 acres. Which farmer has planted planted 19 20 more acres? Show the comparison using symbols. __ Farmer B; 80% , 19 20 Grade 6

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4.7

Problem of the Day Sam is making bread. He compares his recipe to one he found online. Which recipe uses more butter? Sam’s Recipe 5 eggs

Online Recipe 4 eggs

1 1_4 cups butter

1.375 cups butter

Spiral Review

Compare. Use ., ,, or 5. 1. 3_5 ___ 0.6

2. 5_8 ___ _46

3. 2_3 ___ 0.6

4. 2_3 ___ _25

Lesson Quiz For 1–2, use the table.

© Harcourt

Tree Height (meters) Year Tree A Tree B 1 1.5 1 1_3 2

1.8

1 7_8

1. Which tree was taller in Year 1? 2. Which tree grew more by Year 2? Grade 6

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4.7

Problem of the Day Sam is making bread. He compares his recipe to one he found online. Which recipe uses more butter? The online recipe Sam’s Recipe 5 eggs

Online Recipe 4 eggs

1 1_4 cups butter

1.375 cups butter

Spiral Review Compare. Use ., ,, or 5. 1. 3_5 ___ 0.6 5

2. 5_8 ___ 4_6 ,

3. 2_3 ___ 0.6 .

4. 2_3 ___ 2_5 .

Lesson Quiz For 1–2, use the table.

© Harcourt

Tree Height (meters) Year Tree A Tree B 1 1.5 1 1_3 2

1.8

1 7_8

1. Which tree was taller in Year 1? Tree A 2. Which tree grew more by Year 2? Tree B Grade 6

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5.1

Problem of the Day The Delgados are fencing in a pasture on their farm. A tree growing along the western border of the pasture is 1_8 mi 9 from one corner and __ 10 mi from the other corner. About how far is it from one corner to the other? Round the fractions to help you estimate 1 9 _ 1 __ 8 10 .

0

1

2

Spiral Review Compare. Replace ____ with ,, ., or 5. 1. 0.4 ___ 7%

2. 3_4 ___ _57

3. 0.89 ___ 1

4. 20% ___ _15

Lesson Quiz Estimate the sum or difference. 2 1 __ 1. __ 18 2 10

2. 3 6_8 1 2 _47

Estimate to compare. Write , or ..

© Harcourt

1 3. 7_8 1 4 __ 12 __ 6

8 4. 6 3_5 2 2 __ 15 __ 3

In problem 5 below, tell whether an overestimate or an underestimate is needed. Solve. 5. Jim needs 9 cups of apples for a mile-high apple pie recipe. He measures the sliced apples in four batches. The batches measure 3 1_8 c, 1 2_3 c, 2 1_4 c, and 3 1_3 c. Estimate the total amount of apples. Does Jim have enough for his recipe?

Grade 6

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5.1

Problem of the Day The Delgados are fencing in a pasture on their farm. A tree growing along the western border of the pasture is 1_8 mi 9 from one corner and __ 10 mi from the other corner. About how far is it from one corner to the other? Round the fractions to help you estimate 1 9 _ 1 __ 8 10 . 1 8

9 10

0

1

2

Spiral Review Compare. Replace ____ with ,, ., or 5. 1. 0.4 ___ 7% .

2. 3_4 ___ 5_7 ,

3. 0.89 ___ 1 ,

4. 20% ___ 1_5 5

Lesson Quiz Estimate the sum or difference. Possible answers are shown. 2 1 __ 1. __ 18 2 10 0

2. 3 6_8 1 2 4_7 6 1_2

Estimate to compare. Write , or ..

© Harcourt

1 __ 6 __ 3. 7_8 1 4 12 ,

8 . 4. 6 3_5 2 2 __ 15 __ 3

In problem 5 below, tell whether an overestimate or an underestimate is needed. Solve. 5. Jim needs 9 cups of apples for a mile-high apple pie recipe. He measures the sliced apples in four batches. The batches measure 3 1_8 c, 1 2_3 c, 2 1_4 c, and 3 1_3 c. Estimate the total amount of apples. Does Jim have enough for his recipe? underestimate; 9 c of apples; yes Grade 6

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5.2

Problem of the Day The Delgados are fencing in a pasture on their farm. The eastern border is 2_5 mi long. The western border is 1_3 mi long. How many miles of fencing do the Delgados need for the eastern and western borders of the pasture? Use fraction bars to solve.

Spiral Review 1. 8_9 1 _58

7 _3 2. __ 15 1 5

3. 3 7_8 2 1 4_9

4. 8_9 2 2_5

Lesson Quiz Use a common denominator to rewrite the problem using equivalent fractions. 1 1. 2_3 1 __ 10

__ 2 _1 2. 16 21 6

© Harcourt

Estimate. Then write the sum or difference in simplest form. 3.

1 _78

4. 6_7 2 _13

5. In a neighborhood, 1_8 of the houses have finished basements. Half of the houses have full, unfinished basements. Another 1 _ of the houses have partial, unfinished basements. The rest of 4 the houses have no basement at all. How many houses in the neighborhood do not have a basement?

Grade 6

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5.2

Problem of the Day The Delgados are fencing in a pasture on their farm. The eastern border is 2_5 mi long. The western border is 1_3 mi long. How many miles of fencing do the Delgados need for the eastern and western borders of the __ pasture? 11 15 Use fraction bars to solve.

Spiral Review 1. 8_9 1 5_8 1 1_2

7 3 _ 2. __ 15 1 5 1

3. 3 7_8 2 1 4_9 2 21_

4. 8_9 2 _25

_1 2

Lesson Quiz Use a common denominator to rewrite the problem using equivalent fractions. 1 1. 2_3 1 __ 10

20 __ 30

1

3 __ 30

__ 2 _1 2. 16 21 6

32 __ 42

2

7 __ 42

© Harcourt

Estimate. Then write the sum or difference in simplest form. 3.

3 _ 5

__ 1 7_8 1 1_2 ; 1 19 40

4. 6_7 2 1_3 1_2 ;

11 __ 21

5. In a neighborhood, 1_8 of the houses have finished basements. Half of the houses have full, unfinished basements. Another 1 _ of the houses have partial, unfinished basements. The rest of 4 the houses have no basement at all. How many houses in the neighborhood do not have a basement? 1_8 Grade 6

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5.3

Problem of the Day The Delgados are fencing in a pasture on their farm. The northern section of the fence will be 1 1_8 mi long. It will connect with a fence that measures 2 1_2 mi. What is the total length of the two sections of fence? 8

1 81 221

Spiral Review Write the sum or difference in simplest form. 1. 1_3 1 _16

7 _1 2. __ 10 2 5

3. 6_7 1 1_3

4. 5_9 2 _13

Lesson Quiz

© Harcourt

Write the sum or difference in simplest form. 1. 2 1_5 1 3 _12

__ 2 2 _3 2. 5 17 20 4

3. 14 7_8 2 11 1_3

4. 5 1_3 1 3 3_4

5. Sandi ran 6 1_3 miles on Saturday. Her friend Janelle ran 1 1_8 miles farther. How far did Janelle run?

Grade 6

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5.3

Problem of the Day The Delgados are fencing in a pasture on their farm. The northern section of the fence will be 1 1_8 mi long. It will connect with a fence that measures 2 1_2 mi. What is the total length of the two sections of fence? 3 5_8 mi 8

1 81 221

Spiral Review Write the sum or difference in simplest form. 1. 1_3 1 _16 _12

7 _1 _1 2. __ 10 2 5 2

4 3. 6_7 1 1_3 1 __ 21

4. 5_9 2 _13 2_9

Lesson Quiz

© Harcourt

Write the sum or difference in simplest form. 7 1. 2 1_5 1 3 1_2 5 __ 10

1 __ 2 2 3_ 3 __ 2. 5 17 10 20 4

13 __ 3. 14 7_8 2 11 1_3 3 24

1 __ 4. 5 1_3 1 3 34_ 9 12

5. Sandi ran 6 1_3 miles on Saturday. Her friend Janelle ran 1 1_8 miles farther. How far did __ mi Janelle run? 7 11 24

Grade 6

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5.4

Problem of the Day The Delgados are fencing in a pasture on their farm. When they are finished, 3 5_8 mi along the northern border of their farm will be fenced. The north side of their property is 5 mi long. How many miles will be unfenced? Use fraction bars to solve the problem.

Spiral Review 1. 7_8 2 _14

9 _2 2. __ 10 2 5

3. 3_4 2 _16

4. 5_8 2 _14

Lesson Quiz

© Harcourt

Use fraction bars to find the difference. Write the answer in simplest form. 1. 4 2 3 _14

2. 5 2 1 _45

3. 4 1_3 2 2 _23

4. 2 1_2 2 1 _78

5. 5 2 2 _13

Grade 6

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5.4

Problem of the Day The Delgados are fencing in a pasture on their farm. When they are finished, 3 58_ mi along the northern border of their farm will be fenced. The north side of their property is 5 mi long. How many miles will be unfenced? 1 3_8 Use fraction bars to solve the problem.

Spiral Review 1. 7_8 2 _14 _58

9 2 _ 2. __ 10 2 5

7 3. 3_4 2 _16 __ 12

4. 5_8 2

5 __ 10 1 _ 3_ 4 8

or

1 _ 2

Lesson Quiz

© Harcourt

Use fraction bars to find the difference. Write the answer in simplest form. 1. 4 2 3 _14 _34

2. 5 2 1 4_5 3 1_5

3. 4 1_3 2 2 2_3 1 2_3

4. 2 1_2 2 1 78_ _58

5. 5 2 2 1_3 2 2_3

Grade 6

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5.5

Problem of the Day The Delgados are fencing in a pasture on their farm. The total length of the fence will be 7 1_8 mi. The combined lengths of the northern, eastern, and western borders of the fence is 4 1_4 mi. How long, in miles, is the southern border of the fence?

Spiral Review What fraction bars can you use to rename 6 1_3 ?

Lesson Quiz

© Harcourt

Estimate. Then write the difference in simplest form. 1. 5 1_2 2 3 _78

2. 10 2_5 2 3 _23

3. 8 2 6 _47

3 _3 4. 6 __ 10 2 2 4

5. The door to Leo’s room is 32 1_8 inches wide. The door to his closet is 29 3_4 inches wide. How much wider is the door to his room?

Grade 6

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8/30/07 1:41:42 PM

5.5

Problem of the Day The Delgados are fencing in a pasture on their farm. The total length of the fence will be 7 1_8 mi. The combined lengths of the northern, eastern, and western borders of the fence is 4 1_4 mi. How long, in miles, is the southern border of the fence? 2 7_8 mi

Spiral Review What fraction bars can you use to rename 6 1_3 ? Possible answers: five whole and four 1_3 bars or nineteen 13_ bars

Lesson Quiz Estimate. Then write the difference in simplest form. Possible estimates shown. © Harcourt

1. 5 1_2 2 3 7_8 1 1_2 ; 1 85_ 3. 8 2 6 _47

1 1_2 ; 1 3_7

__ 2. 10 2_5 2 3 2_3 7; 6 11 15 3 3 __ _ 3 1_ ; 3 11 4. 6 __ 2 20 10 2 2 4

5. The door to Leo’s room is 32 1_8 inches wide. The door to his closet is 29 3_4 inches wide. How much wider is the door to his room? 2 3_8 in. Grade 6

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5.6

Problem of the Day The Delgados are fencing in a pasture on their farm. They purchase 3 miles of fencing. The northern and southern borders of the pasture each measure 1 1_8 mi. The eastern border measures 2 _ mi; the western, 1_ mi. 5 3 After fencing the northern and southern borders, will the Delgados have enough fencing left over for both the eastern and western border? Explain.

Spiral Review 1. 3 1_3 2 11_4

2. 12 1_3 2 9 2_3

3. 5 2 1_14

4. 2 2 _23

Lesson Quiz © Harcourt

1. Mark has 1 5_8 lb flour. He needs 7_8 for muffins. Is there enough left for a second recipe that calls for 1_2 lb? Explain. 2. If 5_8 of a lot is occupied by the house and 1 driveway and __ 10 is occupied by a deck, how much is left for the yard?

Grade 6

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8/30/07 1:41:46 PM

5.6

Problem of the Day The Delgados are fencing in a pasture on their farm. They purchase 3 miles of fencing. The northern and southern borders of the pasture each measure 1 1_8 mi. The eastern border measures 2 _ mi; the western, 1_ mi. 5 3 After fencing the northern and southern borders, will the Delgados have enough fencing left over for both the eastern and western border? Explain. Yes. Possible 2 _ explanation: 3 2 2 1_4 5 2_4 and 2_4 . 5 1 1_3

Spiral Review 1 __ 1. 3 1_3 2 11_4 2 12

2. 12 1_3 2 9 2_3 2 2_3

3. 5 2 1_14 3 3_ 4

4. 2 2 2_3 1 1_3

Lesson Quiz © Harcourt

1. Mark has 1 5_8 lb flour. He needs 7_8 for muffins. Is there enough left for a second recipe that calls for 1_2 lb? Explain. Yes, there is 3_4 lb left and 3_4 . 1_2 . 2. If 5_8 of a lot is occupied by the house and 1 driveway and __ 10 is occupied by a deck, how much __ is left for the yard? 11 40

Grade 6

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5.7

Problem of the Day The Delgados are fencing in a pasture on their farm. The Masons’ farm is 3 3_4 mi down the road from the Delgados’ farm. The Bergens’ farm is 1 1_2 miles farther down the road. How far is the Bergens’ farm from the Delgados’ farm?

Spiral Review 1. 8 2 5 _13

2. 3 2_3 1 3 _14

Lesson Quiz Write the sum or difference in simplest form. __ 1 _3 1. 11 20 5

1 2. 85_ 2 __ 12

3. 2 2_3 1 3 5_6 1 _12

4. 8 2 (2 1_5 1 1 3_4 )

© Harcourt

Solve. Then explain how you solved the problem. 5. On Saturday, Parker drove 2 41_ hours to the ski park. Then he skied for 4 1_2 hours. His drive back took 2 3_4 hours because of traffic. Did Parker spend more time driving or skiing on Saturday? Explain.

Grade 6

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8/30/07 1:41:49 PM

5.7

Problem of the Day The Delgados are fencing in a pasture on their farm. The Masons’ farm is 3 3_4 mi down the road from the Delgados’ farm. The Bergens’ farm is 1 1_2 miles farther down the road. How far is the Bergens’ farm from the Delgados’ farm? 5 1_4 mi

Spiral Review 1. 8 2 5 1_3 2 2_3

__ 2. 3 2_3 1 3 1_4 6 11 12

Lesson Quiz Write the sum or difference in simplest form. __ 1 3_ 1 __ 3 1. 11 20 5 20

__ 1 13 __ 2. 5_8 2 12 24

3. 2 2_3 1 3 5_6 1 1_2 7

1 __ 4. 8 2 (2 1_5 1 1 3_4 ) 4 20

© Harcourt

Solve. Then explain how you solved the problem. 5. On Saturday, Parker drove 2 1_4 hours to the ski park. Then he skied for 4 1_2 hours. His drive back took 2 3_4 hours because of traffic. Did Parker spend more time driving or skiing on Saturday? Explain. He spent more time driving on Saturday. Parker’s total driving time was 2 1_4 1 2 3_4 5 4 44_ or 5 hours and 5 . 4 1_2 . Grade 6

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6.1

Problem of the Day Manny is preparing a dinner for his friends. He has 8 cups of rice. If one serving of rice is 7_8 cup, about how many servings of rice does he have?

Spiral Review Round each fraction to 0, 1_2 , or 1. 1 1. __ 16

7 __ 4. 12

2. _38

5. 7_1

3. _79

6. 5_4

Lesson Quiz

© Harcourt

Estimate the product or quotient. 1. 7 3_7 4 _49

2. 4 2_3 3 5 _14

3. 17 7_8 4 6 _16

4. 3_5 3 10

5. A bike trail is 3 3_4 miles long. Mariah rode around the trail 4 times. About how many miles did Mariah ride?

Grade 6

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8/30/07 1:46:31 PM

6.1

Problem of the Day Manny is preparing a dinner for his friends. He has 8 cups of rice. If one serving of rice is 7_8 cup, about how many servings of rice does he have? Round 7_8 to 1. Manny has about 8 4 1, or 8 servings.

Spiral Review Round each fraction to 0, 12_ , or 1. 1 1. __ 16

0

7 __ 4. 12

2. 3_8

1 _ 2

5. 7_1 0

3. 7_9

1

6. 54_ 1

1 _ 2

Lesson Quiz

© Harcourt

Estimate the product or quotient. Possible estimates shown. 1. 7 3_7 4 4_9 14

2. 4 2_3 3 5 14_ 25

3. 17 7_8 4 6 1_6 3

4. 53_ 3 10 5

5. A bike trail is 3 3_4 miles long. Mariah rode around the trail 4 times. About how many miles did Mariah ride? 16

Grade 6

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6.2

Problem of the Day Manny is preparing a dinner for his friends. He buys 3_4 lb of cheese. He serves 1_2 of the cheese with crackers. How much cheese did he serve with crackers?

Spiral Review Estimate the product or quotient. 1. 4_7 3 12

4. 23 7_8 4 5 _56

2. 10 4 _38

5. 3 1_3 3 3 _13

9 3 _ 3. 22 __ 10 4 8 8

6. 3_8 3 _58

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 1. 1_2 3 _37

2. 3_5 3 _14

3. 21 3 _23

3 4. 8_9 3 __ 16

5. Lanny rode 7_8 of a bike trail. Nelida rode 1_3 of Lanny’s distance. What fraction of the bike trail did Nelida ride?

Grade 6

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8/30/07 1:46:34 PM

6.2

Problem of the Day Manny is preparing a dinner for his friends. He buys 3_4 lb of cheese. He serves 1_2 of the cheese with crackers. How much cheese did he serve with crackers? 1_2 3 3_4 5 3_8 ; He served 3_8 lb of cheese with crackers.

Spiral Review Estimate the product or quotient. 1. 4_7 3 12 ¯ 6

4. 23 7_8 4 5 5_6 ¯ 4

2. 10 4 3_8 ¯ 20

5. 3 1_3 3 3 1_3 ¯ 9

9 3 _ 3. 22 __ 10 4 8 8 ¯ 3

6. 3_8 3 5_8 ¯ _14

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 3 1. 1_2 3 3_7 __ 14

3 2. 53_ 3 _14 __ 20

3. 21 3 2_3 14

1 3 _ __ 4. 8_9 3 16 6

5. Lanny rode 7_8 of a bike trail. Nelida rode 1_3 of Lanny’s distance. What fraction of the bike trail 7 did Nelida ride? __ 24 Grade 6

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6.3

Problem of the Day Manny is preparing a dinner for his friends. He made 3 1_2 bowls of spaghetti sauce. If each bowl holds 1 1_4 quarts, how much sauce did Manny make?

Spiral Review Find the product. Write it in simplest form. 1. 5_7 3 _12

4. 2_9 3 _23

2. 1_5 3 3

5. 39 3 _23

3 3. 5_6 3 __ 10

6. 1_5 3 _58

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 1. 1 1_4 3 2 2_3

2. 5 3 2 1_3

3. 4_5 3 4 _38

4. 3 6_7 3 3 _19

5. Kelly drank 1 7_8 pints of juice. Ralph drank 2 1_5 times as much juice as Kelly. How much juice did Ralph drink?

Grade 6

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6.3

Problem of the Day Manny is preparing a dinner for his friends. He made 3 1_2 bowls of spaghetti sauce. If each bowl holds 1 1_4 quarts, how much sauce did Manny make? Multiply 3 1__2 3 1 1__4 5 7 __ 5 35 3 __ ___ __ 2 3 4 5 8 5 4 8 . Manny made 4 3_8 quarts of spaghetti sauce.

Spiral Review Find the product. Write it in simplest form. 1. 5_7 3 1_2

4. 2_9 3 _23

2. 1_5 3 3

5 __ 14 3 _ 5

3 3. 5_6 3 __ 10

1 _ 4

6. 1_5 3 5_8

4 __ 27

5. 39 3 2_3 26 1 _ 8

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 1. 1 1_4 3 2 2_3 3 1_3

2. 5 3 2 13_ 11 2_3

3. 4_5 3 4 3_8 3 1_2

4. 3 67_ 3 3 1_9 12

5. Kelly drank 1 78_ pints of juice. Ralph drank 2 1_5 times as much juice as Kelly. How much juice did Ralph drink? 4 1_8 pints Grade 6

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6.4

Problem of the Day Manny is preparing a dinner for his friends. He makes 2 cups of vegetable dip for an appetizer. Each serving is 1_2 cup. Use a model to find the total number of servings.

Spiral Review 1. 2_5 3 _57

3 2. 5_6 3 __ 10

3. 1 1_2 3 1_3

4. 1 1_2 3 1 1_2

5. 9 3 2 1_4

6. 1_3 3 16

Lesson Quiz

© Harcourt

Find the quotient. Write it in simplest form. 2. 2_5 4 _13

3. 3_8 4 _45

4. 6 4 _19

__ lb of sunflower seeds 5. Vivian wants to divide 15 16 into bags that each contain 1_8 lb of sunflower seeds. How many 1_8 -lb bags can she make?

Grade 6

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1. 7 4 _37

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Problem of the Day Manny is preparing a dinner for his friends. He makes 2 cups of vegetable dip for an appetizer. Each serving is 1_2 cup. Use a model to find the total number of servings. 4 servings

Spiral Review 1. 2_5 3 5_7 3. 1 1_2 3 _13

3 2. 5_6 3 __ 10

2 _ 7

1 _ 4

4. 1 1_2 3 1 1_2 2 1_4

1 _ 2

5. 9 3 2 1_4 20 1_4

6. 1_3 3 16 5 1_3

Lesson Quiz

© Harcourt

Find the quotient. Write it in simplest form. 1. 7 4 3_7 16 1_3

2. 2_5 4 13_ 1 1_5

15 __ 3. 3_8 4 _45 32

4. 6 4 1_9 54

__ lb of sunflower seeds 5. Vivian wants to divide 15 16 into bags that each contain 81_ lb of sunflower seeds. How many 1_8 -lb bags can she make? 7 1_2 bags

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He makes 6 2_3 cups of squash. How many bowls can he fill if each bowl holds 2 2_3 cups?

Spiral Review Multiply. 1. 4_5 4 4_5 5 ___ 1 16 __ 2. 3_8 4 __ 16 5 ___ 3 1

3. 7_8 4 1_4 5 ___ 4. 3_5 4 1_5 5 ___ 3 4 _ 5. 4_5 4 __ 10 5 5 3 ___

6. 1_4 4 1_8 5 ___

Lesson Quiz 2. 3 3_4 4 1 _14

3. 9_4 4 _47

4. 7_8 4 1 _78

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5. Greta is making pillow covers with 9 3_8 yards of fabric. If each pillow cover requires 1 7_8 yards of fabric, how many pillow covers can she make? Write and solve a division problem to find the answer.

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He makes 6 23_ cups of squash. How many bowls can he fill if each bowl holds 2 32_ cups? 2 1_2 bowls

Spiral Review Multiply. 1 1. 4_5 4 4_5 5 ___

3 _ 1 5 ___ __ __ 8 3 16 2. 3_8 4 16 1

3 1_2 3. 7_8 4 1_4 5 ___ 3 4. 3_5 4 1_5 5 ___

10 __ 3 5 4 _ 3 ___ 3 5. 4_5 4 __ 10 5

2 6. 1_4 4 1_8 5 ___

Lesson Quiz 1. 1 2_3 4 2_5 4 1_6

2. 3 34_ 4 1 1_4 3

__ 3. 9_4 4 4_7 3 15 16

7 4. 87_ 4 1 78_ __ 15

© Harcourt

5. Greta is making pillow covers with 9 3_8 yards of fabric. If each pillow cover requires 1 7_8 yards of fabric, how many pillow covers can she make? Write and solve a division problem to find the 8 __ 5 75 __ 3 __ answer. 9 3_8 4 1 7_8 5 7 5_8 4 15 8 8 15 5 5; Greta can make 5 pillow covers. Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He wants to find out how many pints of sherbet he will need for 4 servings, if each serving is 5_8 pint. Choose the operation and solve the problem.

Spiral Review Rewrite each division problem as a multiplication problem. 1. 3_4 4 _23

2. 5_6 4 4

3. 1 3_4 4 1 _23

4. 4 4 1 _12

Lesson Quiz Solve.

1. Kyle worked 3 1_3 hours on Monday and 2 3_4 hours on © Harcourt

Tuesday. Choose the operation to find how many more hours he worked on Monday than on Tuesday. Then solve.

2. Inez has 4 quarts of lemonade. Choose the

operation to find how many 1 1_2 -quart pitchers she can fill. Then solve.

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He wants to find out how many pints of sherbet he will need for 4 servings, if each serving is 5_8 pint. Choose the operation and solve the problem. Multiply; 1

4

@ 5 3 _58 5 4_1 3 _ 5 5_2 , or @ 8

2

2 1_2 pt

Spiral Review Rewrite each division problem as a multiplication problem. 5 _ 6

1 _ 4

1. 3_4 4 2_3 3_4 3 _32

2. 65_ 4 4

3. 1 3_4 4 1 _23 7_4 3 _35

4. 4 4 1 _12 4_1 3 _23

3

Lesson Quiz Solve.

1. Kyle worked 3 1_3 hours on Monday and 2 3_4 hours on © Harcourt

Tuesday. Choose the operation to find how many more hours he worked on Monday than on Tuesday. 7 hour Then solve. Subtraction; 3 1_3 2 2 3_4 5 __ 12

2. Inez has 4 quarts of lemonade. Choose the

operation to find how many 1 1_2 -quart pitchers she can fill. Then solve. Division; 4 4 1 1_2 5 2 2_3 pitchers

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He buys 4 pounds of salmon. Use mental math to find how many servings of salmon Manny can make if each serving is 1_2 pound.

1. 11 3

_1 7

Spiral Review 2. 8 3 _23

4 3. 3_8 3 __ 15

4. 7_8 4 _12

5 8 __ 5. __ 12 3 15

6. 7 1_3 4 5 _12

Lesson Quiz

© Harcourt

Solve. Choose mental math, paper and pencil, or a calculator. 1. 4_9 2 _12

2. 15 4 _12

5 3. 1 5_8 2 __ 12

4. 7_8 4 12_

5. Linda makes 9 tuna sandwiches. She uses 5_6 oz of tuna for each sandwich. How much tuna does Linda use for all 9 sandwiches?

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He buys 4 pounds of salmon. Use mental math to find how many servings of salmon Manny can make if each serving is 1_2 pound. Think: 4 5 8 3 12_ . So, 4 4 1_2 5 8. Manny can make 8 servings of salmon.

Spiral Review

1. 11 3 1_7 77

2. 8 3 2_3 5 1_3

4 3. 3_8 3 __ 15

1 __ 10

4. 7_8 4 1_2 1 3_4

5 8 __ 5. __ 12 3 15

2 _ 9

6. 7 1_3 4 5 1_2 1 1_3

Lesson Quiz

© Harcourt

Solve. Choose mental math, paper and pencil, or a calculator. 1. 4_9 2 _12

1 _ 9

5 5 __ 3. 1 5_8 2 __ 12 1 24

2. 15 4 1_2 30 4. 87_ 4 1_2 1 3_4

5. Linda makes 9 tuna sandwiches. She uses 5_6 oz of tuna for each sandwich. How much tuna does Linda use for all 9 sandwiches? 7 1_2 oz

Grade 6

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Unit 3 • Problem of the Day

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Tyler and Ana each toss a fair number cube ten times. What are some comparisons you can make about their tosses?

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Mrs. Parker’s class is collecting data about sixth graders’ computer usage. In her class, 5 students used the computer 22 minutes a day, 3 used it 15 minutes a day, 7 used it 25 minutes a day, and 2 used it 45 minutes a day. If 3 of the students who originally used the computer 25 minutes started to increase their usage to 45 minutes a day, would the mean, median, mode, and range increase, decrease, or remain unchanged?

Grade 6

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Unit 3 • Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. In her class, 5 students used the computer 22 minutes a day, 3 used it 15 minutes a day, 7 used it 25 minutes a day, and 2 used it 45 minutes a day. If 3 of the students who originally used the computer 25 minutes started to increase their usage to 45 minutes a day, would the mean, median, mode, and range increase, decrease, or remain unchanged? The mean would increase, the median and the range would remain unchanged, and the mode would have two values, one higher and one lower.

7

Tyler and Ana each toss a fair number cube ten times. What are some comparisons you can make about their tosses? Possible answer: the actual numbers showing on the number cubes; the number of times each student tossed an even number, the number of times each tossed an odd number, or the number of times each tossed a prime number.

8

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Antonio said that he used the computer every day. The number of hours he spent on the computer last week were 3, 2, 4, 3, 1, 5, and 3. What is the average time, or mean time, that Antonio spent on the computer last week?

Spiral Review Solve. Use mental math, paper and pencil, or a calculator. 1. 3 3 1 _23

5 3. 5_6 4 __ 12

2. 4 3_5 4 _15 4. 4 2_3 3 _67

Lesson Quiz The table below shows the number of minutes Sonia exercised during a two-week training period. Use the table to answer 1–4.

© Harcourt

NUMBER OF MINUTES EXERCISING Week 1 25 20 29 30 30 30 29 Week 2 35 30 35 40 40 35 40 1. What is the mode?

2. What is the mean?

3. What is the median?

4. What is the range?

5. Sonia wanted to exercise an average of 35 minutes daily. How many more total minutes should she have exercised to reach this mean goal? Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Antonio said that he used the computer every day. The number of hours he spent on the computer last week were 3, 2, 4, 3, 1, 5, and 3. What is the average time, or mean time, that Antonio spent on the computer last week? 3 hours

Spiral Review Solve. Use mental math, paper and pencil, or a calculator. 1. 3 3 1 _23 5

2. 4 3_5 4 _15 23 4. 4 2_3 3 6_7 4

5 3. 5_6 4 __ 12 2

Lesson Quiz The table below shows the number of minutes Sonia exercised during a two-week training period. Use the table to answer 1–4.

© Harcourt

NUMBER OF MINUTES EXERCISING Week 1 25 20 29 30 30 30 29 Week 2 35 30 35 40 40 35 40 1. What is the mode? 30 minutes

2. What is the mean? 32 minutes

3. What is the median? 30 minutes 4. What is the range? 40 minutes 2 20 minutes = 20 minutes 5. Sonia wanted to exercise an average of 35 minutes daily. How many more total minutes should she have exercised to reach this mean goal? 42 minutes Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Anna is a sixth grader who was surveyed. Over the past 10 days, she was on the computer for the following number of hours: 3, 4, 2, 3, 3, 5, 3, 1, 2, 3. On how many days did Anna spend fewer than 4 hours on the computer?

Spiral Review Find the mean, median, mode, and range. 1. 8, 6, 7, 7, 4, 10, 7

2. 12, 16, 10, 17, 18, 10, 15

3. 30, 31, 36, 31, 42

4. 100, 98, 94, 100, 89, 93, 98

Lesson Quiz A survey asked 20 people how many different websites they visit in a day. Use the table to answer 1–4.

Number of Web Sites Visited in a Day 2 12

6 0

4 1

6 7

8 5

1 6

9 2

8 3

7 6

6 9

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1. Make a line plot for the data. 2. Complete the frequency table. and identify any outliers in Number of Websites Visited in a Day the plot. Number of Visited Websites

Frequency

Cumulative Frequency

0–4 5–9 10–12

7

10–14 19

1

3. If the survey were extended to include 20 more people, what do you predict the results would be? Explain.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Anna is a sixth grader who was surveyed. Over the past 10 days, she was on the computer for the following number of hours: 3, 4, 2, 3, 3, 5, 3, 1, 2, 3. On how many days did Anna spend fewer than 4 hours on the computer? 8 days

Spiral Review Find the mean, median, mode, and range. 1. 8, 6, 7, 7, 4, 10, 7 mean 57; median 5 7; mode 57; range 5 6

2. 12, 16, 10, 17, 18, 10, 15 mean 5 14; median 5 15; mode 5 10; range 5 8

3. 30, 31, 36, 31, 42 4. 100, 98, 94, 100, 89, 93, 98 mean 5 34; median 5 31; mean 5 96; median 5 98; mode 5 31; range 5 12 mode 5 98 and 100; range 5 11

Lesson Quiz A survey asked 20 people how many different websites they visit in a day. Use the table to answer 1–4.

Number of Web Sites Visited in a Day 2 12

6 0

4 1

6 7

8 5

1 6

9 2

8 3

7 6

6 9

1. Make a line plot for the data. 2. Complete the frequency table. and identify any outliers in Number of Websites Visited in a Day the plot. © Harcourt

X X X XX XXXX XXX X X X XXXX X 0 1 2 3 4 5 6 7 8 9 10 11 12

Number of Visited Websites

Frequency

Cumulative Frequency

0–4 5–9 10–12

7

10–14 19

12 1

20

3. If the survey were extended to include 20 more people, what do you predict the results would be? Explain. Possible answer: Most people would visit between 5 and 9 Web sites a day. This category had the largest frequency and the data seems to cluster around 5–9. Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Ted wants to survey a sixth-grade class. Elana wants to survey every tenth student from a list of sixth graders at the school. If the survey needs to be completed within two hours, which method should they choose?

Spiral Review Free Throws Made During Tournament 0–5 6–11 12–17

Frequency 4 3

Cumulative Frequency 4 14

Refer to the frequency table above. 1. What is the total cumulative frequency? 2. How many times were more than 11 free throws made?

Lesson Quiz For 1–4, tell the best sampling method to use. 1. Mrs. Townson wants to know if her middle school students prefer having time in the morning to do homework or time in the afternoon. She wants to survey every third student from her class attendance list.

© Harcourt

2. The guidance department wants to know which elective classes sixth graders enjoy most. They want each sixth-grade student to have an equal chance of being selected. 3. Candidate Simmons wants to know if the planned community center is a popular idea with the voters. They plan to survey shoppers at the local mall. 4. The sixth-grade class is allowed to choose the destination for their class trip. Students will be surveyed at the school library. 5. The drama teacher wants to know what type of movies her students enjoy most. There are a total of 95 students in her classes. Describe how she could perform a systematic sample.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Ted wants to survey a sixth-grade class. Elana wants to survey every tenth student from a list of sixth graders at the school. If the survey needs to be completed within two hours, which method should they choose? They should survey a sixth-grade class. This will take less time than surveying every tenth student from the list of sixth-grade students.

Spiral Review Free Throws Made During Tournament 0–5 6–11 12–17

Frequency 4

Cumulative Frequency 4 14

3

Refer to the frequency table above. 1. What is the total cumulative frequency? 17 2. How many times were more than 11 free throws made? 3

Lesson Quiz For 1–4, tell the best sampling method to use. 1. Mrs. Townson wants to know if her middle school students prefer having time in the morning to do homework or time in the afternoon. She wants to survey every third student from her class attendance list. systematic sampling

© Harcourt

2. The guidance department wants to know which elective classes sixth graders enjoy most. They want each sixth-grade student to have an equal chance of being selected. random sampling 3. Candidate Simmons wants to know if the planned community center is a popular idea with the voters. They plan to survey shoppers at the local mall. convenience sampling

4. The sixth-grade class is allowed to choose the destination for their class trip. Students will be surveyed at the school library. convenience sampling 5. The drama teacher wants to know what type of movies her students enjoy most. There are a total of 95 students in her classes. Describe how she could perform a systematic sample. Possible answer: She could combine her class lists and survey every fifth student on the new list.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. The class has a topic, but needs a good survey question. What question might work for this survey?

Spiral Review Given the following survey guidelines, what is the best sampling method to use for a survey of 6th graders? 1. First fifty 6th graders entering the cafeteria are surveyed.

2. Every fifth student on the 6th-grade enrollment list is surveyed.

3. 6th graders' names are 4. All 6th graders are surveyed. placed in a bag and thirty are selected for the survey.

Lesson Quiz Use the following survey information to answer questions 1–5. Mr. Balsom’s 6th-grade class has 24 students. Every third student on his class list is asked to complete a survey in which students are asked if they walk to school or ride a bus. Six of the students say that they ride a bus. 1. What is the topic of the survey?

© Harcourt

2. What population is surveyed? 3. What is the survey question? 4. Can you make a prediction based on the information in the survey? 5. How can you check the information in the survey to see if it is reasonable?

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. The class has a topic, but needs a good survey question. What question might work for this survey? Answers will vary. Possible answer: When do you use a computer the most—before school, during school, or after school?

Spiral Review Given the following survey guidelines, what is the best sampling method to use for a survey of 6th graders? 1. First fifty 6th graders entering the cafeteria are surveyed. convenience sampling

2. Every fifth student on the 6th-grade enrollment list is surveyed. systemic sampling

3. 6th graders' names are 4. All 6th graders are surveyed. No sampling; the entire placed in a bag and population of 6th graders thirty are selected for the is surveyed. survey. random sampling

Lesson Quiz Use the following survey information to answer questions 1–5. Mr. Balsom’s 6th-grade class has 24 students. Every third student on his class list is asked to complete a survey in which students are asked if they walk to school or ride a bus. Six of the students say that they ride a bus. 1. What is the topic of the survey? Transportation to school

© Harcourt

2. What population is surveyed? A sampling of 6th graders. 3. What is the survey question? Do you walk or ride a bus to school? 4. Can you make a prediction based on the information in the survey? Possible answer: Most 6th-grade students ride a bus to school. 5. How can you check the information in the survey to see if it is reasonable? Possible answer: Repeat the survey using a larger number of students by either using random or systematic sampling method to survey the entire 6th grade. You can also research the number of 6th-grade students who walk or ride the bus to school.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. A survey showed that 60 students use the computer in the morning, 90 students use the computer in the afternoon, and 30 students use the computer at both times. How many students use the computer in the morning only? In the afternoon only?

Spiral Review Suppose you are designing a survey about music. 1. List two topics that you could use.

2. Describe the population you will use in your survey. 3. Write two survey questions.

4. Develop a prediction.

Lesson Quiz

© Harcourt

Draw a diagram to solve. 1. To get to soccer practice, Kate’s mom drives 2 1_2 mi north, 3 mi east, 3 mi south to Kate’s school. Then she drives east to the soccer field. If she drives 10 mi altogether, how far east does she drive from the school to the soccer field? 2. Aaron wants to frame his rectangular painting. Two sides of his painting are 18 in. long and two sides are 12 in. long. How many inches of framing material does Aaron need?

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. A survey showed that 60 students use the computer in the morning, 90 students use the computer in the afternoon, and 30 students use the computer at both times. How many students use the computer in the morning only? In the afternoon only? Thirty students use the computer in the morning only; 60 students use the computer in the afternoon only.

Spiral Review Suppose you are designing a survey about music. 1. List two topics that you could use. Possible answers: favorite artist, favorite type of music

2. Describe the population you will use in your survey. Possible answers: all students in your school, all sixth-grade students in your school 3. Write two survey questions. Possible answers: Who is your favorite musical artist? What is your favorite type of music? 4. Develop a prediction. Answers will vary.

Lesson Quiz

© Harcourt

Draw a diagram to solve. 1. To get to soccer practice, Kate’s mom drives 2 1_2 mi north, 3 mi east, 3 mi south to Kate’s school. Then she drives east to the soccer field. If she drives 10 mi altogether, how far east does she drive from the school to the soccer field? 1 1_2 mi – see diagram 2. Aaron wants to frame his rectangular painting. Two sides of his painting are 18 in. long and two sides are 12 in. long. How many inches of framing material does Aaron need? 60 inches; see diagram

Grade 6

3 mi 2 1 mi 2

3 mi ? mi

12 in. 18 in.

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Problem of theof Day the Problem

8.1

Day

Tyler and Ana each toss a number cube ten times. What is the best way to show how the results of their tosses compare?

Spiral Review A tile pattern uses 3-inch-long red tiles and 7-inch-long black tiles. The space between each tile and the next is 1 inch. Solve by drawing a diagram. 1. How long is a pattern row with 2 red tiles and 1 black tile? 3. How long is a pattern row with 5 red tiles and 3 black tiles?

2. How long is a pattern row with 4 red tiles and 6 black tiles? 4. A pattern row is 27 in. long. If there are 3 black tiles, how many red tiles are there?

Lesson Quiz Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. The boys’ and girls’ favorite kind of zoo animal.

© Harcourt

2. The number of mp3 players purchased in Illinois and New York in the last four years. 3. The number of students in the school who ride the bus compared to the number of students who walk. 4. Amount of rain over a period of a month in Cleveland and Philadelphia. 5. During a school election, one candidate polled the students to find which of five issues they felt was most important.

Grade 6

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Problem of theof Day the Problem

8.1

Day

Tyler and Ana each toss a number cube ten times. What is the best way to show how the results of their tosses compare? A double-bar graph can be used to compare two sets of data.

Spiral Review A tile pattern uses 3-inch-long red tiles and 7-inch-long black tiles. The space between each tile and the next is 1 inch. Solve by drawing a diagram. 1. How long is a pattern row with 2 red tiles and 1 black tile? 15 in. 3. How long is a pattern row with 5 red tiles and 3 black tiles? 43 in.

2. How long is a pattern row with 4 red tiles and 6 black tiles? 63 in. 4. A pattern row is 27 in. long. If there are 3 black tiles, how many red tiles are there? 1 red tile

Lesson Quiz Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. The boys’ and girls’ favorite kind of zoo animal. double-bar graph

© Harcourt

2. The number of mp3 players purchased in Illinois and New York in the last four years. double-line graph 3. The number of students in the school who ride the bus compared to the number of students who walk. circle graph 4. Amount of rain over a period of a month in Cleveland and Philadelphia. double-line graph 5. During a school election, one candidate polled the students to find which of five issues they felt was most important. circle graph Grade 6

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Problem of the Day Tyler and Ana each toss a number cube ten times. Tyler’s tosses represent the tens digit in a number and Ana’s represent the ones digit. How could they organize their tosses in a stemand-leaf plot?

Spiral Review Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. Favorite music of sixth-graders 2. Out of 5 color choices, the compared to the favorite music number of students in a class of their parents who prefer red over blue 3. Compare the length of daylight 4. Compare the percents of in each day in December to the students who like English length of daylight in each day best and students who like in July. mathematics best.

Lesson Quiz The data in the table represents the results of a survey of 12 people. Use the data to answer the questions.

Ounces of water consumed per day 16 20

48 24

30 48

8 36

48 32

64 54

© Harcourt

1. Make a stem-and-leaf plot of the data in the table.

2. Using your plot, find the median and the mode of the data. 3. Make a histogram of the data in the table using intervals starting at 0–20 ounces. 4. How many people consumed less than 64 ounces of water daily? 5. Ema redrew the histogram using intervals starting at 0–9. What frequencies

were represented by the bars? Grade 6

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Problem of the Day Tyler and Ana each toss a number cube ten times. Tyler’s tosses represent the tens digit in a number and Ana’s represent the ones digit. How could they organize their tosses in a stemand-leaf plot? Tyler’s tosses are the stems and Ana’s are the leaves in the plot.

Spiral Review Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. Favorite music of sixth-graders 2. Out of 5 color choices, the compared to the favorite music number of students in a class of their parents who prefer red over blue double-bar graph circle graph 3. Compare the length of daylight 4. Compare the percents of in each day in December to the students who like English length of daylight in each day best and students who like in July. double-line graph mathematics best. circle graph

Lesson Quiz Use the data to answer the questions. 1. Make a stem-and-leaf plot of the data in the table.

© Harcourt

Stems 0 1 2 3 4 5 6

Leaves 8 6 0 4 0 2 6 8 8 8 4 4

Ounces of water consumed per day 16 20

48 24

30 48

8 36

48 32

64 54

Ounces of Water Consumed Per Day Frequency (number of responses)

The data in the table represents the results of a survey of 12 people.

5 4 3 2 1 0

0–19 20–39 40–59 60–79

Ounces

2. Using your plot, find the median and the mode of the data. median: 34, mode: 48 3. Make a histogram of the data in the table using intervals starting at 0–20 ounces. 4. How many people consumed less than 64 ounces of water daily? 11 5. Ema redrew the histogram using intervals starting at 0–9. What frequencies were represented by the bars? 1, 1, 2, 3, 3, 1, 1 Grade 6

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Problem of the Day Tyler and Ana each toss a fair number cube ten times. How could the data showing the totals for each number tossed be graphed?

Spiral Review Choose a histogram or stem-and-leaf plot to best represent each set of data. 1. Number of minutes Josh spends on math homework each day for two weeks

2. Weights of wrestlers grouped by weight class

3. Level of baseball players based on ranges of runs scored during a season

4. Joanne’s top 15 scores on her favorite computer game

Lesson Quiz Compare the graphs. 1. Which graph shows when most students buy lunch?

40

2. Which graph tells you if more students prefer to buy lunch or

30

bring lunch? 3. What is the average number of students who buy lunch? Which graph did you use to find your answer? © Harcourt

Students Buying Lunch

4. Do more students buy lunch at the end of the week or the beginning? Which graph shows this? 5. The manager of the school cafeteria needs to decide how

20 10 0 Mon

Thurs

Fri

40 30 20

to find this information?

10 0

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Average Student Lunch Habits

much food to prepare each day. Which graph should he use

Grade 6

Tues

Buy Lunch

Bring Lunch

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8.3

Problem of the Day Tyler and Ana each toss a fair number cube ten times. How could the data showing the totals for each number tossed be graphed? A circle graph could compare the percent of times a number is tossed out of the total number of tosses. A bar graph could show the number of occurrences for each number tossed.

Spiral Review Choose a histogram or stem-and-leaf plot to best represent each set of data. 1. Number of minutes Josh spends on math homework each day for two weeks stem-and-leaf plot

2. Weights of wrestlers grouped by weight class histogram

3. Level of baseball players based on ranges of runs scored during a season histogram

4. Joanne’s top 15 scores on her favorite computer game stem-and-leaf plot

Lesson Quiz Compare the graphs.

Students Buying Lunch

1. Which graph shows when most students buy lunch? line graph 2. Which graph tells you if more students prefer to buy lunch or bring lunch? bar graph 3. What is the average number of students who buy lunch? © Harcourt

Which graph did you use to find your answer? 15; bar graph 4. Do more students buy lunch at the end of the week or the beginning? Which graph shows this? at the end of the week; line graph 5. The manager of the school cafeteria needs to decide how

40 30 20 10 0 Mon

Wed

Thurs

Fri

Average Student Lunch Habits 40 30

much food to prepare each day. Which graph should he use

20

to find this information? line graph

10 0

Grade 6

Tues

Buy Lunch

Bring Lunch

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8.4

Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler wants to show the results of their tosses using a line graph and Ana wants to use a bar graph. Whose graph would be the best to use? Explain.

Spiral Review The day and night temperatures for a week are graphed using a double-line graph and a double-bar graph. Choose the better graph to analyze each situation. 1. the trend in temperatures for the week

2. the difference in Wednesday’s temperatures

3. the time when the temperatures varied the most

4. the exact information for each day

Lesson Quiz Choose the most appropriate type of graph to make for each data set: a bar or double-bar graph, a line or double line-graph, a circle graph, a pictograph, or a histogram. 1. Your height measured once each month for a year

© Harcourt

2. The amount of time spent on homework for each subject 3. The number of hours practiced in one week by five dance teams 4. The number of wins and losses for six soccer teams 5. A science experiment tracked the monthly growth of two plants—one in the sun and one in the shade. Which graph would best show how to compare the plant growth?

Grade 6

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8.4

Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler wants to show the results of their tosses using a line graph and Ana wants to use a bar graph. Whose graph would be the best to use? Explain. A line graph shows how data changes over time. Since tosses are not affected by time, a bar graph would be the better choice.

Spiral Review The day and night temperatures for a week are graphed using a double-line graph and a double-bar graph. Choose the better graph to analyze each situation. 1. the trend in temperatures for the week double-line graph 3. the time when the temperatures varied the most double-line graph

2. the difference in Wednesday’s temperatures double-bar graph 4. the exact information for each day double-bar graph

Lesson Quiz Choose the most appropriate type of graph to make for each data set: a bar or double-bar graph, a line or double line-graph, a circle graph, a pictograph, or a histogram. Possible answers are given. 1. Your height measured once each month for a year line graph

© Harcourt

2. The amount of time spent on homework for each subject circle graph 3. The number of hours practiced in one week by five dance teams 4. The number of wins and losses for six soccer teams double-bar graph pictograph 5. A science experiment tracked the monthly growth of two plants—one in the sun and one in the shade. Which graph would best show how to compare the plant growth? double-line graph

Grade 6

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8.5

Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler tosses twice as many even numbers as Ana. What conclusion could you make from the results of the tosses? Explain.

Spiral Review Choose the most appropriate type of graph for each data set based on a sixth-grade student survey about sports. 1. boys’ favorite sports compared to girls’ favorite sports

2. increase or decrease in sport activity every week for 3 months

3. a comparison of the number of students who chose a specific sport to the total number of students surveyed.

4. totals for type of favorite sport displayed using symbols

Lesson Quiz Average Hours of Sleep

Use the graph to answer the questions.

© Harcourt

1. A group of sixth-graders was surveyed to find out how many hours of sleep they averaged during May, June, and July. Using the data in the graph, what conclusion can you make about their sleep patterns during these months?

8 6 4 2 0

May

Jun

Jul

2. What do you think would happen if the graph were extended three more months?

Grade 6

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10

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8.5

Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler tosses twice as many even numbers as Ana. What conclusion could you make from the results of the tosses? Explain. Possible answer: Tyler and Ana have different cubes. Tyler’s cube had more even numbers or is weighted.

Spiral Review Choose the most appropriate type of graph for each data set based on a sixth-grade student survey about sports. 1. boys’ favorite sports compared to girls’ favorite sports double-bar graph 3. a comparison of the number of students who chose a specific sport to the total number of students surveyed. circle graph

2. increase or decrease in sport activity every week for 3 months line graph 4. totals for type of favorite sport displayed using symbols pictograph

Lesson Quiz Average Hours of Sleep

© Harcourt

Use the graph to answer the questions. 1. A group of sixth-graders was surveyed to find out how many hours of sleep they averaged during May, June, and July. Using the data in the graph, what conclusion can you make about their sleep patterns during these months? Possible answer: The students sleep for longer periods of time with each month.

10 8 6 4 2 0

May

Jun

Jul

2. What do you think would happen if the graph were extended three more months? Possible answer: You might predict that the number of hours of sleep would continue to increase. However, the conclusion would be wrong if students are out of school during the summer months and can sleep longer in June and July. When they are back in school in September, the number of hours of sleep would decrease after school starts.

Grade 6

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Unit 4 • Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers.

9

Keisha makes a deposit of $50 and a withdrawal of $18. Write an integer to represent each situation.

Natalie enjoys playing basketball with her friends. Every week, they compete to see who shoots the most successful baskets in 20 throws.

10

© Harcourt

This week, Natalie made 12 baskets. What fraction of her throws were successful?

Grade 6

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Unit 4 • Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers.

9

Keisha makes a deposit of $50 and a withdrawal of $18. Write an integer to represent each situation. 1 50, 218

Natalie enjoys playing basketball with her friends. Every week, they compete to see who shoots the most successful baskets in 20 throws.

10

© Harcourt

This week, Natalie made 12 baskets. What fraction of her throws were successful? 3_5

Grade 6

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9.1

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes deposits of $50, $25, and $10. She makes withdrawals of $15, $10, $23, and $12. Write an integer to represent each situation and order them from least to greatest.

Spiral Review 1. What type of graph examines change over time? 2. How would you represent 25% of a circle graph? 3. What type of graph represents percentages of a whole? 4. Determine 20% of 420.

Lesson Quiz 1. Write an integer to represent a weight gain of 10 pounds

© Harcourt

2. Write an integer to represent a $25 discount 3. What is the absolute value of 4? 4. Use , or = to compare 27 and 6 5. Average temperatures for five days in December were 21°F, 25°F, 1°F, 24°F, and 4°F. Place the temperatures in order from least to greatest.

Grade 6

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9.1

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes deposits of $50, $25, and $10. She makes withdrawals of $15, $10, $23, and $12. Write an integer to represent each situation and order them from least to greatest. 2 23, 2 15, 2 12, 2 10, 10, 25, 1 50

Spiral Review 1. What type of graph examines change over time? Line graph 2. How would you represent 25% of a circle graph? Shade in 1_4 of the graph. 3. What type of graph represents percentages of a whole? Circle graph 4. Determine 20% of 420. 84

Lesson Quiz 1. Write an integer to represent a weight gain of 10 pounds 10

© Harcourt

2. Write an integer to represent a $25 discount 2 25 3. What is the absolute value of 4? 4 4. Use , or = to compare 27 and 6 2 7 , 6 5. Average temperatures for five days in December were 21°F, 25°F, 1°F, 24°F, and 4°F. Place the temperatures in order from least to greatest. 2 5°F, 2 4°F, 2 1°F, 1°F, 4°F

Grade 6

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9.2

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Explain how to use a number line to model a withdrawal of $20.

Spiral Review 1. Place in order from least to greatest: 1 _ , 0.01, 3_ 4 8 2. Place in order from greatest to least: 2 , 2.10 1.02, 1 __ 10

© Harcourt

Lesson Quiz Use counters to find each sum. 1. 6 1 26

2. 22 1 27

3. 3 1 28

4. 21 1 9

5. 23 1 22 Grade 6

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9.2

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Explain how to use a number line to model a withdrawal of $20. Start at the current balance, move 20 units to the left.

Spiral Review 1. Place in order from least to greatest: 1 _ , 0.01, 3_ 0.01, 1_ , 3_ 4 8 4 8 2. Place in order from greatest to least: 2 , 1.02 2 , 2.10 2.10, 1 __ __ 1.02, 1 10 10

© Harcourt

Lesson Quiz Use counters to find each sum. 1. 6 1 26 0

2. 22 1 27 2 9

3. 3 1 28 2 5

4. 21 1 9 8

5. 23 1 22 2 5 Grade 6

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9.3

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the sum of a withdrawal of $10 and a deposit of $15.

Spiral Review Use a model to find each sum. 1. 4 1 1 3. 3 1 27

2. 6 1 22 4. 23 1 25

Lesson Quiz

© Harcourt

Find the sum. 1. 7 1 29

2. 13 1 28

3. 4 1 16

4. 26 1 6

5. A business had a profit of $40 in March and a loss of $50 in April. What was the total profit or loss for both months?

Grade 6

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9.3

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the sum of a withdrawal of $10 and a deposit of $15. 2 10 1 15

Spiral Review Use a model to find each sum. Check students’ models. 1. 4 1 1 5 2. 6 1 22 4 3. 3 1 27 24 4. 23 1 25 28

Lesson Quiz

© Harcourt

Find the sum. 1. 7 1 29 2 2

2. 13 1 28 5

3. 4 1 16 20

4. 26 1 6 0

5. A business had a profit of $40 in March and a loss of $50 in April. What was the total profit or loss for both months? 2 $10

Grade 6

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9.4

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use a number line to represent a deposit of $10 that is cancelled.

Spiral Review 1. 8 1 7 2. 23 1 211 3. 12 1 –5 4. 28 1 13 5. 217 1 9 6. 12 1 222

© Harcourt

Lesson Quiz Find the difference using counters. 1. 6 2 7 5 3. 8 2 24 5

2. 23 2 25 5 4. 2 2 21 5

5. 6 2 4 5

Grade 6

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9.4

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use a number line to represent a deposit of $10 that is cancelled. Move 10 units to the right, then 10 units to the left.

Spiral Review 1. 8 1 7 15 2. 23 1 211 2 14 3. 12 1 –5 7 4. 28 1 13 2 5 5. 217 1 9 2 8 6. 12 1 222 2 10

© Harcourt

Lesson Quiz Find the difference using counters. 1. 6 2 7 5 2 1 3. 8 2 24 5 12

2. 23 2 25 5 2 4. 2 2 21 5 3

5. 6 2 4 5 2

Grade 6

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9.5

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write two expressions to represent a deposit of $100 and a withdrawal of $50.

Spiral Review Use counters to find each difference. 1. 4 2 3 3. 27 2 2

2. 5 2 6 4. 25 2 28

Lesson Quiz

© Harcourt

Find the difference by rewriting each subtraction problem as an addition problem. 2. 12 2 211

3. 4 2 9

4. 0 2 7

5. Paul’s dog’s weight was 3 lb below its normal weight. One month later its weight was 2 lb above its normal weight. Write and solve a subtraction problem to find how much weight Paul’s dog gained. Grade 6

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1. 6 2 25

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8/30/07 2:47:50 PM

9.5

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write two expressions to represent a deposit of $100 and a withdrawal of $50. 100 1 2 50; 100 2 50

Spiral Review Use counters to find each difference. Check students’ models. 1. 4 2 3 1 2. 5 2 6 2 1 3. 27 2 2 2 9 4. 25 2 28 3

Lesson Quiz

© Harcourt

Find the difference by rewriting each subtraction problem as an addition problem. 1. 6 2 25 6 1 5 5 11

2. 12 2 211 12 1 11 5 1

3. 4 2 9 4 1 2 9 5 2 5

4. 0 2 7 0 1 2 7 5 2 7

5. Paul’s dog’s weight was 3 lb below its normal weight. One month later its weight was 2 lb above its normal weight. Write and solve a subtraction problem to find how much weight Paul’s dog gained. 2 2 2 3 5 5 Grade 6

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9.6

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the product of 5 withdrawals of $25 each.

Spiral Review Find the sum or difference. 1. 3 1 25 2. 36 1 215 3. 27 2 8 4. 76 2 (223)

Lesson Quiz © Harcourt

Find the product. 1. 28 3 2

2. 24 3 21

3. 5 3 3

4. 11 3 27

5. The temperature on Monday was 3°F. If the temperature on Tuesday was 3 times as cold, what was the temperature on Tuesday? Grade 6

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9.6

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the product of 5 withdrawals of $25 each. 5 3 2 25

Spiral Review Find the sum or difference. 1. 3 1 25

2

2

2. 36 1 215 12 3. 27 2 8 2 15 4. 76 2 (223) 99

Lesson Quiz © Harcourt

Find the product. 1. 28 3 2 2 16

2. 24 3 21 4

3. 5 3 3 15

4. 11 3 27 2 77

5. The temperature on Monday was 3°F. If the temperature on Tuesday was 3 times as cold, what was the temperature on Tuesday? 2 9˚F Grade 6

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9.7

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. The total of 5 equal withdrawals is $45. Write an expression to represent the amount of 1 withdrawal.

Spiral Review Find the sum or product. 1. 18 1 25 2. 4 3 26 3. 221 1 27 4. 22 323

Lesson Quiz

© Harcourt

Find the quotient. 1. 25 4 25

2. 32 4 8

3. 218 4 22

4. 2100 4 10

5. A plane’s altitude changed by 8,000 ft over 4 hr. What was the average change per hour?

Grade 6

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9.7

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. The total of 5 equal withdrawals is $45. Write an expression to represent the amount of 1 withdrawal. 2 45 4 5

Spiral Review Find the sum or product. 1. 18 1 25 13 2. 4 3 26 2 24 3. 221 1 27 2 28 4. 22 323 6

Lesson Quiz

© Harcourt

Find the quotient. 1. 25 4 25 2 5

2. 32 4 8 4

3. 218 4 22 9

4. 2100 4 10 2 10

5. A plane’s altitude changed by 8,000 ft over 4 hr. What was the average change per hour? 2,000 ft

Grade 6

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9.8

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes one withdrawal that is $10 greater than another withdrawal. Write two integers that could represent the amount of each withdrawal.

Spiral Review 1. 4 1 2 2 8 5

2. 8 2 9 1 3 5

3. 7 2 4 2 11 5

4. 6 1 24 2 3 5

5. 212 2 16 1 28 5

5. 5 2 210 1 2 2 28 5

Lesson Quiz

© Harcourt

1. The sum of two negative integers is 29. When the lesser integer is subtracted from the greater integer, the difference is 5. What are the two integers? 2. The perimeter of a rectangle is 20 ft. The length is 4 times as long as the width. What is the length and width of the rectangle?

Grade 6

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9.8

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes one withdrawal that is $10 greater than another withdrawal. Write two integers that could represent the amount of each withdrawal. Possible answer: 2 50, 2 60

Spiral Review 1. 4 1 2 2 8 52 2

2. 8 2 9 1 3 5 2

2 4. 6 1 24 2 3 5 1 2 5. 212 2 16 1 28 5 36 5. 5 2 210 1 2 2 28 525

3. 7 2 4 2 11 52 8

Lesson Quiz

© Harcourt

1. The sum of two negative integers is 29. When the lesser integer is subtracted from the greater integer, the difference is 5. What are the two integers? 2 2, 2 7 2. The perimeter of a rectangle is 20 ft. The length is 4 times as long as the width. What is the length and width of the rectangle? 8 ft, 2 ft Grade 6

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9.9

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use addition and multiplication to write an expression representing three deposits, each of which includes a check for $10 and a check for $15.

Spiral Review 1. (4 3 5) 3 8 5

2. 7 3 (50 4 5) 5

3. 4 1 ( 1_2 3 24) 5

4. ( 3_4 3 1_2 ) 1 3_4 5

Lesson Quiz Find the value of the expression. 1. 2(6 2 26) 1 28 © Harcourt

2. 27 3 23 1 4 3. (9 1 25)2 4. 1 1 24 3 24 1 1 5. Find the missing integers in the pattern 2, 22, 26, __ , __ , Grade 6

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9.9

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use addition and multiplication to write an expression representing three deposits, each of which includes a check for $10 and a check for $15. 3 3 (10 1 15)

Spiral Review 1. (4 3 5) 3 8 5 160 2. 7 3 (50 4 5) 5 70 3. 4 1 ( 1_2 3 24) 5 16 4. ( 3_4 3 1_2 ) 1 3_4 5 1 1_8

Lesson Quiz Find the value of the expression. 1. 2(6 2 26) 1 28 16 © Harcourt

2. 27 3 23 1 4 25 3. (9 1 25)2 16 4. 1 1 24 3 24 1 1 18 5. Find the missing integers in the pattern 2, 22, 26, __ , __ , 2 10, 2 14 Grade 6

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10.1

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie misses 6 baskets. What fraction of the throws were baskets?

Spiral Review 1. (3 1 12) 2 (24 1 5)

2. (4 3 6) 3 (22 3 4)

3. (12 2 18) 1 (4 2 6)

4. 27 3 (6 2 11)

Lesson Quiz Write the rational number in the form _ba . 1. 3.74 2.

2

2 4_7

Find a rational number between the two given rational numbers.

© Harcourt

__ 3. 28 and 2 30 4 __ 4. 3.1 and 33 10

5. Andrew collected 31 3_5 pounds of canned goods for his school’s charity drive. Marcus collected 31 5_6 pounds of canned goods for the charity drive. If Leslie collected an amount between what Andrew and Marcus collected, how many pounds of canned goods could she have collected?

Grade 6

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10.1

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie misses 6 baskets. What fraction of the throws were baskets? 14 7 __ , or __ 20

10

Spiral Review 1. (3 1 12) 2 (24 1 5) 15 2 1 5 14 3. (12 2 18) 1 (4 2 6) 6 1 22 5 28

2

2. (4 3 6) 3 (22 3 4) 24 3 28 5 2192 4. 27 3 (6 2 11) 7 3 25 5 35

2

Lesson Quiz Write the rational number in the form _ba . 187 1. 3.74 ___ 50

2.

__ 2 4_7 2 18 7

2

Find a rational number between the two given rational numbers.

© Harcourt

__ 2 31 __ 3. 28 and 2 30 4 4 33 16 __ 4. 3.1 and __ 10 5

5. Andrew collected 31 3_5 pounds of canned goods for his school’s charity drive. Marcus collected 31 5_6 pounds of canned goods for the charity drive. If Leslie collected an amount between what Andrew and Marcus collected, how many pounds of canned goods could she have collected? Possible answer: 31 2_3 pounds of canned goods

Grade 6

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10.2

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie makes 14 baskets and her friend Tasha makes 12 baskets. Express the fraction of baskets Natalie makes and the fraction of baskets Tasha makes as decimals. Then compare these numbers using . or ,.

Spiral Review 7 7 1. Order 23 1_8 , 23.2, 23.14 2. Order 1.8, _4 , 1 _8 from least to greatest. from least to greatest.

3. Write 24 1_3 in the form _ba .

3 4. Write 7 __ 16 in the form _ba .

Lesson Quiz Compare. Write >, < or = for each d. 1. 23 d 22.5 2. 4.82 d 4.812 © Harcourt

__ 3. 25.45 d 25 17 20

4. 6.3 1 3.2 d 5.7 1 3.8 5. Arrange the following numbers in order from least to greatest: 22 87_ , 22 81_ , 22 41_ , 23 21_ .

Grade 6

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10.2

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie makes 14 baskets and her friend Tasha makes 12 baskets. Express the fraction of baskets Natalie makes and the fraction of baskets Tasha makes as decimals. Then compare these numbers __ , is 0.7 and 12 __ 0.6; Possible using . or ,. 14 20 20 comparisons: 0.7 . 0.6, or 0.6 , 0.7.

Spiral Review 7 7 1. Order 23 1_8 , 23.2, 23.14 2. Order 1.8, _4 , 1 _8 from least to greatest. from least to greatest. _ 2 2 2 1 7 _ , 1.8, 1 7_ 3.2, 3.14, 3 8 4 8 3 in the __ 4. Write 7 16 3. Write 24 1_3 in the 115 __ form _ba . ___ form _ba . 2 13 16 3

Lesson Quiz Compare. Write >, < or = for each d. 1. 23 d 22.5 , 2. 4.82 d 4.812 . © Harcourt

__ 3. 25.45 d 25 17 20

.

4. 6.3 1 3.2 d 5.7 1 3.8 5 5. Arrange the following numbers in order from least to greatest: 22 87_ , 22 81_ , 22 41_ , 23 21_ . 2 1 3 _2 , 22 7_8 , 22 1_4 , 22 1_8

Grade 6

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10.3

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. Over the course of three weeks, Natalie made 13, 16, and 17 baskets, while Danielle made 16, 13, and 14 baskets. What fraction of her throws did Natalie make? Danielle?

Spiral Review Compare the rational numbers using ., ,, or 5. 1. 3.65 ___ 3 5_8 2. 22.23 ___ 22.228 __ ___ 2.74 3. 2 39 50

__ ___ 249 ___ 4. 83 8 24

Lesson Quiz For 1–4, evaluate each expression. 1. 3 1_4 3 (1.4 1 3.2 1 22.4) © Harcourt

2. 6 3 3.2 1 22 4 8 3. 4 2_3 3 (2 1_5 1 4) 1 8 _23 4. (4.75 1 1 1_4 ) 4 (3 3_4 3 22.5) 5. Change Exercise 4 to make the answer an integer

Grade 6

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10.3

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. Over the course of three weeks, Natalie made 13, 16, and 17 baskets, while Danielle made 16, 13, and 14 baskets. What fraction of her throws did Natalie make? Danielle? __ 5 23 __ ; Danielle 43 __ Natalie, 46 60 30 60

Spiral Review Compare the rational numbers using ., ,, or 5. 1. 3.65 ___ 3 5_8 . 2. 22.23 ___ 22.228 , 39 __ ___ 2.74 . 3. 2 50

__ ___ 249 ___ 5 4. 83 8 24

Lesson Quiz For 1–4, evaluate each expression. 3 1. 3 1_4 3 (1.4 1 3.2 1 22.4) 7.15 or 7 __ 20 © Harcourt

__ 2. 6 3 3.2 1 22 4 8 18.95 or 18 19 20

3. 4 2_3 3 (2 1_5 1 4) 1 8 23_

4 20 __ 15

2

2 16 4. (4.75 1 1 1_4 ) 4 (3 34_ 3 22.5) ___ 25

5. Change Exercise 4 to make the answer an integer Possible answer: ((4.75 1 1 1_4 ) 4 3 34_ ) 3 22.5 5 24 Grade 6

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10.4

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. During this week’s competition, Natalie makes 14 baskets, Danielle misses 8 shots, and Lisa makes 75% of her shots. What is the difference between the number of baskets made by Danielle and Lisa?

Spiral Review 1. 1.2 1 23.7 1 4.8

2. 0.5 3 (28 3 4.6)

3. 3_4 1 2 1_4 1 2 _18

4. 24.1 1 3.6 3 1.6 4 23

Lesson Quiz

© Harcourt

1. The Nile River is about 4,160 miles long, which makes it the longest river in the world. The Amazon River is approximately 4,000 miles long. The Mississippi-Missouri-Red Rock River is the longest river in the United States, at about 3,710 miles. What is the difference in length between the Nile and the Mississippi-Missouri-Red Rock rivers? 2. Sean works in a shoe store where he earns commission on every pair of shoes that he sells. On Monday, he sold 15 pairs of shoes. On Wednesday, he sold 22 pairs of shoes. On Friday, he sold twice as many pairs of shoes as he did on Monday. On Saturday, he sold twice as many pairs of shoes as he sold on Monday and Wednesday combined. How many pairs of shoes did he sell on Saturday?

Grade 6

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Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. During this week’s competition, Natalie makes 14 baskets, Danielle misses 8 shots, and Lisa makes 75% of her shots. What is the difference between the number of baskets made by Danielle and Lisa? 3

Spiral Review 1. 1.2 1 23.7 1 4.8 2.3

2. 0.5 3 (28 3 4.6) 2 18.4

3. 3_4 1 2 1_4 1 2 1_8 2 5_8

4. 24.1 1 3.6 3 1.6 4 23 2 3.38

Lesson Quiz

© Harcourt

1. The Nile River is about 4,160 miles long, which makes it the longest river in the world. The Amazon River is approximately 4,000 miles long. The Mississippi-Missouri-Red Rock River is the longest river in the United States, at about 3,710 miles. What is the difference in length between the Nile and the Mississippi-Missouri-Red Rock rivers? 450 miles 2. Sean works in a shoe store where he earns commission on every pair of shoes that he sells. On Monday, he sold 15 pairs of shoes. On Wednesday, he sold 22 pairs of shoes. On Friday, he sold twice as many pairs of shoes as he did on Monday. On Saturday, he sold twice as many pairs of shoes as he sold on Monday and Wednesday combined. How many pairs of shoes did he sell on Saturday? 74 pairs of shoes

Grade 6

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Unit 5 • Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join.

11

© Harcourt

If the variable m represents the price of renting one movie, what might the expression 5 1 m mean?

Alex and Sasha are making a quilt. They use the pattern shown. What will be the next shape in their pattern?

12

Morgan decorates scarves to sell at festivals. She sells cotton scarves for $12 and wool scarves for $18. She would like to make at least $180 at each fair. What are some different combinations of cotton and wool scarves that she can sell in order to make $180?

13

Grade 6

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Unit 5 • Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join.

11

© Harcourt

If the variable m represents the price of renting one movie, what might the expression 5 1 m mean? Possible answer: The expression might represent a $5.00 fee to join plus the cost, m, of renting one movie.

Alex and Sasha are making a quilt. They use the pattern shown. What will be the next shape in their pattern?

12

Morgan decorates scarves to sell at festivals. She sells cotton scarves for $12 and wool scarves for $18. She would like to make at least $180 at each fair. What are some different combinations of cotton and wool scarves that she can sell in order to make $180? Possible answers: (0,10), (3,8), (6,6), (9,4), (12,2), (15,0)

13

Grade 6

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11.1

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. One video store has no fee to join, but it charges $6 for each movie. What is an algebraic expression for the total cost of renting m movies?

Spiral Review 1. 4 1 8 2 16 5

2. 4 2 8 3 16 5

3. (4 2 8) 3 16 5

4. (4 2 8)2 3 16 5

5. 4 2 8 3 162 1 8 5

6. (4 1 8) 2 16 3 82 5

Lesson Quiz For exercises 1–3, write an algebraic expression for each word expression. 1. the product of 48 and a number 2. 6 less than the product of a number and 9 © Harcourt

3. the square of a number decreased by 17 4. Write a word expression for the following algebraic expression: 8(n 2 7). 5. Jake has d dollars in his pocket. He also has $5.10 in his wallet. Write an algebraic expression for the total amount of money Jake has.

Grade 6

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Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. One video store has no fee to join, but it charges $6 for each movie. What is an algebraic expression for the total cost of renting m movies? 6m

Spiral Review 1. 4 1 8 2 16 5 2 4 3. (4 2 8) 3 16 5 2 64

2. 4 2 8 3 16 5 2 124 4. (4 2 8)2 3 16 5 256

5. 4 2 8 3 162 1 8 52 2,036 6. (4 1 8) 2 16 3 82 5 2 1,012

Lesson Quiz For exercises 1–3, write an algebraic expression for each word expression. 1. the product of 48 and a number 48n 2. 6 less than the product of a number and 9 9n 2 6 © Harcourt

3. the square of a number decreased by 17 n2 2 17 4. Write a word expression for the following algebraic expression: 8(n 2 7). a number decreased by 7 which is then multiplied by 8 5. Jake has d dollars in his pocket. He also has $5.10 in his wallet. Write an algebraic expression for the total amount of money Jake has. 5.10 1 d

Grade 6

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11.2

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 10 1 4m shows the total cost at a store that charges $10 to join and $4 per movie. What is the total cost if Carla joins and rents 5 movies?

Spiral Review 1. Write an algebraic expression for seven more than twice a number n. 2. Write an algebraic expression for seven less than a number n.

Lesson Quiz Simplify each expression. Then evaluate each expression for the given value of the variable. 1. 5r 1 6r 2 2 for r 5 3 2. 7n 2 4n 1 5 for n 5 2

© Harcourt

3. 15 2 2d for d 5 6 4. 2 3 2 1 3x 1 12 for x 5 2 5. Fran plants a garden in the shape of a triangle in a corner of her back yard. The area of the garden is given by the expression 1_2 bh, where b is the base of the triangle and h is the height. If the base is 3 meters and the height is 4 meters, what is the area of the garden in square meters? Grade 6

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Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 10 1 4m shows the total cost at a store that charges $10 to join and $4 per movie. What is the total cost if Carla joins and rents 5 movies? $30

Spiral Review 1. Write an algebraic expression for seven more than twice a number n. 2n 1 7 2. Write an algebraic expression for seven less than a number n. 2n 2 7

Lesson Quiz Simplify each expression. Then evaluate each expression for the given value of the variable. 1. 5r 1 6r 2 2 for r 5 3 11r 2 2 5 11 3 3 2 2 5 31 2. 7n 2 4n 1 5 for n 5 2 3n 1 5 5 3 3 2 1 5 5 11

© Harcourt

3. 15 2 2d for d 5 6 15 1 d 5 15 1 6 5 21 4. 2 3 2 1 3x 1 12 for x 5 2 4 1 3x 1 12 5 3x 1 16 5 3(2) 1 16 5 22 5. Fran plants a garden in the shape of a triangle in a corner of her back yard. The area of the garden is given by the expression 1_2 bh, where b is the base of the triangle and h is the height. If the base is 3 meters and the height is 4 meters, what is the area of the garden in square meters? 1_2 bh 5 1_2 3 3 3 4 5 6 square meters Grade 6

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11.3

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents.Some stores also charge a fee to join. The expression 25 1 3m shows the total cost at a store. What equation could you use to find the number of movies rented if Carla spends $34 at the store?

Spiral Review 1. Write an expression. 5 more than 3 times a number 2. Evaluate 3x 1 4 for x 5 4. 3. Evaluate 3x 1 4 for x 5 6.

Lesson Quiz Write an equation for the word sentence. © Harcourt

1. 30 fewer than x is 10. 2. Three-fourths of y is 15. 3. 10 more than twice a number is 18.

Grade 6

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11.3

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents.Some stores also charge a fee to join. The expression 25 1 3m shows the total cost at a store. What equation could you use to find the number of movies rented if Carla spends $34 at the store? 25 1 3m 5 34

Spiral Review 1. Write an expression. 5 more than 3 times a number 3x 1 5 2. Evaluate 3x 1 4 for x 5 4. 3 3 4 1 4 5 16 3. Evaluate 3x 1 4 for x 5 6. 3 3 6 1 4 5 22

Lesson Quiz Write an equation for the word sentence. © Harcourt

1. 30 fewer than x is 10. x 2 30 5 10 2. Three-fourths of y is 15. 3 _ y 5 15 4 3. 10 more than twice a number is 18. 2n 1 10 5 18

Grade 6

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11.4

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 5 1 m represents the total cost to rent the first movie at a discount video store. Use algebra tiles to model this expression.

Spiral Review Write an algebraic expression for the word expression. 1. 23 more than a number

2. four times the sum of six and a number

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a model. 1. x 1 5 5 14

2. x 1 4 5 12

3. x 2 3 5 7

4. x 2 6 5 15

5. x 1 2 5 2

Grade 6

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11.4

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 5 1 m represents the total cost to rent the first movie at a discount video store. Use algebra tiles to model this expression. one green rectangle and five yellow square tiles

Spiral Review Write an algebraic expression for the word expression. 1. 23 more than a number x 1 23

2. four times the sum of six and a number 4 3 (6 1 n)

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a model. Check students’ models. 1. x 1 5 5 14 9

2. x 1 4 5 12 8

3. x 2 3 5 7 10

4. x 2 6 5 15 21

5. x 1 2 5 2 0

Grade 6

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11.5

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Let f be the joining fee. After two months, Carla has spent $12 on movies. What expression shows the total she has spent on fees and movies? If she has spent $27 total, what equation could you use to find the fee?

Spiral Review 1. Use algebra tiles to model 8 2 4 5 x.

2. Use algebra tiles to model 7 1 x 5 12.

Lesson Quiz © Harcourt

Solve and check. 1. m 1 8 5 27

2. 3 1_2 5 x 1 1

3. 7.2 1 n 5 31

4. d 1 4 5 –11

5. During the last week of August, 1 3_4 inches of rain fell in an area. This made the monthly total 4 inches. How much rain had already fallen?

Grade 6

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11.5

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Let f be the joining fee. After two months, Carla has spent $12 on movies. What expression shows the total she has spent on fees and movies? f 1 12 If she has spent $27 total, what equation could you use to find the fee? f 1 12 5 27

Spiral Review 1. Use algebra tiles to model 8 2 4 5 x. Check students’ models.

2. Use algebra tiles to model 7 1 x 5 12. Check students’ models.

Lesson Quiz © Harcourt

Solve and check. 1. m 1 8 5 27 19

2. 3 1_2 5 x 1 1 2 1_2

3. 7.2 1 n 5 31 23.8

4. d 1 4 5 –11 –15

5. During the last week of August, 1 3_4 inches of rain fell in an area. This made the monthly total 4 inches. How much rain had already fallen? 2 1_4 inches

Grade 6

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11.6

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Since joining the local video store, Carla has spent $18 total and $14 on renting movies. What equation could represent this situation if j represents the joining fee?

Spiral Review If you have one green variable tile and five red tiles on one side of the equation, what do you do to both sides of the equal sign to solve the equation?

Lesson Quiz © Harcourt

Solve and check. 1. n 2 8 5 20

2. 31 5 s 2 8.6

3. p 2 2 5 7

4. d 2 2.4 5 –7.4

5. Kim estimated the hours of homework she has. After completing 1 5_8 hours, she still has 1 _58 hours left. What was her estimate? Grade 6

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11.6

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Since joining the local video store, Carla has spent $18 total and $14 on renting movies. What equation could represent this situation if j represents the joining fee? Possible answer: 18 5 j 1 14

Spiral Review If you have one green variable tile and five red tiles on one side of the equation, what do you do to both sides of the equal sign to solve the equation? You place five yellow tiles on both sides of the equation.

Lesson Quiz © Harcourt

Solve and check. 1. n 2 8 5 20 28

2. 31 5 s 2 8.6 39.6

3. p 2 2 5 7 9

4. d 2 2.4 5 –7.4

2

5

5. Kim estimated the hours of homework she has. After completing 1 58_ hours, she still has 1 5_8 hours left. What was her estimate? 3 1_4 hours Grade 6

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11.7

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The most Carla can spend the first two months is $45. The equation 25 1 4m shows the total cost for a $25 joining fee and m movies at $4 each. Predict how many movies she will be able to rent, and then test your prediction.

Spiral Review Solve and check. 1. t 2 14 5 10

2. 9 1 x 5 22

3. z 2 5.5 5 12

4. j 1 34.3 5 54.2

Lesson Quiz

© Harcourt

1. During the summer, Rafa read 36 books. She read twice as many nonfiction books as fiction books. How many of each did she read? 2. Some children and parents went to a movie. Each child ticket cost $2.75, and each adult ticket cost $3.50. The total cost was $24.25. How many children and how many adults went to the movie?

Grade 6

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11.7

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The most Carla can spend the first two months is $45. The equation 25 1 4m shows the total cost for a $25 joining fee and m movies at $4 each. Predict how many movies she will be able to rent, and then test your prediction. 5 movies; 25 1 4 3 5 5 45

Spiral Review Solve and check. 1. t 2 14 5 10 t 5 24

2. 9 1 x 5 22 x 5 13

3. z 2 5.5 5 12 z 5 17.5

4. j 1 34.3 5 54.2 j 5 19.9

Lesson Quiz

© Harcourt

1. During the summer, Rafa read 36 books. She read twice as many nonfiction books as fiction books. How many of each did she read? 12 fiction books; 24 nonfiction books 2. Some children and parents went to a movie. Each child ticket cost $2.75, and each adult ticket cost $3.50. The total cost was $24.25. How many children and how many adults went to the movie? 5 children and 3 adults

Grade 6

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11.8

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. If one movie rental costs $5.00 and her purchase total is $40, how many movies did Carla rent? Use algebra tiles to model this equation.

Spiral Review Solve and check. 1. x 1 2.5 5 4; x 5

2. 9 5 3.4 1 y ; y 5

3. 4 5 c 2 4; c 5

4. x 2 4.5 5 5; x 5

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a picture. 1. 4m 5 8

2. 7p 5 28

3. 4x 5 40

4. 6r 5 24

5. 42 5 6y Grade 6

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11.8

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. If one movie rental costs $5.00 and her purchase total is $40, how many movies did Carla rent? Use algebra tiles to model this equation. Check students' models of 5r 5 40, r 5 8; 8 movies

Spiral Review Solve and check. 1. x 1 2.5 5 4; x 5 1.5

2. 9 5 3.4 1 y ; y 5 5.6

3. 4 5 c 2 4; c 5 8

4. x 2 4.5 5 5; x 5 9.5

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a picture. Check students’ models. 1. 4m 5 8 m 5 2

2. 7p 5 28 p 5 4

3. 4x 5 40 x 5 10

4. 6r 5 24 r 5 4

5. 42 5 6y y 5 7 Grade 6

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11.9

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The total cost at Store A with no joining fee is given by the expression 8m. Store B also has no joining fee, but it charges half the price of Store A to rent a video. What expression shows the price at Store B?

Spiral Review How do you solve each equation? 1. 10 5 2.5 1 x

2. a 1 3.1 5 8

3. y 2 3 5 2

4. 5 5 c 2 2.4

Lesson Quiz © Harcourt

Solve and check. 1. 7r 5 56

2. 9h_ 5 18

n __ 3. 8 5 21

4. 9.5 5 3.8x

5. Fiona bought 8 notebooks for school. The total cost of the notebooks before tax was $7.84. How much did each notebook cost?

Grade 6

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11.9

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The total cost at Store A with no joining fee is given by the expression 8m. Store B also has no joining fee, but it charges half the price of Store A to rent a video. What expression shows the price at Store B? 8m 4 2, or 4m

Spiral Review How do you solve each equation? 1. 10 5 2.5 1 x Subtract 2.5 from both sides 3. y 2 3 5 2 Add 3 to both sides

2. a 1 3.1 5 8 Subtract 3.1 from both sides 4. 5 5 c 2 2.4 Add 2.4 to both sides

Lesson Quiz © Harcourt

Solve and check. 1. 7r 5 56 r 5 8

2. 9h_ 5 18 h 5 162

n n 5 168 __ 3. 8 5 21

4. 9.5 5 3.8x x 5 2.5

5. Fiona bought 8 notebooks for school. The total cost of the notebooks before tax was $7.84. How much did each notebook cost? $0.98

Grade 6

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Problem of the Day

11.10

Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some charge a fee to join. Carla is charged a fee and the cost of 5 movies. If each movie costs $5 and the total purchase is $29.50, what is the amount of the fee?

Spiral Review Solve and check. y 1. _2 5 18: y 5 ?

2. 32 5 _4c : c 5 ?

3. _2x 5 4.8: x 5 ?

4. 45 5 d 2 15: d 5 ?

© Harcourt

Lesson Quiz 1. Kenny has to leave his house for a soccer game at 4 p.m. Before he leaves he needs to spend 30 minutes doing chores and 1 1_2 hours doing homework. What time should Kenny start his homework or chores? 2. The current temperature outside is 75° F. When Tom woke up the temperature was 25° F less than the current temperature. When Tom went to bed the night before, the temperature was 35° F. How much did the temperature change while Tom was asleep?

Grade 6

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11.10

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some charge a fee to join. Carla is charged a fee and the cost of 5 movies. If each movie costs $5 and the total purchase is $29.50, what is the amount of the fee? $4.50

Spiral Review Solve and check. y 1. _2 5 18: y 5 ? 36

2. 32 5 _4c : c 5 ? 128

3. _2x 5 4.8: x 5 ? 9.6

4. 45 5 d 2 15: d 5 ? 60

© Harcourt

Lesson Quiz 1. Kenny has to leave his house for a soccer game at 4 p.m. Before he leaves he needs to spend 30 minutes doing chores and 1 1_2 hours doing homework. What time should Kenny start his homework or chores? 2 p.m. 2. The current temperature outside is 75° F. When Tom woke up the temperature was 25° F less than the current temperature. When Tom went to bed the night before, the temperature was 35° F. How much did the temperature change while Tom was asleep? 15° F

Grade 6

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12.1

Problem of the Day Alex and Sasha are making a quilt. The first row has 1 blue square, the second row has 3 blue squares, the third row has 5 blue squares, and the fourth row has 7 blue squares. How many more blue squares does each row have compared to the previous row?

27 1 6 5 28 3 2 5 25 3 6 5

Spiral Review

7 2 25 5 224 4 8 5 215 2 3 5

Lesson Quiz Write a rule for the sequence using a variable. Use the rule to find the next term. 1. 1_2 , 1 1_2 , 4 1_2 , 13 1_2 , . . . 2. 500, 100, 20, 4, . . .

© Harcourt

3. 22, 18, 14, 10, . . . 4. 1_2 , 3_4 , 1, 1 1_4 , . . . 5. Justin is training for a triathlon. On Monday he biked 10 miles and on Tuesday he biked 18 miles. On Wednesday, he biked 26 miles and on Thursday he biked 34 miles. If this pattern continues, how many miles will he bike on Saturday? Grade 6

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12.1

Problem of the Day Alex and Sasha are making a quilt. The first row has 1 blue square, the second row has 3 blue squares, the third row has 5 blue squares, and the fourth row has 7 blue squares. How many more blue squares does each row have compared to the previous row? Each row has 2 more blue squares than the previous row.

Spiral Review 27 1 6 5 2 1 28 3 2 5 2 16 25 3 6 5 2 30

7 2 25 5 12 224 4 8 5 2 3 215 2 3 5 2 18

Lesson Quiz Write a rule for the sequence using a variable. Use the rule to find the next term. Rules and terms are given. 1. 1_2 , 1 1_2 , 4 1_2 , 13 1_2 , . . . 3n; 40 1_2 2. 500, 100, 20, 4, . . . n_5 ; _45

© Harcourt

3. 22, 18, 14, 10, . . . n 2 4; 6 4. 1_2 , 3_4 , 1, 1 1_4 , . . . n 1 1_ ; 1 1_ 4 2 5. Justin is training for a triathlon. On Monday he biked 10 miles and on Tuesday he biked 18 miles. On Wednesday, he biked 26 miles and on Thursday he biked 34 miles. If this pattern continues, how many miles will he bike on Saturday? 50 miles Grade 6

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12.2

Problem of the Day Alex and Sasha are making a quilt. The table shows the fabric needed for different numbers of Number of Amount of Quilt Fabric squares. How much fabric is needed to make 6 squares?

Squares

(square inches)

1

4

2

8

3

12

Explain.

Spiral Review 1. Write a rule for the pattern: 2, 4, 6, ... 2. Write a rule for the pattern: 1, 1, 2, 3, 5, 8, ... 3. Write a rule for the nth term: 2, 4, 6, ... 4. Find the next three possible numbers in the pattern: 3, 26, 12, ...

Lesson Quiz Write an equation to represent the function. Then use the equation to find the unknown term.

© Harcourt

1.

3.

j

14

16

k

7

8

f

15

20

25

g

12

17

22

18

20

22

10

11

30

35 32

2.

4.

p

1

2

q

4

6

x

30

50

y

70

3

4

5

10

12

70

90

110

150

190

230

5. It costs $22 per ticket, plus $15 per group of tickets ordered, to attend a play. Write an equation that represents the cost for a group of s people to attend the play. If Melinda purchases 6 tickets at one time, what is the cost? Grade 6

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12.2

Problem of the Day Alex and Sasha are making a quilt. The table shows the fabric needed for different numbers of Number of Amount of Quilt Fabric squares. Squares

(square inches)

1 4 How much fabric 2 8 is needed to 3 12 make 6 squares? Explain. Each square has 4 square inches of fabric. So they will need 4 3 6 5 24 square inches of fabric.

Spiral Review 1. Write a rule for the pattern: 2, 4, 6, ... Add 2 to previous term. 2. Write a rule for the pattern: 1, 1, 2, 3, 5, 8, ... Add the two previous terms to get the term. 3. Write a rule for the nth term: 2, 4, 6, ... n 3 2 4. Find the next three possible numbers in the pattern: 3, 26, 12, ... 2 24, 48, 2 96

Lesson Quiz Write an equation to represent the function. Then use the equation to find the unknown term. Equations and terms are given. 1.

j

14

16

18

20

22

k

7

8

9

10

11

2.

© Harcourt

1

2

3

4

5

q

4

6

8

10

12

50 110

70

90

110

150

190

230

2p + 2 = q

0.5j 5 k 3.

p

f

15

20

25

g

12

17

22

f 2 3 5 g; 27

30 27

35 32

4.

x

30

y

70

2x 1 10 5 y; 110

5. It costs $22 per ticket, plus $15 per group of tickets ordered, to attend a play. Write an equation that represents the cost for a group of s people to attend the play. If Melinda purchases 6 tickets at one time, what is the cost? 15 1 22s 5 t; $147 Grade 6

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12.3

Problem of the Day Alex and Sasha are making a quilt. Four quilt squares in the first row are shown below. Assuming there is a pattern, draw the next two possible squares in the row.

Spiral Review Make a function table to represent the equation. 1. y 5 5x

2. d 5 3 1 r

Lesson Quiz Draw the next two possible figures. 1.

2.

© Harcourt

3. Draw the next possible figure. 4. 5. Alex is designing a wallpaper border for his room. The first 3 squares for the border are shown. Draw the next two squares.

Grade 6

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12.3

Problem of the Day Alex and Sasha are making a quilt. Four quilt squares in the first row are shown below. Assuming there is a pattern, draw the next two possible squares in the row. Possible answer: red

Spiral Review Make a function table to represent the equation. Answers will vary. 1. y 5 5x

2. d 5 3 1 r

Lesson Quiz Draw the next two possible figures. Possible answers are shown. 1.

2.

© Harcourt

3. Draw the next possible figure. 4. 5. Alex is designing a wallpaper border for his room. The first 3 squares for the border are shown. Draw the next two squares.

Grade 6

Daily Transparency DT12.3

12.4

Problem of the Day Alex and Sasha are making a quilt. They have 3 red squares in the first row, 5 red squares in the second row, 7 red squares in the third row, and 9 red squares in the fourth row. If this pattern continues, how many red squares will be in the eight row?

Spiral Review 1.

What is the next possible shape in the pattern?

2.

What are the next two possible shapes in the pattern?

© Harcourt

Lesson Quiz 1. Kira has a set of six bookshelves in her room. She arranged her books so there are 6 books on the top shelf, 11 on the second shelf, 16 on the third, and 21 on the fourth. If the pattern continues, how many books are on the sixth shelf? 2. Find the area of the figure below. 8 ft 19 ft

6 ft

14 ft 19 ft

Grade 6

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12.4

Problem of the Day Alex and Sasha are making a quilt. They have 3 red squares in the first row, 5 red squares in the second row, 7 red squares in the third row, and 9 red squares in the fourth row. If this pattern continues, how many red squares will be in the eight row? 17 red squares

Spiral Review 1.

What is the next possible shape in the pattern?

2.

What are the next two possible shapes in the pattern?

© Harcourt

Lesson Quiz 1. Kira has a set of six bookshelves in her room. She arranged her books so there are 6 books on the top shelf, 11 on the second shelf, 16 on the third, and 21 on the fourth. If the pattern continues, how many books are on the sixth shelf? 31

2. Find the area of the figure below. 262 ft2 8 ft 19 ft

6 ft

14 ft 19 ft

Grade 6

Daily Transparency DT12.4

13.1

Problem of the Day Morgan decorates scarves to sell at festivals. She can finish 10 scarves in one week. Morgan spends at most 40 hours each week decorating scarves. If h represents the number of hours it takes Morgan to finish one scarf, write an inequality to represent this situation.

Spiral Review Marge is designing a pattern for one of her scarves. The first row of knitting is red. The second row is green. The next 2 rows are red. The next 2 rows are green, the next 3 rows are red, and the next 3 rows are green. If she continues alternating red and green, what color will the 25th row of knitting be?

Lesson Quiz 1. Solve and graph the inequality on a number line: 2k $ 36.

2. Solve and graph the inequality on a number line: r 1 15 . 3.

© Harcourt

3. Which of the numerical values, 4, 5, or 6, are solutions to the inequality 7x , 42? 4. Write an inequality for the following word sentence. The value of 6 less than f is more than 20. 5. The sum of the ages of three friends, Casey, Rene, and Ford, is at least 39. Casey is 13 and Rene is 14. Write an inequality that relates the age of Ford, f, to the sum of the ages of the three friends. Then solve the inequality.

Grade 6

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8/30/07 2:52:32 PM

13.1

Problem of the Day Morgan decorates scarves to sell at festivals. She can finish 10 scarves in one week. Morgan spends at most 40 hours each week decorating scarves. If h represents the number of hours it takes Morgan to finish one scarf, write an inequality to represent this situation. 10h # 40; h # 4

Spiral Review Marge is designing a pattern for one of her scarves. The first row of knitting is red. The second row is green. The next 2 rows are red. The next 2 rows are green, the next 3 rows are red, and the next 3 rows are green. If she continues alternating red and green, what color will the 25th row of knitting be? The 25th row will be red.

Lesson Quiz 1. Solve and graph the inequality on a number line: 2k $ 36. k $ 18

17

2. Solve and graph the inequality on a number line: r 1 15 . 3. r . 212

–

© Harcourt

3. Which of the numerical values, 4, 5, or 6, are solutions to the inequality 7x , 42? 4 and 5

13

1

18

19

12

–

2

11

–

3

20 21

8

23

10

–

–

–

4

5

6

7

–

9

22

7

4. Write an inequality for the following word sentence. The value of 6 less than f is more than 20. f 2 6 . 20 5. The sum of the ages of three friends, Casey, Rene, and Ford, is at least 39. Casey is 13 and Rene is 14. Write an inequality that relates the age of Ford, f, to the sum of the ages of the three friends. Then solve the inequality. Possible inequalities: f 1 14 1 13 $ 39 or f 1 27 $ 39; f $ 12

Grade 6

Daily Transparency DT13.1

13.2

Problem of the Day Morgan decorates scarves to sell at y festivals. She embroiders 4 A 2 flowers on the scarves C x B 4 2 0 2 4 in the pattern shown on E 2 D the coordinate plane. 4 Write the ordered pair for each point. –

–

– –

Spiral Review 1. Solve and graph the inequality on a number line. x 1 7 # 13

2. Solve and graph the inequality on a number line. y 2 5 $ 14

Lesson Quiz Write the ordered pair for each point and the quadrant where it is located. y

© Harcourt

2. point B 3. point C 4. point D

A

4

1. point A

B

2 4

–

2

C

0

–

2

4

x

2

–

4

–

D

5. Find the distance between point A and point C. Grade 6

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13.2

Problem of the Day Morgan decorates scarves to sell at y festivals. She embroiders 4 A 2 flowers on the scarves C x B 4 2 0 2 4 in the pattern shown on E 2 D the coordinate plane. 4 Write the ordered pair for each point. A (2 2,2), B (0,0), C (2,2), D (2,2 2), E (2 2,2 2) –

–

– –

Spiral Review 1. Solve and graph 2. Solve and graph the inequality on the inequality on a number line. a number line. x 1 7 # 13 x # 6; y 2 5 $ 14 y $ 19; 1 2 3 4 5 6 7

18 19 20 21 22 23 24

Lesson Quiz Write the ordered pair for each point and the quadrant where it is located. y

© Harcourt

2. point B (4,2) quadrant I 3. point C (2,0); x-axis 4. point D (1,25); quadrant IV

A

4

1. point A (2,4) quadrant I

B

2

x

C 4

–

2

0

–

2

4

2

–

4

–

D

5. Find the distance between point A and point C. 4 units Grade 6

Daily Transparency DT13.2

13.3

Problem of the Day Morgan decorates scarves to sell at festivals. It takes her 5 hours to decorate one scarf. Write ordered pairs to show how many hours it takes her to decorate 1, 2, 3, 4, and 5 of these scarves.

Spiral Review Solve. 1. 3_x 5 3; x 5 j

3. 2x 1 4 5 16; x 5 j

3. 24 5 _3x ; x 5 j

4. 3 5 3x; x 5 j

Lesson Quiz Use the table for questions 1–4. x y

2

2 4

2

1 2

0 0

1 j

2 1

2

1. Write the data as ordered pairs. 2. Graph the function on a coordinate plane. 3. Write an equation relating y to x.

© Harcourt

4. Find the missing value of y. 5. Jim earns $5.00 for each car he washes. Graph his earnings for 1, 2, 3, 4, and 5 cars. Then write a rule for the function.

Grade 6

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13.3

Problem of the Day Morgan decorates scarves to sell at festivals. It takes her 5 hours to decorate one scarf. Write ordered pairs to show how many hours it takes her to decorate 1, 2, 3, 4, and 5 of these scarves. (1,5), (2,10), (3,15), (4,20), (5,25)

Spiral Review Solve. 1. 3_x 5 3; x 5 j 9

3. 2x 1 4 5 16; x 5 j 6

3. 24 5 _3x ; x 5 j 72

4. 3 5 3x; x 5 j 1

Lesson Quiz Use the table for questions 1–4. x y

2 4

2

1 2

2

0 0

1 j

y

2 1

4

2

2

x

1. Write the data as ordered pairs. (–2, 4), (–1,2), (0,0), (1, 2), (2, –1) 2. Graph the function on a coordinate plane.

4

2

–

0

–

2

4

2

–

4

–

3. Write an equation relating y to x. y 5 22x 5. Jim earns $5.00 for each car he washes. Graph his earnings for 1, 2, 3, 4, and 5 cars. Then write a rule for the function. y 5 5x

Amount Earned

© Harcourt

4. Find the missing value of y. 22 $25 $20 $15 $10 $5 0

1

2 3 4

5

Cars Washed

Grade 6

Daily Transparency DT13.3

13.4

Problem of the Day Morgan decorates scarves to sell at festivals. One of her expenses is driving to and from the festivals. The equation d 5 0.25m relates her miles (m) to her driving cost in dollars (d ). Find three ordered pairs that are solutions to this equation.

Spiral Review Solve. 1. 3x 5 18; x 5 ?

2. x_3 5 21; x 5 ?

3. 7 5 x_7 ; x 5 ?

4. 9x 5 27; x 5 ?

Lesson Quiz 1. Which table represents the graph on the coordinate plane? y

A

B x y

0 2 1

1 0

2 1

4

x y

0 2 2

1 0

2 2

2 –

4

–

2

0

2

4

x

2

–

4

–

Graph the equation on a coordinate plane. 3. y 5 23x

4. y = 2x 1 2

© Harcourt

2. y 5 x 2 3

5. The cost for renting a canoe can be shown using the equation c 5 15h 1 10, where h represents the number hours the canoe is rented and c represents the total cost. Graph the equation on a coordinate plane.

Grade 6

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13.4

Problem of the Day Morgan decorates scarves to sell at festivals. One of her expenses is driving to and from the festivals. The equation d 5 0.25m relates her miles (m) to her driving cost in dollars (d ). Find three ordered pairs that are solutions to this equation. Possible answers: (10, 2.50), (20, 5.00), (30, 7.50)

Spiral Review Solve. 1. 3x 5 18; x 5 ? 6

2. x_3 5 21; x 5 ? 63

3. 7 5 x_7 ; x 5 ? 49

4. 9x 5 27; x 5 ? 3

Lesson Quiz 1. Which table represents the graph on the coordinate plane? B y

A

B 0 2 1

x y

1 0

2 1

4

0 2 2

x y

1 0

2

2 2

x –

4

–

2

0 –

–

Graph the equation on a coordinate plane. 2. y 5 x 2 3

3. y 5 23x

8

6

8 6

4

2 6 –4

2 0 – 2

–

© Harcourt

–

4

–

6

–

8

–

2

4

6

x

6 –4

2 0 – 2

–

2

4

6

2

x 6 –4

–

2 0 – 2

–

4

–

6

–

8

–

– –

–

2

4

6

x

4

6 8

5. The cost for renting a canoe can be shown using the equation c 5 15h 1 10, where h represents the number hours the canoe is rented and c represents the total cost. Graph the equation on a coordinate plane.

Grade 6

4

4

2 –

2

y

8 6

4

4

4. y = 2x 1 2

y

y

2

y 40 20

x –

40

–

20

0 –

–

20

40

20

40

Daily Transparency DT13.4

13.5

Problem of the Day Morgan decorates scarves to sell at festivals. One day a week she drives to various stores, picking up supplies at each store. Which graph could be used to represent this situation?

A

B

Spiral Review Graph the equation on a coordinate plane. 1. y 5 3x

2. y 5 24x 2 2

3. y 5 22x 1 1

4. y 5 25x

Lesson Quiz Speed

For 1-3, interpret the graph on the right. 1. Describe the graph.

Time

2. Tell a story about what the graph could possibly show.

© Harcourt

3. Suppose the vertical axis were labeled Altitude. Given this new information, tell a story about what the graph could possibly show.

4. Sketch a graph that could be used to represent the speed of a race car at the beginning of a race, over time, as it travels around an oval track. 5. Ask a question about your graph.

Grade 6

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13.5

Problem of the Day Morgan decorates scarves to sell at festivals. One day a week she drives to various stores, picking up supplies at each store. Which graph could be used to represent this situation? Graph B

A

B

Spiral Review Graph the equation on a coordinate plane. y

y

1. y 5 3x

3

3

1 3

–

2

–

1 0 – 1

–

2. y 5 4x 2 2

2

2

2

x 1

2

3

1 –3 –2 –1 0 – 1

x 1

2

3

2

–

2

–

3

–

3

–

y

3. y 5 22x 1 1

1 3

–

2

–

1 0 – 1

–

y

4. y 5 25x

3 2

3 2 1

x 1

2

3

3

–

2

–

1 0 – 1

–

2

–

3

–

–

–

x 1

2

3

2 3

Lesson Quiz 1. Describe the graph. As time passes, speed remains constant. Then speed rapidly decreases over time to zero. Speed remains at zero for some time and then rapidly increases before Time returning to the previous constant rate. 2. Tell a story about what the graph could possibly show. The graph could show a car trip. The car is traveling at a constant rate of speed until it slows down and comes to a complete stop at a stop light, and then rapidly accelerates from zero back to the same constant speed. 3. Suppose the vertical axis were labeled Altitude. Given this new information, tell a story about what the graph could possibly show. The graph could show a helicopter at a constant altitude, and then descending to ground level while time passes. After sitting on the ground for a time, the helicopter takes off again, gaining altitude, until it levels off to the same constant altitude again. Racing on an Oval Track 4. Sketch a graph that could be used to represent the speed of a race car at the beginning of a race, over time, as it travels around an oval track. 5. Ask a question about your graph. Check students’ work

Grade 6

Speed

© Harcourt

Speed

For 1-3, interpret the graph on the right.

Time

Daily Transparency DT13.5

13.6

Problem of the Day Morgan decorates scarves to sell at festivals. Due to bad weather, she offers a discount today. She will sell each cotton scarf for $10 and each wool scarf for $15. She would like to collect $150 today. Use ordered pairs to show all the possible combinations of scarves she could sell to collect $150 (# of cotton scarves, # of wool scarves).

Spiral Review 1. A bicyclist rides slowly up a hill, stops at the top for a drink of water, and then races down the hill as fast as he can. Draw a line graph to represent his speed.

2. Tell a story about what the graph below could possibly show.

Lesson Quiz 1. What type of graph could you use to help you compare the number of DVRs in homes in Ohio and Missouri over a 5-year period?

© Harcourt

2. The PTSA needs to raise $7,000 to help buy new band uniforms. They are having a plant sale. The plan is to sell pansies for $15 a flat and shrubs for $20 each. What are some different combinations of pansies and flats that they can sell in order to raise $7,000? Make a graph to solve.

Grade 6

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Daily Transparency

DT13.6

8/31/07 9:42:58 AM

13.6

Problem of the Day Morgan decorates scarves to sell at festivals. Due to bad weather, she offers a discount today. She will sell each cotton scarf for $10 and each wool scarf for $15. She would like to collect $150 today. Use ordered pairs to show all the possible combinations of scarves she could sell to collect $150 (# of cotton scarves, # of wool scarves). Possible answers: (0,10), (3,8), (6,6), (9,4), (12,2), (15,0)

Spiral Review 1. A bicyclist rides slowly up a hill, stops at the top for a drink of water, and then races down the hill as fast as he can. Draw a line graph to represent his speed.

2. Tell a story about what the graph below could possibly show. Possible answer: bicyclist is slowing down from a high speed, he speeds up while going down a hill, then slows down and stops.

Lesson Quiz

Shrubs

© Harcourt

1. What type of graph could you use to help you compare the number of DVRs in homes in Ohio and Missouri over a 5-year period? Possible Answer: A double line graph. 2. The PTSA needs to raise $7,000 to help buy new band uniforms. They are having a plant sale. The plan is to Plant Sale sell pansies for $15 a flat and shrubs for 500 $20 each. What are some different 400 combinations of pansies and flats that 300 they can sell in order to raise $7,000? 200 Make a graph to solve. 100 Possible answers: (0,350), (4,347), (8,344), (12,341), (16,338), (20,335), (24,332), (28,329)….(464,2)

Grade 6

0 100 200 300 400 500

Pansies

Daily Transparency DT13.6

© Harcourt

Unit 6 • Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. How many angles are formed from this intersection?

14

Van wants to add a rock garden to his front yard. While he is sketching triangular designs, he notices that the longest side of a triangle always seems to be opposite the greatest angle in the triangle. Draw a diagram to test Van’s conjecture and explain why you agree or disagree with him.

15

Sam has a colored ink pad and some rubber stamps. If his stamp had the figure of a circle on it, how many lines of symmetry would it have?

16

Mrs. Justice has the students in her class work with different types of solid figures. Ginger records the number of faces of three different pyramids. She counts each base as a face.

17

Triangular Base 4 faces

Square Base 5 faces

Pentagonal Base 6 faces

How many faces can she expect to count on a pyramid with an octagonal base?

Grade 6

MXENl09ATE6_U06UDT.indd 1

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DT • Unit 6

8/30/07 2:46:16 PM

© Harcourt

Unit 6 • Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. How many angles are formed from this intersection? Possible answer: 4 angles

14

Van wants to add a rock garden to his front yard. While he is sketching triangular designs, he notices that the longest side of a triangle always seems to be opposite the greatest angle in the triangle. Draw a diagram to test Van’s conjecture and explain why you agree or disagree with him. Students’ diagrams will vary but should support Van’s conjecture.

15

Sam has a colored ink pad and some rubber stamps. If his stamp had the figure of a circle on it, how many lines of symmetry would it have? Endless; any diameter would be a line of symmetry.

16

Mrs. Justice has the students in her class work with different types of solid figures. Ginger records the number of faces of three different pyramids. She counts each base as a face.

17

Triangular Base 4 faces

Square Base 5 faces

Pentagonal Base 6 faces

How many faces can she expect to count on a pyramid with an octagonal base? 9 faces Grade 6

Daily Transparency DT • Unit 6

14.1

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. His friends Brandon, Cally, Danielle, and Ethan each live at a point on one of the two streets. According to the map, which points are NOT on A E the same line as point A, which represents C B where Alvin lives? D

Spiral Review Find the next two figures or terms in the pattern. 1. 2. 2, 4, 8, 16,

Lesson Quiz Name the geometric figure. 1.

J

2.

F

G

K

O

For 3 and 4, use the figure at the right.

© Harcourt

3. Name the figure. 4. Name the line segment.

M P L N

5. Draw a line with points A and B that intersects a line with points C and D at point E.

Grade 6

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14.1

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. His friends Brandon, Cally, Danielle, and Ethan each live at a point on one of the two streets. According to the map, which points are NOT on A E the same line as point A, which represents C B where Alvin lives? D B and E

Spiral Review Find the next two figures or terms in the pattern. 1. 2. 2, 4, 8, 16, 32, 64

Lesson Quiz Name the geometric figure. 1.

J

ray KJ

2.

F

G

K

O

For 3 and 4, use the figure at the right.

© Harcourt

3. Name the figure. plane LMN

M P L

4. Name the line segment. OP or PO 5. Draw a line with points A and B that intersects a line with points C and D at point E.

N D A

E C

Grade 6

line segment FG

B

Daily Transparency DT14.1

14.2

Problem of the Day Alvin draws a map of A the street on which E he lives, as well as an intersecting street. He C B knows that the streets intersect at right angles. D How can he make sure that the streets on his drawing intersect at right angles?

Spiral Review 1. What is the geometric term for an exact location in space? 2. What is the geometric figure that is a part of a line that has one endpoint and extends without end in one direction?

Lesson Quiz Name each angle. Measure it with a protractor. 1.

© Harcourt

B

3.

2. D

A E

C

F

K L

M

Identify the angle as acute, right, obtuse, or straight. 4. 1808

Grade 6

M09ATE6_C014DT.indd 2

5. 958

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14.2

Problem of the Day Alvin draws a map of A the street on which E he lives, as well as an intersecting street. He C B knows that the streets intersect at right angles. D How can he make sure that the streets on his drawing intersect at right angles? He can use a protractor to measure the angle where the streets intersect on the diagram.

Spiral Review 1. What is the geometric term for an exact location in space? point 2. What is the geometric figure that is a part of a line that has one endpoint and extends without end in one direction? ray

Lesson Quiz Name each angle. Measure it with a protractor. 1.

© Harcourt

B

3.

2. D

A C

/ABC, 908

E

F

/ DEF, 408

K L

M

/ KLM, 1458

Identify the angle as acute, right, obtuse, or straight. 4. 1808 straight

Grade 6

5. 958 obtuse

Daily Transparency DT14.2

14.3

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street.

Wilson St. 1 2 Charles St. 4 3

He wants to compare the angles created by the intersection of the streets. Which pairs of angles are congruent?

Spiral Review Identify the angle as acute, right, obtuse, or straight. 1.

2. 42˚

90˚

3.

4. (.'ñ 109˚

Lesson Quiz Use the figure at the right. 1. Name a pair of vertical angles.

2

2. Name two pairs of adjacent angles.

1

5

© Harcourt

3. Name two pairs of supplementary angles. Find the unknown angle measure. 4. 498

Grade 6

M09ATE6_C014DT.indd 3

3 4

5. Two lines intersect so that one angle measure is 73°. What is the measure of the supplementary angle?

Daily Transparency

DT14.3

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14.3

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street.

Wilson St.

Charles St.

1 2 4 3

He wants to compare the angles created by the intersection of the streets. Which pairs of angles are congruent? /1 and /3 are congruent, and /2 and /4 are congruent.

Spiral Review Identify the angle as acute, right, obtuse, or straight. 1.

2. 42˚

acute

3.

90˚

right

4. (.'ñ 109˚

obtuse

obtuse

Lesson Quiz Use the figure at the right.

© Harcourt

1. Name a pair of vertical angles. / 2 and /5 2. Name two pairs of adjacent angles. /1 and /5, /1 and / 2 3. Name two pairs of supplementary angles. Possible answers: /1 and / 2, / 1 and / 5 Find the unknown angle measure. 4. 498

Grade 6

41°

3 4 2

1

5

5. Two lines intersect so that one angle measure is 73°. What is the measure of the supplementary angle? 107° Daily Transparency DT14.3

14.4

Problem of the Day Alvin draws a map of A C the street on which he lives, as well as an S intersecting street. He wants to make sure that his house is located the same distance from the stop sign at the intersection as his friend Charlie’s house. How can he make sure that AS > CS

Spiral Review Find the missing angle measure. 1.

115˚

3.

2. ?

?

50˚

4. ? 72˚ ?

60˚

Lesson Quiz

© Harcourt

For 1–3, use a compass or protractor to determine if the figures are congruent.

1.

2.

3.

4. Find the measure of angle m. m 758

5. A golf ball hits a wall at a 50°angle. At what angle will the golf ball bounce off the wall? Grade 6

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14.4

Problem of the Day Alvin draws a map of A C the street on which he lives, as well as an S intersecting street. He wants to make sure that his house is located the same distance from the stop sign at the intersection as his friend Charlie’s house. How can he make sure that AS > CS Use___ a compass to measure the length of AS; then use the same compass ___ opening to compare it to CS.

Spiral Review Find the missing angle measure. 1.

115˚

2. ?

65˚ 3.

?

50˚

50˚ 4.

? 60˚

72˚ ?

30˚

108˚

Lesson Quiz

© Harcourt

For 1–3, use a compass or protractor to determine if the figures are congruent. 1. 3.

congruent

2.

not congruent

4. Find the measure of angle m. m

308 congruent 5. A golf ball hits a wall at a 50°angle. At what angle will the golf ball bounce off the wall? 50° 758

Grade 6

Daily Transparency DT14.4

14.5

Problem of the Day Alvin draws a map of A the street on which C he lives, as well as an E intersecting street. He then draws another set of intersecting streets. Which two streets are parallel?

G D F H

B

Spiral Review Trace and bisect the figures below. 1.

A

B

2. E

3.

4.

D

F C

Lesson Quiz Trace the figure and bisect it. X

1.

Y

2.

L M

© Harcourt

3.

4.

A

B

C

C

5. Draw a line segment that is 8 cm long, and then bisect it.

Grade 6

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Daily Transparency

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14.5

Problem of the Day Alvin draws a map of A the street on which C he lives, as well as an E intersecting street. He then draws another set of intersecting streets. Which streets are parallel? ___ two ___ 4 CD and EF are parallel

G D F B

H

Spiral Review Trace and bisect the figures below. 1.

A

B

A

B

3.

2. E

E

4.

D D

F

C C

F

Lesson Quiz Trace the figure and bisect it. 1.

X

Y

X

Y

© Harcourt

3.

2.

L M

M

4.

A

B

L

A

C

C B

C

5. Draw a line segment that is 8 cm long, and then bisect it. H

Grade 6

C

J

Daily Transparency DT14.5

14.6

Problem of the Day Alvin draws a map of the street on which he lives, as A well as an intersecting street. B

C

D His friends Brandon, Carla, S and Denise live on his street. Which friend’s house is located halfway between Alvin’s house and the stop sign at the intersection?If she divides the chalkboard into two equal sections, how wide will each section be?

Spiral Review Use a compass or protractor to determine whether the figures are congruent. 1.

2.

3.

4.

Lesson Quiz

© Harcourt

Identify each pair of lines or planes as intersecting, parallel, or perpendicular, or some combination of the three. 1.

2.

3.

4.

5. Draw AB perpendicular to CD. Draw EF parallel to AB. Describe the relationship between CD and EF.

Grade 6

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14.6

Problem of the Day Alvin draws a map of the street on which he lives, as A well as an intersecting street. B

C

D His friends Brandon, Carla, S and Denise live on his street. Which friend’s house is located halfway between Alvin’s house and the stop sign at the intersection?If she divides the chalkboard into two equal sections, how wide will each section be? Carla’s house

Spiral Review Use a compass or protractor to determine whether the figures are congruent. 1.

2. congruent

not congruent 3.

4. congruent

not congruent

Lesson Quiz Identify each pair of lines or planes as intersecting, parallel, or perpendicular, or some combination of the three. 1.

2.

© Harcourt

parallel 3.

perpendicular and intersecting 4. parallel

intersecting 5. Draw AB perpendicular to CD. Draw EF parallel to AB. Describe the relationship between CD and EF. They are perpendicular.

Grade 6

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14.7

Problem of the Day A

Alvin draws a map of the street on which he lives, as well as an intersecting street.

D S B

His friend Danielle lives on the corner of the intersecting street and a street parallel to the one Alvin lives on. He wants to draw a line to represent the street parallel to his. What would his drawing look like?

Spiral Review Identify each pair as parallel, perpendicular, intersecting, or perpendicular and intersecting. 1.

2.

3.

4.

Lesson Quiz Use a compass and straightedge to perform the construction. 1. Construct a line parallel to AB. 2. Construct a line perpendicular to CD.

© Harcourt

A

C

B

D

3. Construct two lines parallel to EF. 4. Construct two lines perpendicular to GH. E

H F

G

5. If you construct a line LM that is perpendicular to the line NO, and then construct a line PQ that is parallel to the line NO, what is the relationship between LM and PQ? Grade 6

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14.7

Problem of the Day A

Alvin draws a map of the street on which he lives, as well as an intersecting street. His friend Danielle lives on the corner of the intersecting street and a street parallel to the one Alvin lives on. He wants to draw a line to represent the street parallel to his. What would his drawing look like?

D S B A D O S B

Spiral Review Identify each pair as parallel, perpendicular, intersecting, or perpendicular and intersecting. 1.

parallel

2.

intersecting

perpendicular 4. intersecting

3.

parallel

Lesson7.6Quiz Use a compass and straightedge to perform the construction. 1. Construct a line parallel to AB. 2. Construct a line perpendicular to CD.

© Harcourt

A

B

A

B

C

X

Y

D

C

O X Y D

3. Construct two lines parallel to EF. 4. Construct two lines perpendicular to GH. E

E F

S F

X T

Y

H G

X

S G T

H Y

5. If you construct a line LM that is perpendicular to the line NO, and then construct a line PQ that is parallel to the line NO, what is the relationship between LM and PQ? LM is perpendicular to NO. Grade 6

Daily Transparency DT14.7

14.8

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. Each point represents a house. He wants to show where his friends live. They all live on his street. Charlie’s house is not the closest or farthest from the intersection. Ethan lives to the left of Danielle. Alvin lives next door to Brandon, who lives in the second house from the intersection. Danielle does not live in the fourth house. Where does everyone live?

Spiral Review Use a compass and a straightedge to make the following constructions. _ ‹

›

1. line parallel to AB A

B

‹_›

2. line perpendicular to EF E F

© Harcourt

Lesson Quiz 1. A class survey was taken about what pets each student had. 13 students had dogs, 11 students had cats, and 8 students had birds. 5 students had dogs and cats, 3 students had dogs and birds, and 4 students had cats and birds. 7 students only had dogs, 4 students only had cats, and 3 students only had birds. 2 students had dogs, cats, and birds. How many students were surveyed? 2. Karin, Monica, Bobby, and Carl participated in a community walkathon to raise money for the chess club. They walked 1.5 mi, 3 mi, 7 mi, and 10 mi. Carl walked twice as far as Karin, and Monica walked 4 more miles than Carl. Who walked the farthest? Grade 6

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Daily Transparency

DT14.8

8/30/07 2:58:27 PM

14.8

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. Each point represents A B C E a house. He wants to show where his friends live. They all live on his street. Charlie’s house is not the closest or farthest from the intersection. Ethan lives to the left of Danielle. Alvin lives next door to Brandon, who lives in the second house from the intersection. Danielle does not live in the fourth house. Where does everyone live?

D

Spiral Review Use a compass and a straightedge to make the following constructions. _ ‹

›

1. line parallel to AB A A

BB

X

Y

‹_›

2. line perpendicular to EF E

E F

X

F

Y

© Harcourt

Lesson Quiz 1. A class survey was taken about what pets each student had. 13 students had dogs, 11 students had cats, and 8 students had birds. 5 students had dogs and cats, 3 students had dogs and birds, and 4 students had cats and birds. 7 students only had dogs, 4 students only had cats, and 3 students only had birds. 2 students had dogs, cats, and birds. How many students were surveyed? 22 students 2. Karin, Monica, Bobby, and Carl participated in a community walkathon to raise money for the chess club. They walked 1.5 mi, 3 mi, 7 mi, and 10 mi. Carl walked twice as far as Karin, and Monica walked 4 more miles than Carl. Who walked the farthest? Bobby Grade 6

Daily Transparency DT14.8

15.1

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several polygons. He would like it to have four sides (a quadrilateral). Name four polygons from which he can choose.

Spiral Review 1. /1 and /2 are supplementary, and /1 and /3 are complementary. If m/1 5 25°, what are the measures of the other angles? 2. /1 is complementary to /3, and /2 and /5 are obtuse. /4 is acute, and m/5 is 6 times m/3. Match the angles to their measures: 60°, 18°, 102°, 108°, 72°.

Lesson Quiz For 1–4, use the figure to name and identify a polygon with the given number of sides. 1. 6 sides © Harcourt

2. 7 sides

K J

3. 9 sides 4. 10 sides

B

A

C L

Q

E

M F

N O

P I

D

G

H

5. Hal draws two polygons. They do not have the same number of sides. He counts 16 vertices. What polygons did Hal draw?

Grade 6

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15.1

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several polygons. He would like it to have four sides (a quadrilateral). Name four polygons from which he can choose. Possible answers: square, rectangle, parallelogram, trapezoid

Spiral Review 1. /1 and /2 are supplementary, and /1 and /3 are complementary. If m/1 5 25°, what are the measures of the other angles? m/2 5 155°, m/3 5 65° 2. /1 is complementary to /3, and /2 and /5 are obtuse. /4 is acute, and m/5 is 6 times m/3. Match the angles to their measures: 60°, 18°, 102°, 108°, 72°. m/1 5 72°, m/2 5 102°, m/3 5 18°, m/4 5 60°, m/5 5 108°

Lesson Quiz For 1–4, use the figure to name and identify a polygon with the given number of sides. Possible answers are given. 1. 6 sides KLMNHQ, hexagon © Harcourt

2. 7 sides DEGNOLM, heptagon

K J

3. 9 sides AEGNOLPQI, nonagon 4. 10 sides AKBDMEFOLI, decagon

B

A

C L

Q

E

M N

F

O

P I

D

H

G

5. Hal draws two polygons. They do not have the same number of sides. He counts 16 vertices. What polygons did Hal draw? Possible answers: heptagon and nonagon; hexagon and decagon

Grade 6

Daily Transparency DT15.1

15.2

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. One shape is a triangle. 978 8 ft

8 ft

Classify the triangle in Van’s sketch. 12 ft

Spiral Review 1. What is the name of a polygon with 7 sides? 2. What is the name of a polygon with 10 sides? 3. What type of polygon has all sides congruent and all angles congruent? 4. What term names a closed plane figure with straight sides that are connected line segments? 5. What is the name of a polygon with 9 sides? 6. What is the name for the point where line segments in a polygon meet?

Lesson Quiz Classify each triangle by its angles and sides. K 8 mm

© Harcourt

J

368

1088

13 mm

2.

8 mm 368

10.3 ft 298

L

3. Find the measure of /B and classify ∆ABC by its angles.

B

618

5 ft

1.

9 ft

?

A

1188

258

C

4. Could the measures 7 cm, 8 cm, and 5 cm be the side lengths of a triangle? Write yes or no. 5. A right triangle has one angle that measures 33°. What are all the angle measures in the triangle. Grade 6

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Daily Transparency

DT15.2

8/30/07 3:00:34 PM

15.2

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. One shape is a triangle. 978 8 ft

Classify the triangle in Van’s sketch. isosceles obtuse

8 ft

12 ft

Spiral Review 1. What is the name of a polygon with 7 sides? heptagon 2. What is the name of a polygon with 10 sides? decagon 3. What type of polygon has all sides congruent and all angles congruent? regular polygon 4. What term names a closed plane figure with straight sides that are connected line segments? polygongon 5. What is the name of a polygon with 9 sides? nonagon 6. What is the name for the point where line segments in a polygon meet? vertex

Lesson Quiz Classify each triangle by its angles and sides. K

1.

© Harcourt

J

1088

2. 368

368 13 mm

10.3 ft

8 mm

618

5 ft

8 mm

298 9 ft

L

obtuse, isosceles 3. Find the measure of /B and classify ∆ABC by its angles. 37°, obtuse, scalene

right, scalene

B ?

A

1188

258

C

4. Could the measures 7 cm, 8 cm, and 5 cm be the side lengths of a triangle? Write yes or no. yes 5. A right triangle has one angle that measures 33°. What are all the angle measures in the triangle. 33°, 90°, and 57° Grade 6

Daily Transparency DT15.2

15.3

Problem of the Day Van wants to add a rock garden to his front yard. He designs a four-sided garden with exactly two parallel sides. One of the parallel sides is 10 feet long and the other is 12 feet long. Draw a figure that matches the description of Van’s design.

Spiral Review What is true about the angles of an isosceles right triangle?

Lesson Quiz Give the most exact name for each figure. 1.

2.

Find the unknown angle measure. © Harcourt

3.

(',

o

.,

(',

4.

.)

o

5. When a diagonal is drawn in a quadrilateral, two congruent right triangles are formed. What shape is the quadrilateral?

Grade 6

M09ATE6_C015DT.indd 3

Daily Transparency

DT15.3

8/30/07 3:00:49 PM

15.3

Problem of the Day Van wants to add a rock garden to his front yard. He designs a four-sided garden with exactly two parallel sides. One of the parallel sides is 10 feet long and the other is 12 feet long. Draw a figure that matches the description of Van’s design. Possible solution: this trapezoid 10 ft has two right angles, but student’s diagram may not 12 ft have right angles.

Spiral Review What is true about the angles of an isosceles right triangle? One angle is a right angle, and the other two angles are congruent to each other.

Lesson Quiz Give the most exact name for each figure. 1.

2. square

trapezoid

Find the unknown angle measure. © Harcourt

3.

(',

o

.,

(',

4.

.)

o

108º 75º 5. When a diagonal is drawn in a quadrilateral, two congruent right triangles are formed. What shape is the quadrilateral? rectangle Grade 6

Daily Transparency DT15.3

15.4

Problem of the Day Van wants to add a rock garden to his front yard. He plans to use cacti in the garden. Van has round, square, and hexagonal containers. He arranges the containers in a pattern. Which shape should the base of the next container have?

Spiral Review 1. Draw an isosceles triangle with one obtuse angle. 2. Draw an isosceles triangle with 3 acute angles.

Lesson Quiz Find a pattern to solve.

© Harcourt

1. Ted shaded all of a triangle. Then he shaded 1_2 of a square and 1_4 of a pentagon. How much of an octagon will he shade? Write a rule for the pattern.

2. If the pattern continues, how many non-square tiles will be painted by the sixth batch? Batch No. No. of tiles painted No. of square tiles

Grade 6

M09ATE6_C015DT.indd 4

1 10 8

2 20 16

3 30 24

Daily Transparency

DT15.4

8/30/07 3:01:00 PM

15.4

Problem of the Day Van wants to add a rock garden to his front yard. He plans to use cacti in the garden. Van has round, square, and hexagonal containers. He arranges the containers in a pattern. Which shape should the base of the next container have? hexagonal

Spiral Review 1. Draw an isosceles triangle with one obtuse angle. Check students’ work. 2. Draw an isosceles triangle with 3 acute angles. Check students’ work.

Lesson Quiz

© Harcourt

Find a pattern to solve. 1. Ted shaded all of a triangle. Then he shaded 1_2 of a square and 1_4 of a pentagon. How much of an octagon will he 1 shade? Write a rule for the pattern. Possible answer: __ 32 ; the fraction used to determine how much to shade is half of the previous shape’s fraction. 2. If the pattern continues, how many non-square tiles will be painted by the sixth batch? 12 Batch No. No. of tiles painted No. of square tiles

Grade 6

1 10 8

2 20 16

3 30 24

Daily Transparency DT15.4

15.5

Problem of the Day Van wants to add a rock garden to his front yard. One of his design sketches shows a scalene right triangle, with the shortest side measuring 7 ft. Use square dot paper to draw a triangle that fits this description.

Spiral Review 1. Jan draws an octagon with 20 diagonals. In the next row he draws 2 octagons, each with 16 diagonals. How many octagons will be in the fourth row? How many diagonals will each octagon have? 2. What is the rule for determining the next brick?

3. What is the rule for the pattern? 8, 3, 7, 2, 6, 1, 5, 0, 4 4. What are the next 2 figures in the pattern? ∆I#0#I∆I#0#

Lesson Quiz Draw the figure. Use square or isometric dot paper.

© Harcourt

1. a quadrilateral with no right angles

2. a right scalene triangle

Complete each statement. 3. An acute scalene triangle must have ______. 4. A regular nonagon must have _______. 5. Ja’Nila drew a polygon. She drew 3 diagonals in the polygon. The diagonals formed 6 equilateral triangles inside the polygon. What polygon did Ja’Nila draw?

Grade 6

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Daily Transparency

DT15.5

8/31/07 9:58:43 AM

15.5

Problem of the Day Van wants to add a rock garden to his front yard. One of his design sketches shows a scalene right triangle, with the shortest side measuring 7 ft. Use square dot paper to draw a triangle that fits this description.

Spiral Review 1. Jan draws an octagon with 20 diagonals. In the next row he draws 2 octagons, each with 16 diagonals. How many octagons will be in the fourth row? How many diagonals will each octagon have? 4; 8 diagonals 2. What is the rule for determining the next brick? Possible answer:every other square brick is black; every third rectangular brick is gray. Bricks alternate in size. 3. What is the rule for the pattern? 8, 3, 7, 2, 6, 1, 5, 0, 4 Possible answer: subtract 5, add 4. 4. What are the next 2 figures in the pattern? ∆ I # 0 # I ∆ I # 0 # star, triangle

Lesson Quiz Draw the figure. Use square or isometric dot paper.

© Harcourt

1. a quadrilateral with no right angles

2. a right scalene triangle

Complete each statement. 3. An acute scalene triangle must have ______. all acute angles and no congruent sides 4. A regular nonagon must have _______. 9 congruent sides and 9 congruent angles 5. Ja’Nila drew a polygon. She drew 3 diagonals in the polygon. The diagonals formed 6 equilateral triangles inside the polygon. What polygon did Ja’Nila draw? regular hexagon

Grade 6

Daily Transparency DT15.5

15.6

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. Van sketches a circle with a diameter of 11 1_2 ft. What is the radius of the circle?

Spiral Review Draw each polygon. 1. regular octagon 2. equilateral triangle 3. nonagon with no congruent sides 4. quadrilateral with one right angle

Lesson Quiz For 1–3, use the circle. Name the given parts of the circle.

F

1. AB

A

2. EF 3. CAD

E

D

B C

4. Find the unknown angle measure.

© Harcourt

1038 618 1248 ? 5. Fabian baked a round birthday cake. He cut it into 10 equal slices. Each slice formed a congruent central angle. What was the measure of each central angle?

Grade 6

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Daily Transparency

DT15.6

8/30/07 3:01:16 PM

15.6

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. Van sketches a circle with a diameter of 11 1_2 ft. What is the radius of the circle? 5 3_4 ft; 5.75 ft

Spiral Review Draw each polygon. Check students’ drawings. 1. regular octagon 2. equilateral triangle 3. nonagon with no congruent sides 4. quadrilateral with one right angle

Lesson Quiz For 1–3, use the circle. Name the given parts of the circle.

F

1. AB radius

A

2. EF chord 3. CAD central angle

E

D

B C

4. Find the unknown angle measure. 72˚

© Harcourt

1038 618 1248 ? 5. Fabian baked a round birthday cake. He cut it into 10 equal slices. Each slice formed a congruent central angle. What was the measure of each central angle? 360˚ 4 10 5 36˚

Grade 6

Daily Transparency DT15.6

15.7

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. He decides to install a circular garden with a 8 ft regular hexagon inside it. What is the length of one side of the hexagon?

Spiral Review 1. What is the radius of a circle with a diameter of 10 in.? 3. What is the name of a line segment with endpoints on the circle?

2. What is the diameter of a circle with a radius of 7 mi? 4. A circle has 4 central angles that measure 130°, 75°, 115°, and m. Find m.

Lesson Quiz 1. Construct a hexagon with 3-inch sides inside a circle. 2. Construct a hexagon inside a circle with a 4-centimeter radius. © Harcourt

3. Construct a hexagon inside a circle with a 6-centimeter radius. 4. Construct a square inside a circle with a 2-inch radius. 5. Construct a square inside a circle with a 5-centimeter radius.

Grade 6

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Daily Transparency

DT15.7

8/30/07 3:01:26 PM

15.7

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. He decides to install a circular garden with a 8 ft regular hexagon inside it. What is the length of one side of the hexagon? 4 ft

Spiral Review 1. What is the radius of a circle with a diameter of 10 in.? 5 in. 3. What is the name of a line segment with endpoints on the circle? chord

2. What is the diameter of a circle with a radius of 7 mi? 14 mi 4. A circle has 4 central angles that measure 130°, 75°, 115°, and m. Find m. m 5 40˚

Lesson Quiz For 1–5, check students’ drawings. 1. Construct a hexagon with 3-inch sides inside a circle. 2. Construct a hexagon inside a circle with a 4-centimeter radius. © Harcourt

3. Construct a hexagon inside a circle with a 6-centimeter radius. 4. Construct a square inside a circle with a 2-inch radius. 5. Construct a square inside a circle with a 5-centimeter radius. Grade 6

Daily Transparency DT15.7

16.1

Problem of the Day Sam has a colored ink pad and some rubber stamps. He prints the two figures shown. Are the figures congruent? Explain.

Spiral Review Complete the given constructions. 1. Construct a hexagon with 4-cm sides inside a circle. 2. Construct a square inside a circle with a 3-cm radius.

Lesson Quiz Tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1.

4 ft

5 ft 3 ft

3.

8 ft

10 ft 6 ft

2. 2 cm

4.

5 cm

2 cm 2 cm 2 cm

3 cm 5 cm

8 cm © Harcourt

3 cm

8 cm

8 cm

10 cm

10 cm 10 cm

5. Pilar’s garden is a rectangle 10 feet long and 8 feet wide. Roy’s

garden is a rectangle 30 feet long and 24 feet wide. Are the two gardens similar, congruent, or neither? Explain.

Grade 6

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Daily Transparency

DT16.1

8/30/07 3:03:18 PM

16.1

Problem of the Day Sam has a colored ink pad and some rubber stamps. He prints the two figures shown. Are the figures congruent? Explain. No, their shapes are the same, but their sizes are different. The figures are similar.

Spiral Review Complete the given constructions. 1. Construct a hexagon with 4-cm sides inside a circle. Check student’s work. 2. Construct a square inside a circle with a 3-cm radius. Check student’s work.

Lesson Quiz Tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1. 4 ft

5 ft

8 ft

10 ft

2. similar

3 ft 6 ft

3. © Harcourt

congruent

2 cm

4.

5 cm

2 cm 2 cm 2 cm

3 cm

neither

8 cm

8 cm

8 cm

10 cm

3 cm 5 cm 10 cm

similar 5. Pilar’s garden is a rectangle 10 feet long and 8 feet wide. Roy’s 10 cm

garden is a rectangle 30 feet long and 24 feet wide. Are the two gardens similar, congruent, or neither? Explain. The gardens are

similar because they have the same shape, but not the same size. The side lengths of Roy’s garden are three times as long as the side lengths of Pilar’s garden. Grade 6

Daily Transparency DT16.1

16.2

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he makes a print with the stamp below, the result is the image shown. Identify the transformation.

MAS SAM Spiral Review Use , or > to tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1.

cm

2 cm 2 cm cm

2 cm 2 cm

2. cm

cm

Lesson Quiz Identify the transformation. Write translation, rotation, or reflection. 2.

3.

4.

© Harcourt

1.

5. Carolyn is designing a mosaic wall mural made of identical tiles. She creates her design by using a transformation that changes the location, but not the orientation of each tile. What transformation does she use?

Grade 6

M09ATE6_C016DT.indd 2

Daily Transparency

DT16.2

8/30/07 3:03:34 PM

16.2

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he makes a print with the stamp below, the result is the image shown. Identify the transformation. Reflection over a vertical line

MAS MAS SAM SAM Spiral Review

Use , or > to tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1.

2 cm cm

2 cm

2.

cm

2 cm

2 cm

cm cm

congruent

similar

Lesson Quiz Identify the transformation. Write translation, rotation, or reflection. 1.

2. rotation

© Harcourt

3.

translation

4. reflection

rotation or reflection

5. Carolyn is designing a mosaic wall mural made of identical tiles. She creates her design by using a transformation that changes the location, but not the orientation of each tile. What transformation does she use? translation

Grade 6

Daily Transparency DT16.2

16.3

Problem of the Day Sam has a colored ink pad and some rubber stamps. One of his stamps makes the print shown below. Make a model to describe the transformation he could use to make a hexagon.

Spiral Review Tell what transformations were made to transform each figure into its next position. 1.

3.

2.

4.

Lesson Quiz Make a model and tell which transformations you could perform to determine if the two figures are congruent. 1.

© Harcourt

2.

4.

5. Ned is using the pattern shown to draw the letter T. Describe how using the strategy make a model can help you determine if he will be able to fit more than one letter T on a rectangular piece of vinyl without wasting any of the material.

Grade 6

M09ATE6_C016DT.indd 3

3.

Daily Transparency

DT16.3

8/30/07 3:03:56 PM

16.3

Problem of the Day Sam has a colored ink pad and some rubber stamps. One of his stamps makes the print shown below. Make a model to describe the transformation he could use to make a hexagon. Possible answer: reflection over a horizontal line at the top of the figure.

Spiral Review Tell what transformations were made to transform each figure into its next position. translation to the right and down 1. 2.

3.

270˚ clockwise rotation or 90˚ counter clockwise rotation

4. reflection about a vertical line

rotation

Lesson Quiz Make a model and tell which transformations you could perform to determine if the two figures are congruent. 1.

3.

congruent; a reflection about a vertical line, or a translation

© Harcourt

2.

congruent; reflection about a vertical line or a translation 4.

congruent; reflection about a vertical line, followed by a 90˚ countercloskwise rotation 5. Ned is using the pattern shown to draw the letter T. Describe how using the strategy make a model can help you determine if he will be able to fit more than one letter T on a rectangular piece of vinyl without wasting any of the material. You could make a model by tracing and cutting out identical copies of the letter T. You could then try to make a rectangle by transforming and rearranging the letters of the model. not congruent

Grade 6

Daily Transparency DT16.3

16.4

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he prints a rectangular stamp on a coordinate plane, the coordinates of the vertices are (21,2), (21,5), (25,2), and (25,5). What are the coordinates of the same rectangular stamp if it is reflected over the x-axis?

Spiral Review Make a model to determine if the two figures are congruent.

Lesson Quiz Graph the transformation of the figure with the given vertices. 1. A(3,3), B(5,3), C(4,4) translation 1 unit down and 2 units right

9 8 7 6 5 4 3 2 1

y

C A

B y

x 1 2 3 4 5 6 7 8 9

2. E(26,24), F(26,0), G(21,24), H(21,0) reflection over the y-axis 3. R(25,4), S(24,1), T(22,3) 90° counterclockwise rotation about the origin

y T

R

F

H

E

G

x

S

© Harcourt

4. W(-5,-2), X(-5,0), Y(-7,-2), Z(-7,0) reflection over the y-axis, followed by a translation 5 units up and 3 units left 5. Hayley is using a coordinate plane to plan a design for a painting. Predict the results if she rotates pentagon ABCDE 90° clockwise about the origin, and then reflects it across the y-axis. Find the coordinates of the figure after the transformations.

y

Z X

y

ED

M09ATE6_C016DT.indd 4

x

YW

AB

Grade 6

x

x C

Daily Transparency

DT16.4

8/30/07 3:04:26 PM

16.4

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he prints a rectangular stamp on a coordinate plane, the coordinates of the vertices are (21,2), (21,5), (25,2), and (25,5). What are the coordinates of the same rectangular stamp if it is reflected over the x-axis? (2 1,22), (2 1,25), (2 5,22), and (2 5,25)

Spiral Review Make a model to determine if the two figures are congruent. not congruent

congruent

congruent

congruent

Lesson Quiz Graph the transformation of the figure with the given vertices. 1. A(3,3), B(5,3), C(4,4) translation 1 unit down and 2 units right A’(5,2), B’(7,2), C’(6,3)

9 8 7 6 5 4 3 2 1

y

C A

A’

B’

y

x

y

3. R(25,4), S(24,1), T(22,3) 90° counterclockwise rotation about the origin R’(24,25), S’(21,24), T’(23,22)

© Harcourt

C’

1 2 3 4 5 6 7 8 9

2. E(26,24), F(26,0), G(21,24), H(21,0) reflection over the y-axis E’(6, 24), F’(6, 0), G’(1, 24), H’(1,0)

F

H F’

H’ x

E

G E’

G’

T

R S

4. W(-5,-2), X(-5,0), Y(-7,-2), Z(-7,0) reflection over the y-axis, followed by a translation 5 units up and 3 units left W’(2,3), X’(2,5), Y’(4,3), Z’(4,5) 5. Hayley is using a coordinate plane to plan a design for a painting. Predict the results if she rotates pentagon ABCDE 90° clockwise about the origin, and then reflects it across the y-axis. Find the coordinates of the figure after the transformations. After the rotation, the pentagon will be in Quadrant III. The reflection across the y-axis will bring it back to Quadrant IV, but with a different orientation. The coordinates of the figure after the transformations are A”(1,-1), B”(1,-2), C”(2,-3), D”(3,-2), E”(3,-1).

Grade 6

B

R’

x T’ S’

y Z’ X’ Y’ W’

Z X

x

YW

y

x

AB ED

C

E’ A’ B’ C’

D’

Daily Transparency DT16.4

16.5

Problem of the Day Sam has a color ink pad and some rubber stamps. He prints the letter H as shown. Does his letter H stamp have line symmetry? If so, draw the lines of symmetry.

Spiral Review Graph the transformation of the figure with the given vertices. 2. A(0,2), B(0,0), C(4,2), 1. X(2,1), Y(3,5), Z(4,1) D(4,0) reflection over translation 3 units down the x-axis and 3 units left 3. Q(22,24), R(22,22), 4. E(23,1), F(21,2), G(21,5) S(24,24), T(24, 22) 90° clockwise rotation reflection over the y-axis

Tell if the figure has line symmetry. If so, draw the lines of symmetry.

© Harcourt

1.

2.

Tell if the figure has rotational symmetry. If so, identify the symmetry as a fraction of a turn and in degrees. 3.

4.

5. Kathy drew a regular polygon with 45° rotational symmetry. What type of polygon did she draw? Grade 6

M09ATE6_C016DT.indd 5

Daily Transparency

DT16.5

8/31/07 9:44:38 AM

16.5

Problem of the Day Sam has a color ink pad and some rubber stamps. He prints the letter H as shown. Does his letter H stamp have line symmetry? If so, draw the lines of symmetry. Sam’s letter H stamp has 2 lines of symmetry as shown.

Spiral Review Graph the transformation of the figure with the given vertices. Check students’ transformations. 2. A(0,2), B(0,0), C(4,2), 1. X(2,1), Y(3,5), Z(4,1) D(4,0) reflection over translation 3 units down the x-axis and 3 units left 2 2 2 2 3. Q( 2, 4), R( 2, 2), 4. E(23,1), F(21,2), G(21,5) S(24,24), T(24, 22) 90° clockwise rotation reflection over the y-axis

Lesson Quiz Tell if the figure has line symmetry. If so, draw the lines of symmetry.

© Harcourt

1.

Yes, the figure 2. has one line of symmetry.

Yes, the figure has two lines of symmetry.

Tell if the figure has rotational symmetry. If so, identify the symmetry as a fraction of a turn and in degrees. 3.

No, the figure does not have rotational symmetry.

4.

Yes, the figure has 1_6 turn, or 60°, rotational symmetry.

5. Kathy drew a regular polygon with 45° rotational symmetry. What type of polygon did she draw? an octagon Grade 6

Daily Transparency DT16.5

17.1

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Maggie has the figure shown at the right. Name the figure.

Spiral Review State how many lines of symmetry the figure has. Then identify the degree of rotational symmetry for the figures that have rotational symmetry. 1.

2.

3. square

4. regular octagon

Lesson Quiz Name the figure. Is it a polyhedron? 2.

3.

4.

© Harcourt

1.

5. Use the words base, lateral faces, and vertex to describe an octagonal pyramid.

Grade 6

M09ATE6_C017DT.indd 1

Daily Transparency

DT17.1

8/30/07 3:12:24 PM

17.1

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Maggie has the figure shown at the right. Name the figure. hexagonal pyramid

Spiral Review State how many lines of symmetry the figure has. Then identify the degree of rotational symmetry for the figures that have rotational symmetry. 1.

5; 72˚

3. square 4; 90˚

1; no rotational symmetry

2.

4. regular octagon 8; 45˚

Lesson Quiz Name the figure. Is it a polyhedron?

© Harcourt

1.

hexagonal pyramid; yes

2.

pentagonal prism; yes

3.

4.

triangular pyramid; yes

cone; no

5. Use the words base, lateral faces, and vertex to describe an octagonal pyramid. Possible answer: An octagonal pyramid has 1 base, which is an octagon. The lateral faces of an octagonal pyramid are triangles. They meet at 1 point, or vertex.

Grade 6

Daily Transparency DT17.1

17.2

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Lyle has drawn from the views shown at the right.

top

front

side

Spiral Review Draw the following figure. Is it a polyhedron? 1. square pramid

2. cylinder

Lesson Quiz Name the solid figure that has the given views. 1.

2. top

front

top

side

front

side

Draw a top view, a front view, and a side view for each solid. 4.

© Harcourt

3.

5. Name a solid figure whose top view is a triangle, front view is a rectangle, and side view is a rectangle.

Grade 6

M09ATE6_C017DT.indd 2

Daily Transparency

DT17.2

8/30/07 3:12:53 PM

17.2

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Lyle has drawn from the views shown at the right. pentagonal prism

top

front

side

Spiral Review Draw the following figure. Is it a polyhedron? Check students’ drawings. 1. square pramid yes 2. cylinder no

Lesson Quiz Name the solid figure that has the given views. 1.

2. top

front

top

side

triangular pyramid

front

cylinder

side

Draw a top view, a front view, and a side view for each solid. 4.

© Harcourt

3.

top

front and side

side

top

front

side

5. Name a solid figure whose top view is a triangle, front view is a rectangle, and side view is a rectangle. triangular prism

Grade 6

Daily Transparency DT17.2

17.3

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Vera can make from the net.

Spiral Review Name the solid figure that has the given views. top

front

top

front

top

front

side side side

Lesson Quiz

© Harcourt

Identify the figure from its net. 1.

2.

3.

4.

5. What shape should be added to the figure at the right so that the result is a net for a triangular prism?

Grade 6

M09ATE6_C017DT.indd 3

Daily Transparency

DT17.3

8/30/07 3:13:14 PM

17.3

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Vera can make from the net. square pyramid

Spiral Review Name the solid figure that has the given views. top

front

top

front

top

front

side side side

cone octagonal pyramid rectangular prism

Lesson Quiz Identify the figure from its net. 2.

1.

hexagonal pyramid

rectangular prism 4.

3.

© Harcourt

triangular pyramid pentagonal prism 5. What shape should be added to the figure at the right so that the result is a net for a triangular prism? rectangle

Grade 6

Daily Transparency DT17.3

17.4

Problem of the Day Mrs. Justice has the students in her class work with different types of prisms. Prism

Vertices (V)

Faces (F)

Octagonal

16

10

Pentagonal

10

V1F2? 5E

Edges (E) 24

Write a formula to find the number of edges of a prism, based on the number of vertices and faces. How many edges does a pentagonal prism have?

Spiral Review Identify the solid figure from its net.

1.

2.

Lesson Quiz 1. Julian draws the top views of three different pyramids and records the number of visible edges on each view. What type of pyramid has a top view with 18 visible edges? Top View

Triangular pyramid

© Harcourt

Number of visible edges

6

Rectangular pyramid

Pentagonal pyramid

8

10

2. Logan draws and cuts out nets for prisms. To make each net, he draws all the faces, then cuts each face out, and finally uses pieces of tape to make the solid figure.

If Logan makes a net for a hexagonal prism, how many pieces of tape must he use to form the prism?

Grade 6

M09ATE6_C017DT.indd 4

Daily Transparency

DT17.4

8/30/07 3:13:51 PM

17.4

Problem of the Day Mrs. Justice has the students in her class work with different types of prisms. Prism

Vertices (V)

Faces (F)

Octagonal

16

10

Pentagonal

10

V1F2? 5E

Edges (E) 24

Write a formula to find the number of edges of a prism, based on the number of vertices and faces. How many edges does a pentagonal prism have? Formula: V 1 F 2 2 5 E; a pentagonal prism has 15 edges.

Spiral Review Identify the solid figure from its net.

1.

2.

triangular pyramid

rectangular prism

Lesson Quiz 1. Julian draws the top views of three different pyramids and records the number of visible edges on each view. What type of pyramid has a top view with 18 visible edges? Top View

© Harcourt

Triangular pyramid

Rectangular pyramid

Pentagonal pyramid

Number of 6 8 10 visible edges a pyramid with a nonagon for a base 2. Logan draws and cuts out nets for prisms. To make each net, he draws all the faces, then cuts each face out, and finally uses pieces of tape to make the solid figure.

If Logan makes a net for a hexagonal prism, how many pieces of tape must he use to form the prism? 18

Grade 6

Daily Transparency DT17.4

© Harcourt

Unit 7 • Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They crossed the finish line at almost the same time. What units might be appropriate for measuring their times?

18

Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. Kirsty knows the sum of the lengths of two adjoining sides of her garden. How can she find the perimeter of the garden? Explain.

19

The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. What is the minimum area of a pool cover for this pool?

20

Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. If the top of the trailer is left open for dumping, what would the surface area of the model trailer be?

21

Grade 6

MXENl09ATE6_U07UDT.indd 1

Daily Transparency

DT • Unit 7

8/30/07 2:46:55 PM

© Harcourt

Unit 7 • Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They crossed the finish line at almost the same time. What units might be appropriate for measuring their times? Possible answer: hours, minutes, and seconds

18

Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. Kirsty knows the sum of the lengths of two adjoining sides of her garden. How can she find the perimeter of the garden? Explain. Possible explanation: Because the sum of the lengths of any two adjoining sides of a rectangle is equal to the sum of the lengths of the other two adjoining sides, Kirsty can multiply the original sum by 2 to find the perimeter.

19

The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. What is the minimum area of a pool cover for this pool? 2,250 ft2

20

Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. If the top of the trailer is left open for dumping, what would the surface area of the model trailer be? A 5 2 3 8 3 5 1 2 3 15 3 5 1 8 3 15 5 350 cm2.

21

Grade 6

Daily Transparency DT • Unit 7

18.1

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The race began at 9:25 A.M. Katie finished at 3:37 P.M. How long did it take Katie to complete the race?

Spiral Review 1. Subtract 4 1_7 from 7 _37

2. Subtract 3 1_3 from 7 _34

3. 5 2 3 2_5 5

4. 6 1_4 2 4 5_6 5

Lesson Quiz Find the elapsed time.

© Harcourt

1. start: 7:37 A.M. end : 11:06 A.M. Find the end time. 3. start: 1:47 P.M. work for 6 hr 21 min

Grade 6

M09ATE6_C018DT.indd 1

2. start: 10:37 A.M. end : 5:15 P.M.

4. start: 9:47 P.M. sleep for 7 hr 45 min

Daily Transparency

DT18.1

8/30/07 3:16:40 PM

18.1

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The race began at 9:25 A.M. Katie finished at 3:37 P.M. How long did it take Katie to complete the race? 6 hr 12 min

Spiral Review 5 __ 1. Subtract 4 1_7 from 7 37_ 3 2_7 2. Subtract 3 1_3 from 7 3_4 4 12

3. 5 2 3 2_5 5 1 3_5

5 4. 6 1_4 2 4 5_6 5 1 __ 12

Lesson Quiz

© Harcourt

Find the elapsed time. 1. start: 7:37 A.M. end : 11:06 A.M. 3 hr 29 min

2. start: 10:37 A.M. end : 5:15 P.M. 6 hr 38 min

Find the end time. 3. start: 1:47 P.M. work for 6 hr 21 min 8:08 P.M. Grade 6

4. start: 9:47 P.M. sleep for 7 hr 45 min 5:32 A.M. Daily Transparency DT18.1

18.2

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Katie got a flat tire only 15 yd from the starting line. How many feet from the starting line did she get a flat tire?

Spiral Review Find the elapsed time. Start time 5:32 A.M. Start time 6:47 A.M. End time 1:45 P.M. End time 3:25 P.M. Elapsed time ____ Elapsed time___

Lesson Quiz © Harcourt

Convert to the given unit. 1. 4 lb 2 oz 5 t oz

2. 45 in. 5 x ft y in.

3. 8 c 5 k qts Compare. Write , or = for each d . 4. 260 sec d 4 min 50 sec

Grade 6

M09ATE6_C018DT.indd 2

5. 13 sq yd d 117 sq ft

Daily Transparency

DT18.2

8/30/07 3:16:44 PM

18.2

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Katie got a flat tire only 15 yd from the starting line. How many feet from the starting line did she get a flat tire? 45 feet

Spiral Review Find the elapsed time. Start time 5:32 A.M. Start time 6:47 A.M. End time 1:45 P.M. End time 3:25 P.M. Elapsed time ____ Elapsed time___ 8 hr 13 min 8 hr 38 min

Lesson Quiz © Harcourt

Convert to the given unit. 1. 4 lb 2 oz 5 t oz 66 oz

2. 45 in. 5 x ft y in. 3 ft 9 in.

3. 8 c 5 k qts 2 Compare. Write , or = for each d . 4. 260 sec d 4 min 50 sec ,

Grade 6

5. 13 sq yd d 117 sq ft 5

Daily Transparency DT18.2

18.3

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They raced 13 km. One kilometer equals 1,000 m. How many meters did they race?

Spiral Review Convert to the given unit. 1. 120 ft 5 x in.

2. 150 oz 5 x lb y oz

3. 3 pt 3 c 5 n c

4. 511 ft 5 r yd s ft

Lesson Quiz © Harcourt

Convert to the given unit. 1. 325 mL 5 j L

2. 4.89 km 5 j m

3. 0.05 g 5 j kg Compare. Write , or 5 for each d. 4. 45,000 dL d 450 cL

Grade 6

M09ATE6_C018DT.indd 3

5. 90.2 g d 9,002 mg

Daily Transparency

DT18.3

8/30/07 3:16:46 PM

18.3

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They raced 13 km. One kilometer equals 1,000 m. How many meters did they race? 13,000 m

Spiral Review Convert to the given unit. 1. 120 ft 5 x in. 1,440 in. 3. 3 pt 3 c 5 n c 9c

2. 150 oz 5 x lb y oz 9 lb 6 oz 4. 511 ft 5 r yd s ft 170 yd 1 ft

Lesson Quiz © Harcourt

Convert to the given unit. 1. 325 mL 5 j L 0.325 L

2. 4.89 km 5 j m 4,890 m

3. 0.05 g 5 j kg 0.00005 kg Compare. Write , or 5 for each d. 4. 45,000 dL d 450 cL .

Grade 6

5. 90.2 g d 9,002 mg .

Daily Transparency DT18.3

18.4

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Erin needed to drink 4 c of liquids per hour during the 3-hour race. She carried 3 pt of water and 2 qt of energy drink. Did Erin carry enough water and energy drink?

pt c

Water 1 2 2 4

Energy Drink qt 1 2 c 4 8

3 6

Spiral Review Convert to the given unit. 1. kg 5 n g 3. 0.41 L 5 y ml

2. 1.3 m 5 x hm 4. 8.7 cm 5 z mm

Lesson Quiz

© Harcourt

Make a model or make a table to solve. 1. Mrs. Cooper has 7 bird feeders to fill. Each bird feeder can hold 1 qt of birdseed. If Mrs. Cooper has a new bag of seed that contains 30 c of seed, will she have enough to fill all the bird feeders? 2. Ms. Smith is conducting an experimental study. The study involves making observations every 90 sec. If the study requires her to do this for 2 hr, about how many times does she make the observations?

Grade 6

M09ATE6_C018DT.indd 4

Daily Transparency

DT18.4

8/30/07 3:16:50 PM

18.4

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Erin needed to drink 4 c of liquids per hour during the 3-hour race. She carried 3 pt of water and 2 qt of energy drink. Did Erin carry enough water and energy drink? Yes, 6 c of water and 8 c of energy drink is more than the 12 c she wanted to drink during the race.

pt c

Water 1 2 2 4

3 6

Energy Drink qt 1 2 c 4 8

Spiral Review Convert to the given unit. 1. kg 5 n g 10,000 2. 1.3 m 5 x hm 0.013 3. 0.41 L 5 y ml 410 4. 8.7 cm 5 z mm 87

Lesson Quiz

© Harcourt

Make a model or make a table to solve. 1. Mrs. Cooper has 7 bird feeders to fill. Each bird feeder can hold 1 qt of birdseed. If Mrs. Cooper has a new bag of seed that contains 30 c of seed, will she have enough to fill all the bird feeders? Check students’ work; Yes, she needs 28 c and has 30c. 2. Ms. Smith is conducting an experimental study. The study involves making observations every 90 sec. If the study requires her to do this for 2 hr, about how many times does she make the observations? Check students’ work; 80 times Grade 6

Daily Transparency DT18.4

18.5

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Each cyclist’s bicycle was weighed before the race to make sure it met race regulations. Which is the more appropriate unit of measure for a bicycle’s mass— milligrams or kilograms?

Spiral Review Convert to the given unit. 1. 71 mg 5 v g

2. 5 lb 6 oz 5 t oz

3. 4.5 L 5 y mL

4. 72 in. 5 t yd

Lesson Quiz Tell which measurement is more precise.

© Harcourt

1. 19 ft or 6 yd

2. 1 km or 980 m

3. 8 hL or 873 L Choose the more appropriate unit of measure 4. the weight of a horse pounds or ounces

Grade 6

M09ATE6_C018DT.indd 5

5. length of a tennis court meters or hectometers

Daily Transparency

DT18.5

8/30/07 3:16:52 PM

18.5

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Each cyclist’s bicycle was weighed before the race to make sure it met race regulations. Which is the more appropriate unit of measure for a bicycle’s mass— milligrams or kilograms? kilograms

Spiral Review Convert to the given unit. 1. 71 mg 5 v g 0.071 3. 4.5 L 5 y mL 4,500

2. 5 lb 6 oz 5 t oz 86 4. 72 in. 5 t yd 2

Lesson Quiz Tell which measurement is more precise.

© Harcourt

1. 19 ft or 6 yd 19 ft

2. 1 km or 980 m 980 m

3. 8 hL or 873 L 873 L Choose the more appropriate unit of measure 4. the weight of a horse pounds or ounces pounds Grade 6

5. length of a tennis court meters or hectometers meters Daily Transparency DT18.5

18.6

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The mass of each cyclist’s bike was measured before the race. Katie estimates that the mass of her bike is 6.5 kg. Its actual mass is 6,495 g to the nearest gram. Which mass is greater, the measurement or the estimate?

Spiral Review 1. Tell which measurement is more 2. Tell which measurement is more precise. 4 yd or 11 ft precise. 650 mL or 1 L 3. Choose the more appropriate 4. Choose the more appropriate unit. unit. Weight of a peanut butter Food for a baby bird: milliliter sandwich: ounces or pounds or liter

© Harcourt

Lesson Quiz 1. Estimate the length of 2 textbooks. 2. Find the actual lengths of 2 textbooks. 3. Compare the estimate and actual lengths of each textbook.

Grade 6

M09ATE6_C018DT.indd 6

Daily Transparency

DT18.6

8/30/07 3:16:55 PM

18.6

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The mass of each cyclist’s bike was measured before the race. Katie estimates that the mass of her bike is 6.5 kg. Its actual mass is 6,495 g to the nearest gram. Which mass is greater, the measurement or the estimate? The estimate is greater.

Spiral Review 1. Tell which measurement is more 2. Tell which measurement is more precise. 4 yd or 11 ft 11 ft precise. 650 mL or 1 L 650 mL 3. Choose the more appropriate 4. Choose the more appropriate unit. unit. Weight of a peanut butter Food for a baby bird: milliliter sandwich: ounces or pounds or liter milliliter ounces

© Harcourt

Lesson Quiz 1. Estimate the length of 2 textbooks. Answers will vary. 2. Find the actual lengths of 2 textbooks. Answers will vary. 3. Compare the estimate and actual lengths of each textbook. Answers will vary.

Grade 6

Daily Transparency DT18.6

19.1

Problem of the Day Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. The length of the garden is 22 ft and the width is 14 ft. What is the perimeter of the garden? 22 ft 14 ft

Spiral Review 1. a. Estimate the lengths in mm of two small objects in your classroom. Record your estimates. b. Measure the lengths of the objects to the nearest millimeter. Record your measurements. c. Use ,, ., or 5 to compare your estimates to the actual measurements. Record your findings.

Lesson Quiz For 1–3, ﬁnd the perimeter. 1.

9 cm

4 cm

© Harcourt

11 cm

2.

3 21 m

3.

5 41 m

4.2 in. 3.8 in.

6.2 in. 6 in. 5.2 in.

4. Look at the ﬁgure below. 26 ft

28 ft

x 17 ft

If the perimeter is 81 ft, what is the length of the unknown side. 5. A rectangle has width w. Its length is 5 less than 3 times its width. Find the perimeter of the rectangle in terms of w.

Grade 6

M09ATE6_C019DT.indd 1

Daily Transparency

DT19.1

8/30/07 2:55:52 PM

19.1

Problem of the Day Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. The length of the garden is 22 ft and the width is 14 ft. What is the perimeter of the garden? The perimeter of the garden is 72 ft. 22 ft 14 ft

Spiral Review 1. a. Estimate the lengths in mm of two small objects in your classroom. Record your estimates. b. Measure the lengths of the objects to the nearest millimeter. Record your measurements. c. Use ,, ., or 5 to compare your estimates to the actual measurements. Record your findings. Check students’ estimates and measurements.

Lesson Quiz For 1–3, find the perimeter. 1.

2.

9 cm

4 cm

24 cm

11 cm

3. 3 21 m 5 41 m

4.2 in.

© Harcourt

6 in.

3.8 in.

17 1_2 m

5.2 in.

25.4 in.

4. Look at the figure below. 26 ft

6.2 in.

28 ft

x 17 ft

If the perimeter is 81 ft, what is the length of the unknown side. 10 ft 5. A rectangle has width w. Its length is 5 less than 3 times its width. Find the perimeter of the rectangle in terms of w. 8w 2 10 5 P

Grade 6

Daily Transparency DT19.1

19.2

Problem of the Day Kirsty has a circular flower bed in her backyard. She wants to know its circumference. Kirsty knows that the diameter of the flower bed is 6 ft.

6 ft

How can Kirsty estimate the circumference of the flower bed?

Spiral Review 1. A rectangle has sides 2. A square has a perimeter 4 cm and 6 cm. What is of 40 in. What is its side its perimeter? length?

Lesson Quiz Use a compass and a ruler to draw each circle with the given radius. Estimate the circumference of each circle using a string and ruler. 1. radius 5 7 cm

2. radius 5 8.5 cm

© Harcourt

Estimate the circumference of each circle. 3.

5.

Grade 6

M09ATE6_C019DT.indd 2

321 m

4. ('dd

+]k

Daily Transparency

DT19.2

8/30/07 2:56:09 PM

19.2

Problem of the Day Kirsty has a circular flower bed in her backyard. She wants to know its circumference. Kirsty knows that the diameter of the flower bed is 6 ft.

6 ft

How can Kirsty estimate the circumference of the flower bed? multiply the diameter by 3

Spiral Review 1. A rectangle has sides 2. A square has a perimeter 4 cm and 6 cm. What is of 40 in. What is its side its perimeter? 20 cm length? 10 in.

Lesson Quiz Use a compass and a ruler to draw each circle with the given radius. Estimate the circumference of each circle using a string and ruler. 1. radius 5 7 cm 42 cm

2. radius 5 8.5 cm 51 cm

© Harcourt

Estimate the circumference of each circle. 3.

5.

Grade 6

321 m

+]k

10 1_ mi 2

4.

('dd

30 mm

24 ft

Daily Transparency DT19.2

19.3

Problem of the Day Kirsty has a circular flower bed in her backyard. The diameter of the flower bed is 6 ft. Kirsty wants to edge the flower bed with stones.

-]k

What is the circumference of the flower bed?

Spiral Review 1. A circle has a diameter of 6 in. Estimate its circumference.

2. A circle has a radius of 6 in. Estimate its circumference.

Lesson Quiz __ for pi. Find the circumference of each circle. Use 3.14 or 22 7

Round to the nearest whole number. 1.

),d

2.

-*(`e%

© Harcourt

__ for pi. Find the diameter of each circle. Use 3.14 or 22 7 Round to the nearest whole number.

3. circumference 5 15.6 ft 4. circumference 5 4 3_4 mi 5. A hamster’s exercise wheel has a radius of 4 inches. How far will the hamster have run after spinning the wheel 4 complete revolutions?

Grade 6

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8/30/07 2:56:52 PM

19.3

Problem of the Day Kirsty has a circular flower bed in her backyard. The diameter of the flower bed is 6 ft. Kirsty wants to edge the flower bed with stones.

-]k

What is the circumference of the flower bed? about 18.8 ft

Spiral Review 1. A circle has a diameter of 6 in. Estimate its circumference. 18 in.

2. A circle has a radius of 6 in. Estimate its circumference. 36 in.

Lesson Quiz __ for pi. Find the circumference of each circle. Use 3.14 or 22 7

Round to the nearest whole number. 1.

),d

about 79 m

2.

-*(`e%

about 40 in.

© Harcourt

__ for pi. Find the diameter of each circle. Use 3.14 or 22 7 Round to the nearest whole number.

3. circumference 5 15.6 ft d is about 5 ft 4. circumference 5 4 3_4 mi d is about 1 mi 5. A hamster’s exercise wheel has a radius of 4 inches. How far will the hamster have run after spinning the wheel 4 complete revolutions? 100.48 inches or about 100 inches

Grade 6

Daily Transparency DT19.3

19.4

Problem of the Day Kirsty has a circular flower bed in her backyard. The radius of the flower bed is 4 ft. Kirsty wants to edge the flower bed with bricks that cost $2 each. How many bricks will she need? Do you have too much or too little information to solve the problem? Explain.

Spiral Review 1. The diameter of a circle is 6 cm. Find the circumference. Use 3.14 for p. 3. The circumference of a circle is 21.98 m. Find the diameter of the circle. Use 3.14 for p.

2. The radius of a circle is 9 m. Find the circumference. Use 3.14 for p. 4. The circumference of a circle is 28.26 m. Find the radius of the circle. Use 3.14 for p.

Lesson Quiz

© Harcourt

Tell whether each problem has too much, too little, or the right amount of information. Then solve the problem if possible, or describe the information needed to solve it. 1. Peter jogs for 45 min three times a week on a circular track. The track has a diameter of 0.1 mi. How far does Peter jog each week? Use 3.14 for π.

2. Kari has a rectangular piece of poster board that is 18 in. by 24 in. She cuts a piece out of the corner that is 10 in. by 12 in. and uses it to mount a photograph. What is the perimeter of the remaining poster board?

Grade 6

M09ATE6_C019DT.indd 4

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8/30/07 2:57:02 PM

19.4

Problem of the Day Kirsty has a circular flower bed in her backyard. The radius of the flower bed is 4 ft. Kirsty wants to edge the flower bed with bricks that cost $2 each. How many bricks will she need? Do you have too much or too little information to solve the problem? Explain. There is too little information to solve the problem. You need to know the size of the bricks to find out how many she will need. There is also irrelevant information: the price of the bricks.

Spiral Review 1. The diameter of a circle is 2. The radius of a circle is 9 m. 6 cm. Find the circumference. Find the circumference. Use Use 3.14 for p. about 18.84 cm 3.14 for p. about 56.52 m 3. The circumference of a circle 4. The circumference of a circle is 21.98 m. Find the diameter is 28.26 m. Find the radius of of the circle. Use 3.14 for p. the circle. Use 3.14 for p. about 7 m about 4.5 m

Lesson Quiz

© Harcourt

Tell whether each problem has too much, too little, or the right amount of information. Then solve the problem if possible, or describe the information needed to solve it. 1. Peter jogs for 45 min three times a week on a circular track. The track has a diameter of 0.1 mi. How far does Peter jog each week? Use 3.14 for π. Not enough information. You would need to know either the rate at which he is jogging or how many times he runs around the track in 45 minutes. 2. Kari has a rectangular piece of poster board that is 18 in. by 24 in. She cuts a piece out of the corner that is 10 in. by 12 in. and uses it to mount a photograph. What is the perimeter of the remaining poster board? The right amount; 84 in.

Grade 6

Daily Transparency DT19.4

20.1

Problem of the Day The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. A flat-roof tarp is suspended above the pool, extending beyond each edge by 1 ft. Estimate the area of the tarp. 75 ft 30 ft Pool Dimensions

Spiral Review 1. Find the perimeter of a rectangle with a length of 4 m and a width of 7 m. 3. Find the side length of a square with a perimeter of 18 in.

2. Find the circumference of a circle with a radius of 7 in. 4. Find the radius of a circle with a circumference of 314 cm.

Lesson Quiz

© Harcourt

For 1-4, estimate the area. 1.

2.

3.

4.

5. Use graph paper to draw a sandtrap on a golf course with an estimated area of 40 sq ft. Grade 6

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20.1

Problem of the Day The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. A flat-roof tarp is suspended above the pool, extending beyond each edge by 1 ft. Estimate the area of the tarp. about 2,400 ft2 75 ft 30 ft Pool Dimensions

Spiral Review 1. Find the perimeter of a rectangle with a length of 4 m and a width of 7 m. 22 m 3. Find the side length of a square with a perimeter of 18 in. 4.5 in.

2. Find the circumference of a circle with a radius of 7 in. about 44 in. 4. Find the radius of a circle with a circumference of 314 cm. about 50 cm

Lesson Quiz

© Harcourt

For 1-4, estimate the area. 1.

25 sq units

2.

3.

about 15 sq units 4.

58.5 sq units

about 54 sq units

5. Use graph paper to draw a sandtrap on a golf course with an estimated area of 40 sq ft. Check students’ drawings. Grade 6

Daily Transparency DT20.1

20.2

Problem of the Day The high school is renovating its swimming pool. Tiles will cover the bottom of the 75 ft by 30 ft pool. They will not cover the logo in the 10 ft by 8 ft center rectangle. Find the area of the pool floor that needs tiles.

Spiral Review Estimate the area of the figure. Each square represents 1 cm2. 1.

2.

Lesson Quiz Find the area for each. 9 ft

1.

2. 7 in.

3 ft

© Harcourt

4 in. 6m

3. 6m

4.

2m 5m

5. Paula is making a triangular ﬂag that will have base of 3_4 yd and a height of 1 yd. How many square yards of fabric does she need to make the ﬂag? Grade 6

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8/30/07 3:12:05 PM

20.2

Problem of the Day The high school is renovating its swimming pool. Tiles will cover the bottom of the 75 ft by 30 ft pool. They will not cover the logo in the 10 ft by 8 ft center rectangle. Find the area of the pool floor that needs tiles. 2,250 ft2 2 80 ft2 2 2,170 ft2.

Spiral Review Estimate the area of the figure. Each square represents 1 cm2. 1.

2.

9 cm2

17 cm2

Lesson Quiz Find the area for each. 1.

2.

9 ft

7 in.

3 ft

© Harcourt

27 ft2

4 in.

6m

3.

4.

6m

36 m2

14 in.2

2m 5m

10 cm2

5. Paula is making a triangular flag that will have base of 3_4 yd and a height of 1 yd. How many square yards of fabric does she need to make the flag? 3_8 yd2 Grade 6

Daily Transparency DT20.2

20.3

Problem of the Day The high school is renovating its swimming pool. One of the banners from a swim competition is the shape of a trapezoid. Use graph paper and find the trapezoid’s area by counting the squares. ()Zd (*Zd

()Zd

(*Zd

))Zd

Spiral Review Triangle: b 5 18 cm, h 5 10 cm, A 5 ? Triangle: b 5 12.5 cm, h 5 ? cm, A 5 37.5 cm2

Lesson Quiz Find the area. )'`e%

1.

,d

2.

(,`e% ('`e%

0d

.d (-%*d

3.

4. )-%,]k

(/]

0%)Zd *Zd

© Harcourt

()]k

5. The city’s convention center has built a new auditorium for concerts. The stage is 52 feet from front to back. The front length of the stage measures 100 feet. The back length measures 76 feet. What is the area of the stage?

Grade 6

M09ATE6_C020DT.indd 3

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8/30/07 3:12:21 PM

20.3

Problem of the Day The high school is renovating its swimming pool. One of the banners from a swim competition is the shape of a trapezoid. Use graph paper and find the trapezoid’s area by counting the squares. 209 cm2 ()Zd (*Zd

()Zd

(*Zd

))Zd

Spiral Review Triangle: b 5 18 cm, h 5 10 cm, A 5 ? 90 cm2 Triangle: b 5 12.5 cm, h 5 ? cm, A 5 37.5 cm2 6

Lesson Quiz Find the area. )'`e%

1.

(,`e% ('`e%

,d

2. 0d

200 in2

.d

74.55 m2

(-%*d

3.

4. )-%,]k

© Harcourt

()]k

(/]k267

ft2

0%)Zd *Zd

27.6 cm2

5. The city’s convention center has built a new auditorium for concerts. The stage is 52 feet from front to back. The front length of the stage measures 100 feet. The back length measures 76 feet. What is the area of the stage? 4,576 ft2

Grade 6

Daily Transparency DT20.3

20.4

Problem of the Day The high school is renovating its swimming pool. A rectangular whirlpool with a length of 6 ft and a width of 5 ft will be installed next to the pool. Describe a rectangle that has the same perimeter but a different area.

Spiral Review Find the areas of the figures below. 1.

2. 5m

4m

3 in.

6m

2 in. 2 in. 6 in.

3 in.

Lesson Quiz 1. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same area but a different perimeter.

2. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same perimeter but a different area. 9 cm

2 ft

4 cm

© Harcourt

6 ft

3. For each figure, find the perimeter and area. Double the dimensions and sketch a new figure, then find the new perimeter and area.

5 in.

7m 7m

Grade 6

M09ATE6_C020DT.indd 4

4. What’s the Error? Ben said doubling the side lengths and height of angle will double the perimeter and area.

4 in.

5 in.

6 in.

Daily Transparency

DT20.4

8/30/07 3:12:36 PM

20.4

Problem of the Day The high school is renovating its swimming pool. A rectangular whirlpool with a length of 6 ft and a width of 5 ft will be installed next to the pool. Describe a rectangle that has the same perimeter but a different area. Possible answer: The original whirlpool has a perimeter of 22 ft and an area of 30 ft2. A whirlpool with a length of 7 ft and a width of 4 ft also has a perimeter of 22 ft, but an area of 28 ft2.

Spiral Review Find the areas of the figures below. 1.

2. 5m

4m

3 in.

6m

2 in. 2 in. 6 in.

3 in.

24 m2

8 in.2

Lesson Quiz 1. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same area but a different perimeter. 16 ft; 12 ft2

9 cm

3 ft

2 ft 6 ft

© Harcourt

2. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same perimeter but a different area. 26 cm; 36 cm2 4 cm

4 ft

3. For each figure, find the perimeter and area. Double the dimensions and sketch a new figure, then find the new perimeter and area. 28 cm; 49 cm2 14 m

6 ft

4. What’s the Error? Ben said doubling the side lengths and height of angle will double the perimeter and area. 16 in.; 12 in.2 5 in.

7m

5 in. 4 in.

7m

7 ft

14 m

10 in.

10 in. 8 in.

6 in. 12 in.

Grade 6

Daily Transparency DT20.4

20.5

Problem of the Day The high school is renovating its swimming pool. The seat cushions on the chairs by the pool will be covered with material that has the school’s intials. To find the area of the material, the circumference 9 in. of the cushion is traced on graph paper. Estimate the area of the circle.

Spiral Review Find the perimeter and area of a rectangle that has a length of 4 cm and a width of 8 cm. Then describe another rectangle that has the same area but a different perimeter.

Lesson Quiz Find the area of a circle with the given radius. Use 3.14 for π. © Harcourt

1. r 5 3 ft

2. r 5 0.6 m

3. r 5 12 mm __ for π. Find the area of a circle with the given radius. Use 22 7

4. r 5 7_8 in. 5. r 5 14 cm

Grade 6

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8/30/07 3:12:56 PM

20.5

Problem of the Day The high school is renovating its swimming pool. The seat cushions on the chairs by the pool will be covered with material that has the school’s intials. To find the area of the material, the circumference 9 in. of the cushion is traced on graph paper. Estimate the area of the circle. about 250 in2

Spiral Review Find the perimeter and area of a rectangle that has a length of 4 cm and a width of 8 cm. Then describe another rectangle that has the same area but a different perimeter. P 5 24 cm, A 5 32 cm2; Possible answer: l 5 16 cm, w 5 2 cm.

Lesson Quiz Find the area of a circle with the given radius. Use 3.14 for π. © Harcourt

1. r 5 3 ft 28.26 ft2

2. r 5 0.6 m 1.1304 m2

3. r 5 12 mm 452.16 mm2 __ for π. Find the area of a circle with the given radius. Use 22 7 13 __ in.2 4. r 5 7_8 in. 2 32

5. r 5 14 cm 616 cm2

Grade 6

Daily Transparency DT20.5

20.6

Problem of the Day The high school is renovating its swimming pool. The pool will be lighted from within the pool with circular lights. A flat circular light has a diameter of 12 in. What is the area of the light’s surface?

Spiral Review 1. Radius of circle 5 10 cm. Diameter 5 _____? 2. Diameter of circle 5 6 in. Radius 5 _____?

Lesson Quiz Find the area of each circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

2.

-%,`e%

()bd

Find the area of each partial circle to the nearest __ for p. whole number. Use 3.14 or 22 7

© Harcourt

1 circle __ 3. 10

4. 54_ circle

((dd

5. Mr. Kim has a sprinkler system in his front yard. The sprinkler at the corner of the yard covers 1 _ of a circle with a radius of 14 feet. What is the 4 area watered by the sprinkler?

Grade 6

M09ATE6_C020DT.indd 6

()bd

Daily Transparency

DT20.6

8/30/07 3:13:02 PM

20.6

Problem of the Day The high school is renovating its swimming pool. The pool will be lighted from within the pool with circular lights. A flat circular light has a diameter of 12 in. What is the area of the light’s surface? 113 sq in.

Spiral Review cm 1. Radius of circle 5 10 cm. Diameter 5 20 _____? 3 cm 2. Diameter of circle 5 6 in. Radius 5 _____?

Lesson Quiz Find the area of each circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

-%,`e%

2.

133 in.2

113 km2

()bd

Find the area of each partial circle to the nearest __ for p. whole number. Use 3.14 or 22 7

© Harcourt

1 circle __ 3. 10

()bd

45 km2

4. 54_ circle

((dd

304 mm2

5. Mr. Kim has a sprinkler system in his front yard. The sprinkler at the corner of the yard covers 1 _ of a circle with a radius of 14 feet. What is the 4 area watered by the sprinkler? A 5 1_4 p 142 5 49p , 154 ft2 Grade 6

Daily Transparency DT20.6

20.7

Problem of the Day The high school 12 ft is renovating its swimming pool. A locker room will be built according to the 5 ft floor plan shown. All angles are right angles. 5 ft What is the area of the locker room?

5 ft

Spiral Review Find the area of the circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

2. 1 in.

14 cm

Lesson Quiz 1. Rashid is cleaning a ﬂoor with the dimensions as shown. How many square yards of ﬂoor must be cleaned? 10 yd

6 yd

© Harcourt

16 yd

4 yd

2. Liz is painting a wall with the door and window opening as shown. How many square feet of paint will she need to cover the surface of the wall? 22 ft 4 ft 6 ft

Grade 6

M09ATE6_C020DT.indd 7

4 ft 4 ft

10 ft

Daily Transparency

DT20.7

8/30/07 3:13:14 PM

20.7

Problem of the Day The high school 12 ft is renovating its 5 ft swimming pool. A locker room will be built according to the 5 ft floor plan shown. All angles are right angles. 5 ft What is the area of the locker room? 85 ft2

Spiral Review Find the area of the circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

2. 1 in.

14 cm

about 3 in.2

about 154 cm2

Lesson Quiz 1. Rashid is cleaning a floor with the dimensions as shown. How many square yards of floor must be cleaned? 112 yd2 10 yd

6 yd

4 yd

© Harcourt

16 yd

2. Liz is painting a wall with the door and window opening as shown. How many square feet of paint will she need to cover the surface of the wall? 180ft2 22 ft 4 ft 6 ft

Grade 6

4 ft 4 ft

10 ft

Daily Transparency DT20.7

21.1

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the total area of the model’s surface.

,Zd /Zd (,Zd

Spiral Review 1. Parallelogram: base 5 18 in., height 5 9 in., A5? 2. Parallelogram: Area 5 72 in.2, base 5 12 in., height 5 ?

Lesson Quiz Find the surface area of each figure. Use 3.14 for p. 1.

2. -`e%

.%,Zd .%,Zd

© Harcourt

3.

5 cm 7 cm

()`e%

.%,Zd 13 cm

/`e%

,d

4. ()d

4 cm 15 cm

5. The length of a rectangular prism is three times the width. The height is half the width. The length is 12 meters. Find the dimensions and surface area of the prism.

Grade 6

M09ATE6_C021DT.indd 1

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8/30/07 3:10:12 PM

21.1

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the total area of the model’s surface. 470 cm2 ,Zd /Zd

(,Zd

Spiral Review 1. Parallelogram: base 5 18 in., height 5 9 in., A 5 ? 162 in.2 2. Parallelogram: Area 5 72 in.2, base 5 12 in., height 5 ? 6 in.

Lesson Quiz Find the surface area of each figure. Use 3.14 for p. 1.

337.5 cm2

© Harcourt

7 cm

()`e%

.%,Zd

.%,Zd 5 cm

432 in.2

-`e%

.%,Zd

3.

2.

,d

4.

13 cm

/`e%

()d 4 cm 15 cm

291 cm

2

533.8 m2

5. The length of a rectangular prism is three times the width. The height is half the width. The length is 12 meters. Find the dimensions and surface area of the prism. l = 12 m, w = 4 m, h = 2 m; S = 160 m2

Grade 6

Daily Transparency DT21.1

21.2

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the quantity represented by multiplying the length 3 the width 3 the height. What does this quantity represent?

,Zd /Zd (,Zd

Spiral Review 1. The surface area of a cube is _____ times the area of one face. 2. Rectangular prism: / 5 12 in., w 5 10 in., h 5 8 in.; surface area 5 ?

Lesson Quiz Find the volume of each figure. 1.

2. .Zd

© Harcourt

(,Zd 6.9 ft

3.

7.4 ft

5.3 ft

.%)`e% 0%,`e%

/Zd

4.

.%)Zd

*%+`e%

('%+Zd

+%)Zd

5. Concrete is sold by the cubic yard. How many cubic yards of concrete would you need for a patio that is 9 yards by 5.3 yards by 0.16 yard?

Grade 6

M09ATE6_C021DT.indd 2

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DT21.2

8/30/07 3:10:26 PM

21.2

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the quantity represented by multiplying the length 3 the width 3 the height. What does this quantity represent? 600 cm3; this represents the volume of the model.

,Zd /Zd

(,Zd

Spiral Review 1. The surface area of a cube is _____ times the area of one face. 6 2. Rectangular prism: / 5 12 in., w 5 10 in., h 5 8 in.; surface area 5 ? 592 in.2

Lesson Quiz Find the volume of each figure. 1.

840 cm

3

.Zd

© Harcourt

(,Zd

3.

6.9 ft 7.4 ft

2.

.%)`e% 0%,`e%

/Zd

5.3 ft

135.309 ft3

232.56 in.3

4.

.%)Zd

+%)Zd

*%+`e%

('%+Zd

157.248 cm3

5. Concrete is sold by the cubic yard. How many cubic yards of concrete would you need for a patio that is 9 yards by 5.3 yards by 0.16 yard? 7.632 yd3

Grade 6

Daily Transparency DT21.2

21.3

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The model trailer is 15 cm long by 8 cm wide by 5 cm high and has a model of a cylinder-shaped water cooler attached to its rear door. If the radius of the model cooler is 0.5 cm and its height is 1 cm, how can you find the volume of the model cooler?

Spiral Review 1. Rectangular prism: / 5 10 in., w 5 10 in., h 5 8 in., Volume 5 ? 2. Rectangular prism: V 5 640 cm3, w 5 8 cm, / 5 8 cm, h 5 ?

Lesson Quiz For 1–2, use the rectangles to model a cylinder. Estimate the volume of each cylinder. 1.

-Zd

2.

,Zd

((Zd

(/Zd

.]k

,d

3.

4.

© Harcourt

))]k )*d /Zd

5. 0Zd

Grade 6

M09ATE6_C021DT.indd 3

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DT21.3

8/30/07 3:10:39 PM

21.3

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The model trailer is 15 cm long by 8 cm wide by 5 cm high and has a model of a cylinder-shaped water cooler attached to its rear door. If the radius of the model cooler is 0.5 cm and its height is 1 cm, how can you find the volume of the model cooler? You can multiply 0.5 3 0.5 3 3.14 3 1.

Spiral Review 1. Rectangular prism: / 5 10 in., w 5 10 in., h 5 8 in., Volume 5 ? 800 in.3 2. Rectangular prism: V 5 640 cm3, w 5 8 cm, / 5 8 cm, h 5 ? 10 cm

Lesson Quiz For 1–2, use the rectangles to model a cylinder. Estimate the volume of each cylinder. Possible answers shown. 1.

2.

-Zd

(/Zd

about 58 cm3

((Zd .]k

3.

4.

© Harcourt

))]k

,Zd

about 3,385 ft3

/Zd

about 130 cm3

,d

)*d

about 1,805 m3

5. 0Zd

about 1,809 cm3

Grade 6

Daily Transparency DT21.3

21.4

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The container on the back of the transport truck is in the shape of a cylinder. The cylinder is 15 cm long, and the circular bases each have a radius of 8 cm. Find the area of one of the circular bases of the cylinder, and then multiply it by the length of the cylinder. What does this quantity represent?

Spiral Review Estimate the volume of a cylinder with a height of 10 cm and a radius of 5 cm.

Lesson Quiz Find the volume of each figure. Use 3.14 for pi. Round to the nearest unit3. .`e%

1.

2.

(+Zd

(*`e% *,Zd

3.

(.%,]k

4.

© Harcourt

*%,]k

)(%*Zd (/%0Zd

5. An outside cylinder has a radius of 5.7 m. The space between the inside and outside cylinders is 1.2 m. The height of both cylinders is 8.3 m. Calculate the volume of the inside cylinder.

Grade 6

M09ATE6_C021DT.indd 4

Daily Transparency

DT21.4

8/30/07 3:10:50 PM

21.4

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The container on the back of the transport truck is in the shape of a cylinder. The cylinder is 15 cm long, and the circular bases each have a radius of 8 cm. Find the area of one of the circular bases of the cylinder, and then multiply it by the length of the cylinder. What does this quantity represent? 200.96 cm2; 3,014.4 cm3; this represents the volume of the cylinder.

Spiral Review Estimate the volume of a cylinder with a height of 10 cm and a radius of 5 cm. V 5 about 3 3 5 3 5 3 10 5 about 750 cm3

Lesson Quiz Find the volume of each figure. Use 3.14 for pi. Round to the nearest unit3. .`e%

1.

2.

(+Zd

(*`e% *,Zd

2,000 in.3

© Harcourt

3.

(.%,]k

4.

*%,]k

841 ft

3

21,540 cm3

)(%*Zd (/%0Zd

6,731 cm3

5. An outside cylinder has a radius of 5.7 m. The space between the inside and outside cylinders is 1.2 m. The height of both cylinders is 8.3 m. Calculate the volume of the inside cylinder. 528 m3

Grade 6

Daily Transparency DT21.4

21.5

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. He needs to find out how much metal he needs to make the trailer. Which measure should he use to solve this problem?

Spiral Review 1. A cylinder has a radius of 7 in. and a height of 10 in. What is the volume?

2. A cylinder has a diameter of 6 m and a height of 6 m. What is its volume?

3. A cylinder has a radius of 12 ft and a volume of 45,216 ft3. What is the height?

4. A cylinder has a diameter of 20 cm and a volume of 12,560 cm3. What is the height?

Lesson Quiz

© Harcourt

Tell which measure, perimeter, area, surface area, or volume you will use to solve the problem. Then solve the problem. 1. Hallie was selling her homemade hand cream in cylindrical jars. If a jar is 4 in. high with a radius of 4 in., what is the maximum area of the label that can go around the jar?

2. Danielle is making and packaging potpourri to sell. If the box, that will hold the potpourri, is 10 cm by 8 cm by 6 cm, about how much potpourri can she place in the box?

Grade 6

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Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. He needs to find out how much metal he needs to make the trailer. Which measure should he use to solve this problem? surface area

Spiral Review 1. A cylinder has a radius of 7 in. and a height of 10 in. What is the volume? about 1,539 in.3

2. A cylinder has a diameter of 6 m and a height of 6 m. What is its volume? about 169.56 m3

3. A cylinder has a radius of 12 ft and a volume of 45,216 ft3. What is the height? about 100 ft

4. A cylinder has a diameter of 20 cm and a volume of 12,560 cm3. What is the height? about 40 cm

Lesson Quiz

© Harcourt

Tell which measure, perimeter, area, surface area, or volume you will use to solve the problem. Then solve the problem. 1. Hallie was selling her homemade hand cream in cylindrical jars. If a jar is 4 in. high with a radius of 4 in., what is the maximum area of the label that can go around the jar? surface area; about 100.48 in.2 2. Danielle is making and packaging potpourri to sell. If the box, that will hold the potpourri, is 10 cm by 8 cm by 6 cm, about how much potpourri can she place in the box? volume; 480 cm3

Grade 6

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Unit 8 • Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles.

22

The family has traveled 325 mi in 5 hr. What is a ratio that can be used to describe how fast the Edwards family is driving?

The middle school Ski Club plans ski trips and participates in ski competitions.

23

© Harcourt

If 80% of the club members participated in the last competition, what fraction of the club participated?

Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equalsized marbles. The bag contains 3 blue marbles, 7 red marbles, and 2 green marbles. In simplest terms, what is the ratio of the green marbles to all marbles in the bag?

Grade 6

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Unit 8 • Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles.

22

The family has traveled 325 mi in 5 hr. What is a ratio that can be used to describe how fast the ___ , or 65 __ Edwards family is driving? 325 5 1

The middle school Ski Club plans ski trips and participates in ski competitions.

23

If 80% of the club members participated in the last competition, what fraction of the club participated? 80 5 4 ____ __ of the members participated

© Harcourt

100

5

Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equalsized marbles. The bag contains 3 blue marbles, 7 red marbles, and 2 green marbles. In simplest terms, what is the ratio of the green marbles to all marbles 2 1 _ in the bag? __ 12 5 6 , or 1:6, or 1 out of 6 marbles

Grade 6

24

Daily Transparency DT • Unit 8

22.1

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. They have traveled 325 mi in 5 hr. What is the average speed (unit rate) at which the Edwards family is driving?

Spiral Review Complete each number sentence. j 2 5 __ 1. __ 24 12

7 __ 5 __ 2. 14 j 26

5 __ 3. __ 5 15 j 45

10 j 5 __ 4. __ 6 48

Lesson Quiz Write three equivalent ratios.

© Harcourt

32 1. __ 24

6 2. __ 10

3. Write the following ratio in fraction form and then find the unit rate. 240 words in 3 minutes 4. Compare unit rates. Write . 250 mi in 5 hr j 80 mi in 2 hr 5. Gloria rode her bike 16 mi in 2 hr. At the same rate how long will it take her to ride 44 mi? Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. They have traveled 325 mi in 5 hr. What is the average speed (unit rate) at which the Edwards family is driving? 65 mi per hour

Spiral Review Complete each number sentence. j 2 5 __ 1. __ 24 4 12

7 __ 5 __ 2. 14 13 j 26

5 __ 15 3. __ 5 15 j 45

__ j 5 10 4. __ 6 80 48

Lesson Quiz Write three equivalent ratios. Possible answers given.

© Harcourt

32 1. __ 24

16 _ __ , 8 , 4_ 2 6 3

6 __ 2. 10

18 3 24 , __ __ ,_ 40 30 5

3. Write the following ratio in fraction form and then find the unit rate. 240 words in 3 minutes 240 ___ ; 80 words per min. 3 4. Compare unit rates. Write . 250 mi in 5 hr j 80 mi in 2 hr . 5. Gloria rode her bike 16 mi in 2 hr. At the same rate how long will it take her to ride 44 mi? 5.5 hr Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. On the first 5 day Ben drove __ of the distance to 15 Raleigh and on the second day Laura __ of the distance. Determine drove 15 30 whether Ben and Laura drove the same distance.

Spiral Review Write two equivalent ratios. 14 1. __ 28

20 2. __ 25

Determine whether the ratios are equivalent. in. in. ____ 3. 6____ and 18 9 in. 27 in.

mi mi and 25 ____ ____ 4. 24 50 hr 48 hr

Lesson Quiz

© Harcourt

Use cross products or common denominators to determine whether the ratios form a proportion. 1. 2_6 5

3 _ 9

40 3. 8_5 5 __ 50

18 6 5 __ 2. __ 30 10 49 4. 7_5 5 __ 35

6 5. 1_5 5 __ 10

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. On the first 5 __ day Ben drove 15 of the distance to Raleigh and on the second day Laura __ of the distance. Determine drove 15 30 whether Ben and Laura drove the same distance. No; 1_3 ? 1_2 .

Spiral Review Write two equivalent ratios. __ Shown. 1. 14 28

7 ___ 14

and

2 __ 4

20 __ 4_ and 2. 25 5

8 ___ 10

Determine whether the ratios are equivalent. in. in. ____ 3. 6____ and 18 Yes 9 in. 27 in.

mi Yes mi and 25 ____ ____ 4. 24 50 hr 48 hr

Lesson Quiz

© Harcourt

Use cross products or common denominators to determine whether the ratios form a proportion. 1. 2_6 5

3 _ 9

yes

__ no 3. 8_5 5 40 50

6 5 18 __ yes 2. __ 30 10

__ yes 4. 57_ 5 49 35

6 no 5. 1_5 5 __ 10

Grade 6

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22.3

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. If the car used 3 gallons of gasoline to go 105 mi, how many gallons of gasoline would be used after the family has driven 270 miles?

Spiral Review Determine whether the ratios form a proportion. 6 4 and __ 1. __ 15 10

4 and _ 2 2. __ 12 3

Lesson Quiz 28 1. Solve the proportion. 7_3 5 __ n

2. Use a common denominator to form equivalent x fractions. 3_4 5 ___ 200 3. Use proportions to convert to the given unit. 40 oz = x lb © Harcourt

4. Which two of the given ratios can be used to write a 9 6 ,_ proportion? 3_5 , __ 15 9 5. A brownie recipe calls for 1 1_2 c of powdered chocolate and 3 c of flour. Ann made a mistake and used 5 c of flour. How many cups of powdered chocolate should she use to keep the proportion correct?

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. If the car used 3 gallons of gasoline to go 105 mi, how many gallons of gasoline would be used after the family has driven 270 miles? 7 5_7 gal

Spiral Review Determine whether the ratios form a proportion. 6 4 and __ __ 1. 10 Yes 15

4 and 2 _ Yes 2. __ 12 3

Lesson Quiz 28 n 5 12 1. Solve the proportion. 7_3 5 __ n

2. Use a common denominator to form equivalent x fractions. 3_4 5 ___ 200 x 5 150 3. Use proportions to convert to the given unit. 40 oz = x lb x 5 2.5 © Harcourt

4. Which two of the given ratios can be used to write a 9 9 6 , _ 3_ 5 __ proportion? 3_5 , __ 15 15 9 5 5. A brownie recipe calls for 1 1_2 c of powdered chocolate and 3 c of flour. Ann made a mistake and used 5 c of flour. How many cups of powdered chocolate should she use to keep the proportion correct? 2.5 c

Grade 6

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22.4

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 520 miles. If Mr. Edwards drives at an average speed of 65 miles per hour, about how long does the trip take?

Spiral Review 1. Write as a ratio in

lowest terms: 8 pies to 12 cakes.

2. There are 5 girls

and 8 boys on a team. What is the ratio of boys to girls on the team?

Lesson Quiz © Harcourt

Find the missing term in each proportion. 14 1. _n2 5 __ 28

18 __ 5 __ 2. 12 n 4

5 3. n_2 5 __ 20

5 n 4. __ 5 __ 15 12

5. A car travels 85 kilometers in 1 1_6 hours. How far will it travel in 4 1_5 hours?

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 520 miles. If Mr. Edwards drives at an average speed of 65 miles per hour, about how long does the trip take? about 8 hours

Spiral Review 1. Write as a ratio in

lowest terms: 8 pies to 12 cakes. 8 __ 12

5 2_3 2:3

2. There are 5 girls

and 8 boys on a team. What is the ratio of boys to girls on the team? 8 _ or 8:5 5

Lesson Quiz © Harcourt

Find the missing term in each proportion. __ n 5 4 1. _n2 5 14 28

__ 5 18 __ n 5 6 2. 12 n 4

5 1 _ 3. n_2 5 __ 20 n 5 2 or 0.5

5 n n5 4 4. __ 5 __ 15 12

5. A car travels 85 kilometers in 1 1_6 hours. How far will it travel in 4 1_5 hours? 306 kilometers Grade 6

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22.5

Problem of the Day The Edwards family is driving their car from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Along the way, the Edwards children watch the car DVD player, which has a width and height one-fifth as large as their television screen at home. If the screen at home is 40 in. wide and 22.5 in. high, what are the width and height of the car DVD player?

Spiral Review 1. d 5 ?

2. d 5 150 mi

r 5 60 cm per min t 5 10 min

r 5 60 mi per hr t5?

3. d 5 3 km

4. d 5 0.01 m

r5? t 5 12 min

r5? t 5 0.5 hr

Lesson Quiz Tell whether the pair of figures is similar. Explain why or why not. B

Y

1. 21 m

24 m

28 m

2.

32 m

4 in.

E 2 in.

Z

18 m

A

© Harcourt

3. B

398

V

F

938 20 in.

32 in.

Q

T

Q

C 24 in.

G

F

24 m

S

6 in.

3 in.

D X

R

F

488

6 in.

D

E

398

938 8 in.

5 in. 488

G

12 m

U

4.

R

6m

Q

10 m

W

X

4m

S

P

5. Mark makes a triangular flag with sides measuring 4 inches, 7 inches, and 7 inches. Katya makes a triangular flag with sides measuring 6 inches, 8 inches, and 8 inches. Are the triangles similar? Explain.

Grade 6

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22.5

Problem of the Day The Edwards family is driving their car from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Along the way, the Edwards children watch the car DVD player, which has a width and height one-fifth as large as their television screen at home. If the screen at home is 40 in. wide and 22.5 in. high, what are the width and height of the car DVD player? width 5 8 in., height 5 4.5 in.

Spiral Review 1. d 5 ? 600 cm

2. d 5 150 mi

r 5 60 cm per min t 5 10 min

r 5 60 mi per hr t 5 ? 2.5 hr

3. d 5 3 km r 5 ? 1_4 km per min

4. d 5 0.01 m

t 5 12 min

Y

r 5 ? 2.0.02 m per hr t 5 0.5 hr B B

Y 21 m

Lesson Quiz 21 m

X

B

Y

28 m

24 m 24 m 18 m

32 m

28 m

Z

32 m

A

F

24 m

24 m A or F S 6 in. not. R why Tell whether the pair of figures is similar. Explain why F

X

21Ym

1.

X

21 m

18 m 24 m

E 18 m

X

28Bm

24 m

4 in. Z

32 m

2.

Z 28 m A F

32 m 24 m

R A

F

F

© Harcourt

C

3.

24 in.

398 B24 in.

3 in.

20Qin. C 938 488 D 32 in. 20 in.

6 in.

E 6 in.

398 F 938

T 938 8 in. 5 in.

5 in. 488

Z

R 3 in.

F

4 in.

D

24 in.

S

6 in.

G 3 in.

C

Q

CG 938

T TF 938

Q 20 in.

5 in. F Yes, the 938ratios of the6 in.lengths of the 24 in. 20 in. 488 488 398 6 in. 398 938 5 in. 8 in. E G B D 32 in. corresponding sides are equal. 398 488

B

F

938 G

2 in.

S

6 in. 24 m

E2 in.

D

2 in. 3 in. Yes, the ratios ofR the lengths of 6 in. S F E D4 in. G the2 in.corresponding Qsides are Tequal.

D

18 m 4 in. E

4.

398

V 32 in. 12 m 12 m

V

488

U

10 m

E

R R

10 m X

W

G

UD

G Q

8 in. 6m

6m

Q

4m

4 mP

S

12 m V U No, the ratios of the corresponding sides Yes, of 398 Rlengths 488 488 of the 398 the ratios 6m Q 8 in. E G B D 32 in. are not equal. the corresponding 10 m sides are equal. 4m 12 m V U 6 m R Q 5. MarkW makes aX triangular flPag with sides measuring 4 inches, 7 inches, and 7 inches. S 10 m Katya makes a triangular4 mflag with sides measuring 6 inches, 8 inches, and X P 8 Winches. Are theS triangles similar? Explain. No, the ratios of the lengths of the corresponding sides are not equal.

Grade 6

W

X

S

P

Daily Transparency DT22.5

22.6

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. They use 25.75 gal of gas on the trip. Write and solve an equation to find how many miles they traveled per gallon of gas.

Spiral Review Rectangle ABCD has length 4 cm and width 16 cm. Rectangle EFGH has length 6 cm and width 18 cm. Are the rectangles similar? Explain.

© Harcourt

Lesson Quiz 1. A 4-lb bag of peanuts costs $16. If the price per pound remains the same, write and solve an equation to find the cost of a 3-lb bag of peanuts. 2. Randall has 240 stamps in his collection. He organizes them in an album with 8 stamps on each page. Write and solve an equation to find how many pages are in Randall’s stamp collecting album.

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. They use 25.75 gal of gas on the trip. Write and solve an equation to find how many miles they traveled per gallon of gas. 25.75 3 m 5 515; 20 mi/gal

Spiral Review Rectangle ABCD has length 4 cm and width 16 cm. Rectangle EFGH has length 6 cm and width 18 cm. Are the rectangles similar? Explain. No; the ratios of the corresponding sides, 1 _ and 1_ , are not the same. 4 3

© Harcourt

Lesson Quiz 1. A 4-lb bag of peanuts costs $16. If the price per pound remains the same, write and solve an equation to find 4 5 3 _ c 5 12; the cost of a 3-lb bag of peanuts. __ c 16 a 3-lb bag of peanuts costs $12. 2. Randall has 240 stamps in his collection. He organizes them in an album with 8 stamps on each page. Write and solve an equation to find how many pages are in Randall’s stamp collecting album. 8p 5 240, p 5 30; there are 30 pages in Randall’s stamp collecting album.

Grade 6

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22.7

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. The road map that the family is using has a scale of 1 in. 5 75 mi. About how many inches represent the distance they are driving?

Spiral Review 1. If the ratios of sides of similar figures are 8 to 5 and 4 to d, d 5 ? 2. If the ratios of sides of similar figures are 4 to 6 and d to 3, d 5 ?

Lesson Quiz

© Harcourt

Find the unknown dimension. 1. scale: 1 in. = 9 in. drawing length: 12 in. actual length:

3. scale: 2 cm = 5 m drawing length: 6 cm actual length:

2. scale: 4 ft = 8 in. drawing length: actual length: 24 in.

4. scale: 1 in. = 35 mi drawing length: actual length: 105 mi

5. A jeweler is making a scale drawing of a small engraving that is 9 mm wide. The scale is 4 cm = 1 mm. How wide will the engraving be in the drawing?

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. The road map that the family is using has a scale of 1 in. 5 75 mi. About how many inches represent the distance they are driving? Possible answer: about 7 in.

Spiral Review 1. If the ratios of sides of similar figures are 8 to 5 and 4 to d, d 5 ? 2.5 2. If the ratios of sides of similar figures are 4 to 6 and d to 3, d 5 ? 2

Lesson Quiz

© Harcourt

Find the unknown dimension. 1. scale: 1 in. = 9 in. drawing length: 12 in. actual length: 108 in.

3. scale: 2 cm = 5 m drawing length: 6 cm actual length: 15 m

2. scale: 4 ft = 8 in. drawing length: 12 ft actual length: 24 in.

4. scale: 1 in. = 35 mi drawing length: 3 in. actual length: 105 mi

5. A jeweler is making a scale drawing of a small engraving that is 9 mm wide. The scale is 4 cm = 1 mm. How wide will the engraving be in the drawing? 36 cm

Grade 6

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22.8

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Mrs. Edwards estimates that the total cost of all driving expenses averages $2 for every 5 mi traveled. What is her estimate of the total cost of the driving expenses?

Spiral Review 1. scale: 3 cm 5 18 m drawing length: 12 cm actual length: ? 3. scale: 4 cm 5 3 mm drawing length: ? actual length: 6.9 mm

2. map scale: 1 in. 5 4 mi. measured distance: ? actual distance: 48 mi 4. map scale: 1 in. 5 25 mi measured distance: 23 in. actual distance: ?

Lesson Quiz Use proportional reasoning to find the unknown amount. 1. Martin types 60 words in 2 min. How long does it take him to type 90 words? 2. Grace walks 5 mi in 2 hr. How many miles does she walk in 5 hr? 3. Two packages of spaghetti make 8 servings. How many packages make 20 servings? © Harcourt

4. You can buy 24 tulip bulbs for $6.48. How much would 15 bulbs cost? 5. Sharon takes 15 hr to make 6 quilt squares. She expects to complete a quilt with 100 squares within 200 hrs. Is her expectation reasonable? Explain.

Grade 6

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22.8

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Mrs. Edwards estimates that the total cost of all driving expenses averages $2 for every 5 mi traveled. What is her estimate of the total cost of the driving expenses? $206

Spiral Review 1. scale: 3 cm 5 18 m drawing length: 12 cm actual length: ? 72 m 3. scale: 4 cm 5 3 mm drawing length: ? 9.25 cm actual length: 6.9 mm

2. map scale: 1 in. 5 4 mi. measured distance: ? 12 in. actual distance: 48 mi 4. map scale: 1 in. 5 25 mi measured distance: 23 in. actual distance: ? 575 mi

Lesson Quiz Use proportional reasoning to find the unknown amount. 1. Martin types 60 words in 2 min. How long does it take him to type 90 words? 3 min 2. Grace walks 5 mi in 2 hr. How many miles does she walk in 5 hr? 12.5 mi 3. Two packages of spaghetti make 8 servings. How many packages make 20 servings? 5 © Harcourt

4. You can buy 24 tulip bulbs for $6.48. How much would 15 bulbs cost? $4.05 5. Sharon takes 15 hr to make 6 quilt squares. She expects to complete a quilt with 100 squares within 200 hrs. Is her expectation reasonable? Explain. No. Think: If it takes her 15 hr to make 6 squares, it takes her 5 hr to make 2 squares. Since 100 squares is 50 3 2 squares, it should also take 50 3 5 hr, or 250 hr to make the quilt.

Grade 6

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23.1

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty out of every 100 students at the middle school belong to the ski club. Write 20 out of 100 as a percent.

Spiral Review Express as a decimal number. 1. _38

2. _45

3. 1 5_8

4. _34

Lesson Quiz

© Harcourt

Compare. Write , .. or 5 for each n. 2. 0.35% n 30%

3. 3_4 % n 0.75%

4. 110% n 210%

5. Kim, Jerry, and Emmett each had $50 to spend at the mall. Kim spent 60% of $50, Jerry spent 65% of $50, and Emmett spent 62% of $50. Write the percents in order from least to greatest.

Grade 6

M09ATE6_C023DT.indd 1

1. 15% n 12%

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty out of every 100 students at the middle school belong to the ski club. Write 20 out of 100 as a percent. 20%

Spiral Review Express as a decimal number. 1. 3_8 0.375

2. 4_5 0.8

3. 1 5_8 1.625

4. 3_4 0.75

Lesson Quiz

© Harcourt

Compare. Write , .. or 5 for each n. 1. 15% n 12% .

2. 0.35% n 30% ,

3. 3_4 % n 0.75% 5

4. 110% n 210% ,

5. Kim, Jerry, and Emmett each had $50 to spend at the mall. Kim spent 60% of $50, Jerry spent 65% of $50, and Emmett spent 62% of $50. Write the percents in order from least to greatest. 60%, 62%, 65% Grade 6

Daily Transparency DT23.1

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty students belong to the ski club. Out of those 20 students, 7 also 7 as a enjoy snowboarding. Write __ 20 percent.

Spiral Review Write ,, ., or 5 to make the statement true. 1. 34%

40%

2. 55%

55.05%

3. 40%

40.0%

4. 100%

10%

Lesson Quiz Write each number as a percent. 1. 0.08

4 __ 2. 25

3. Write 135% as a decimal and as a fraction in simplest form. © Harcourt

4. Which number is greater, 53_ or 65%? 5. At a middle school, 43_ of sixth graders, 72% of seventh graders, and 0.7 of eighth graders attended a pep rally. Write each number as a percent. Then order the percents from greatest to least.

Grade 6

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23.2

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty students belong to the ski club. Out of those 20 students, 7 also 7 as a __ enjoy snowboarding. Write 20 35 7 5 ___ percent. __ 35% 20 100

Spiral Review Write ,, ., or 5 to make the statement true. 1. 34%

40% ,

2. 55%

3. 40%

40.0% 5 4. 100%

55.05% , 10% .

Lesson Quiz Write each number as a percent. 1. 0.08 8%

4 __ 2. 25 16%

3. Write 135% as a decimal and as a fraction in 7 simplest form. 1.35, 1 __ 20

© Harcourt

4. Which number is greater, 53_ or 65%? 65% 5. At a middle school, 43_ of sixth graders, 72% of seventh graders, and 0.7 of eighth graders attended a pep rally. Write each number as a percent. Then order the percents from greatest to least. 75%, 72%, 70% Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. There are 20 students in the Ski Club. If 25% can go on the next trip, how many members can go?

Spiral Review 1. Write 0.004 as a percent.

2. Write 5.0 as a percent.

3. Write 27% as a decimal.

4. Write 35% as a fraction in simplest form. 6. Write 0.6% as a fraction in simplest form.

5. Write 3.8% as a decimal.

Lesson Quiz 1. Find 150% of 64. © Harcourt

2. Find 0.5% of 400. 3. Estimate a 20% tip for $5.75. 4. Estimate a 15% tip for $7.20. 5. There are 80 students in sixth grade. If 15 percent of them can play the piano, and 20 percent can play the guitar, how many students can play a musical instrument?

Grade 6

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23.3

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. There are 20 students in the Ski Club. If 25% can go on the next trip, how many members can go? 20 3 0.25 5 5 members

Spiral Review 1. Write 0.004 as a percent. 0.4%

2. Write 5.0 as a percent. 500%

3. Write 27% as a decimal. 0.27

4. Write 35% as a fraction in 7 simplest form. __ 20 6. Write 0.6% as a fraction 3 ___ in simplest form. 500

5. Write 3.8% as a decimal. 0.038

Lesson Quiz 1. Find 150% of 64. 96 © Harcourt

2. Find 0.5% of 400. 2 3. Estimate a 20% tip for $5.75. Possible answer: about $1.20 4. Estimate a 15% tip for $7.20. Possible answer: about $1.05 5. There are 80 students in sixth grade. If 15 percent of them can play the piano, and 20 percent can play the guitar, how many students can play a musical instrument? 28

Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Each of 18 club members will compete in the first race, 6 members will compete in the second, and 9 members in the third. Construct a circle graph using this information.

Spiral Review 1. Find 2% of 25.

2. Find 150% of 36.

3. Use mental math to find 15% of 80.

4. Write an equation to find 20% of 6.30.

© Harcourt

Lesson Quiz Convert the following to degrees. 1. 35%

2. 85%

90 3. ___ 200

80 4. ___ 200

21 ___ 5. 150

Grade 6

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23.4

Problem of the Day The middle school Ski Club Members Competing Ski Club plans Race 1 16.7% ski trips and Race 3 participates in Race 2 50% 33.3% ski competitions. Each of 18 club members will compete in the first race, 6 members will compete in the second, and 9 members in the third. Construct a circle graph using this information.

Spiral Review 1. Find 2% of 25. 0.5

2. Find 150% of 36. 0.54

3. Use mental math to find 15% of 80. 12

4. Write an equation to find 20% of 6.30. 0.2 3 6.30 5 1.26

© Harcourt

Lesson Quiz Convert the following to degrees. 1. 35% 126˚

2. 85% 306˚

90 3. ___ 200 45% 5 162˚

80 4. ___ 200 40% 5 144˚

21 5. ___ 150 14% 5 50.4˚

Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The graph below shows the number of races won by club members in each of the last six weeks. How many races were won during week 5?

Number of Races

Races Won by Members 14 12 10 8 6 4 2 0

1

2

3

4

6

5

Week

Spiral Review Convert each percent to degrees in a circle graph. 1. 25%

2. 30%

3. 55%

4. 80%

5. _34

9 6. __ 10

A student is doing a science experiment on plant growth. One plant is fed water and fertilizer and the other just water. The results are shown in the graph.

Plant Growth

10 Growth in Inches

© Harcourt

Lesson Quiz

1. How much did the plant fed with fertilizer grow between weeks 1 and 3?

8

with fertilizer without fertilizer

6 4 2 0

1

2 3 4 5 Number of Weeks

6

2. How many inches per week did each plant grow?

Grade 6

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23.5

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The graph below shows the number of races won by club members in each of the last six weeks. How many races were won during week 5? 7

Number of Races

Races Won by Members 14 12 10 8 6 4 2 0

1

2

3

4

6

5

Week

Spiral Review Convert each percent to degrees in a circle graph. 1. 25% 90°

2. 30% 108°

3. 55% 198°

4. 80% 288°

5. _34 270°

9 324° 6. __ 10

A student is doing a science experiment on plant growth. One plant is fed water and fertilizer and the other just water. The results are shown in the graph.

10 Growth in Inches

© Harcourt

Lesson Quiz Plant Growth

8

with fertilizer without fertilizer

6 4 2

1. How much did the plant fed with 1 2 3 4 5 Number of Weeks fertilizer grow between weeks 1 and 3? 3 inches 2. How many inches per week did each plant grow? The plant with fertilizer grew 1.3 inches per week. The plant without fertilizer grew 1 inch per week. 0

Grade 6

6

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23.6

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The regular price of a one-day lift ticket at a local ski resort is $32. Members of the club receive a 5% discount. What will be the total cost for 12 of the members to ride the ski lift for one day?

Spiral Review 1. Find 20% of 35.

2. Find 18% of 224.

3. Find 80% of 350.

4. Find 105% of $5.75.

5. Find 95% of 25.

6. Find 108% of $23.75.

Lesson Quiz Find the discount. 1. 45% of $24.00

2. 15% of $70.00

© Harcourt

Find the discounted price. 3. 25% off $60.00

4. 30% off $85.00

5. The price to go to an amusement park is $35.00. If you have a coupon for 15% off, how much will you pay if a 5% sales tax is applied to the discounted price?

Grade 6

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23.6

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The regular price of a one-day lift ticket at a local ski resort is $32. Members of the club receive a 5% discount. What will be the total cost for 12 of the members to ride the ski lift for one day? $364.80

Spiral Review 1. Find 20% of 35. 7 3. Find 80% of 350. 280 5. Find 95% of 25. 23.75

2. Find 18% of 224. 40.32 4. Find 105% of $5.75. $6.04 6. Find 108% of $23.75. $25.65

Lesson Quiz Find the discount. 1. 45% of $24.00 $10.80

2. 15% of $70.00 $10.50

© Harcourt

Find the discounted price. 3. 25% off $60.00 $45.00

4. 30% off $85.00 $59.50

5. The price to go to an amusement park is $35.00. If you have a coupon for 15% off, how much will you pay if a 5% sales tax is applied to the discounted price? $31.24

Grade 6

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24.1

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. What is the probability that Mikayla will roll 4 or 5 on the number cube?

Spiral Review 1. Hardcover books are on sale at a 15% discount. The regular price of a book is $35. What is the sale price? 2. A helmet is priced at $19.95. Quinn buys the helmet and pays 7.25% sales tax. What is his total purchase cost? 3. Find the discount rate used when the regular price is $72 and the sale price is $39.60.

Lesson Quiz

© Harcourt

Walter has a bag that contains 3 New Jersey quarters, 5 Massachusetts quarters, 3 Ohio quarters, and 4 Pennsylvania quarters. Find each probability. 1. P(Massachusetts)

2. P(Massachusetts or Ohio)

3. P(not New Jersey)

4. P(New Jersey or Pennsylvania)

5. Do the statements P(New Jersey or Massachusetts) and P(Ohio or Pennsylvania) represent complementary events? Why or why not?

Grade 6

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24.1

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. What is the probability that Mikayla will roll 4 or 5 on the number cube? 1_3

Spiral Review 1. Hardcover books are on sale at a 15% discount. The regular price of a book is $35. What is the sale price? $29.75 2. A helmet is priced at $19.95. Quinn buys the helmet and pays 7.25% sales tax. What is his total purchase cost? $21.40 3. Find the discount rate used when the regular price is $72 and the sale price is $39.60. 45%

Lesson Quiz

© Harcourt

Walter has a bag that contains 3 New Jersey quarters, 5 Massachusetts quarters, 3 Ohio quarters, and 4 Pennsylvania quarters. Find each probability. 1. P(Massachusetts) _13

8 2. P(Massachusetts or Ohio) __ 15

3. P(not New Jersey) 4_5

7 4. P(New Jersey or Pennsylvania) __ 15

5. Do the statements P(New Jersey or Massachusetts) and P(Ohio or Pennsylvania) represent complementary events? Why or why not? yes; Sample answer: Complementary events are events whose probabilities add up to 1. Since P(New Jersey or Massachusetts) 1 8 7 5 1, the statements 1 __ P(Ohio or Pennsylvania) 5 __ 15 15 represent complementary events.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She records that she tossed heads 15 times and tails 10 times. What is the experimental probability of tossing heads?

Spiral Review A bag contains equally-sized cards numbered 1 to 15. One card is drawn randomly. Find each probability. 1. P(2)

4. P(5 or 10)

2. P(not 7)

5. P(greater than 8)

3. P(odd)

6. P(less than or equal to 12)

Lesson Quiz A vending machine in a restaurant randomly dispenses four types of prizes. The restaurant owner, Glen, records the first 40 prizes in a table. Find each experimental probability. ring 12 1. P(ring)

ball 8

bracelet 9 2. P(ball)

eraser 11 3. P(eraser)

© Harcourt

4. How many times can Glen expect the machine to dispense a ring in the next 30 wins? 5. If there were equal amounts of each prize, what would the theoretical probability be of winning a bracelet? 6. Compare the experimental and theoretical probability of winning a bracelet.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She records that she tossed heads 15 times and tails 10 times. What is the experimental probability of tossing heads? 3_5

Spiral Review A bag contains equally-sized cards numbered 1 to 15. One card is drawn randomly. Find each probability. 1 2 1. P(2) __ 4. P(5 or 10) __ 15

15

7 5. P(greater than 8) __ 15

__ 2. P(not 7) 14 15 8 3. P(odd) __

6. P(less than or equal to 12) 4_

15

5

Lesson Quiz A vending machine in a restaurant randomly dispenses four types of prizes. The restaurant owner, Glen, records the first 40 prizes in a table. Find each experimental probability. ring 12

ball 8

3 1. P(ring) __ 10

bracelet 9

eraser 11

2. P(ball) 1_ 5

__ 3. P(eraser) 11

40

© Harcourt

4. How many times can Glen expect the machine to dispense a ring in the next 30 wins? 9 times 5. If there were equal amounts of each prize, what would the theoretical probability be of winning a bracelet? 1_ 4

6. Compare the experimental and theoretical probability of winning 9 , 1 _ : The experimental probability is less than the a bracelet. __ 4 40 theoretical probability.

Grade 6

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24.3

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. Mikayla knows there are 10 marbles in her bag and that 3 of them are red. Can she predict the number of red marbles in a bag of 50 marbles? Why or why not?

Spiral Review When tossing a fair 6-sided number cube, P(NOT 4) 5 ? Explain.

Lesson Quiz Cross multiply to solve for x. 1. 3_8 5 _9x

1 x 2. ___ 5 __ 100 50

Latoya buys a small box of 20 cookies. In the box, there are 10 chocolate chip, 5 almond, and 5 peanut butter cookies. 3. What is the P(almond cookie)?

© Harcourt

5 x 5 __ 4. Predict how many almond cookies are in a box of 60. __ 20 60

5. Can Latoya predict how many cookies are not peanut butter in a box of 60 cookies? Explain.

Grade 6

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24.3

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. Mikayla knows there are 10 marbles in her bag and that 3 of them are red. Can she predict the number of red marbles in a bag of 50 marbles? Why or why not? Possible answer: Probably not. She would need to know that the bag of 50 marbles has the same proportion of red marbles as the bag of 10. Otherwise, she cannot make a valid prediction.

Spiral Review When tossing a fair 6-sided number cube, P(NOT 4) 5 ? Explain. Five possible favorable events (1, 2, 3, 5, 6) out of 6 possible outcomes, (1, 2, 3, 4, 5, 6), so P(NOT 4) 5 5_6

Lesson Quiz Cross multiply to solve for x. 1. 3_8 5 9_x 24

1 x 1 _ 2. ___ 5 __ 100 50 2

Latoya buys a small box of 20 cookies. In the box, there are 10 chocolate chip, 5 almond, and 5 peanut butter cookies. 5 5 _14 3. What is the P(almond cookie)? __ 20

© Harcourt

5 x 5 __ 4. Predict how many almond cookies are in a box of 60. __ 20 60 x 5 15 almond cookies 5. Can Latoya predict how many cookies are not peanut butter in a box of 60 cookies? Explain. Yes; possible answer: since there are equal amounts of almond and peanut butter cookies, we can use the results for almond cookies. 60 total cookies 2 15 peanut butter cookies 5 45 cookies that are not peanut x butter cookies, or P(not peanut butter) 5 1 2 1_4 5 3_4 . So, 3_4 5 __ . 60 x 5 45. 45 cookies are not peanut butter cookies.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has a red box, a green box, and a blue box. In each box she wants to place 2 marbles, each a different color. There are 4 different colors of marbles for her to choose from. How many combinations of marbles and boxes are there?

Spiral Review A spinner has 8 equal sections that are either blue, green, or yellow. Sam spins the pointer of the spinner 30 times and records 9 blue spins, 15 green spins, and 6 yellow spins. Find each experimental probability. 1. P(blue) 2. P(green) 3. P(yellow)

Lesson Quiz An ice cream parlor offers chocolate, strawberry, or vanilla ice cream. You can buy it in a cup or a cone. The available toppings are nuts, sprinkles, and hot fudge. 1. How many possible choices are there? © Harcourt

2. How many choices do you have if you leave the topping off? 3. June definitely wants a cup. How many choices does she have? 4. Izzy does not like strawberry. How many choices does she have? 5. Suppose the parlor adds mint chip as an additional flavor and stops serving nuts. How many possible ice cream choices are there now?

Grade 6

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24.4

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has a red box, a green box, and a blue box. In each box she wants to place 2 marbles, each a different color. There are 4 different colors of marbles for her to choose from. How many combinations of marbles and boxes are there? There are 18 different combinations

Spiral Review A spinner has 8 equal sections that are either blue, green, or yellow. Sam spins the pointer of the spinner 30 times and records 9 blue spins, 15 green spins, and 6 yellow spins. Find each experimental probability. 3 1. P(blue) __ 2. P(green) 1_ 3. P(yellow) 1_ 2 10

5

Lesson Quiz An ice cream parlor offers chocolate, strawberry, or vanilla ice cream. You can buy it in a cup or a cone. The available toppings are nuts, sprinkles, and hot fudge. 1. How many possible choices are there? 18 © Harcourt

2. How many choices do you have if you leave the topping off? 6 3. June definitely wants a cup. How many choices does she have? 9 4. Izzy does not like strawberry. How many choices does she have? 12 5. Suppose the parlor adds mint chip as an additional flavor and stops serving nuts. How many possible ice cream choices are there now? 16

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. How many outcomes are possible for the compound events of flipping the coin and rolling the number cube?

Spiral Review 1. How many different outfits can be made from 3 pairs of pants, 3 shirts, and 2 jackets? 2. How many different outfits can be made from 3 pairs of pants, 2 shirts, and 2 jackets?

Lesson Quiz Use the Fundamental Counting Principle to find the number of possible outcomes for each event. 1. Rolling a 6-sided number cube and flipping two coins 2. Visiting one of 3 friends on a day during the week 3. Spinning the points of 3 spinners, each with 3 sections

© Harcourt

4. Choosing a number from 0 to 9 and flipping a coin 5. Andrew is ordering shirts for the soccer team. He has 4 sizes to choose from (small, medium, large, and extra large), 3 colors (white, blue, and black) and 2 styles (short sleeve and long sleeve). Make a list of all possible outcomes. How many different shirts does Andrew have to choose from?

Grade 6

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24.5

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. How many outcomes are possible for the compound events of flipping the coin and rolling the number cube? 12

Spiral Review 1. How many different outfits can be made from 3 pairs of pants, 3 shirts, and 2 jackets? 3 3 3 3 2 5 18 2. How many different outfits can be made from 3 pairs of pants, 2 shirts, and 2 jackets? 3 3 2 3 2 5 12

Lesson Quiz Use the Fundamental Counting Principle to find the number of possible outcomes for each event. 1. Rolling a 6-sided number cube and flipping two coins 24 2. Visiting one of 3 friends on a day during the week 21 3. Spinning the points of 3 spinners, each with 3 sections 27

© Harcourt

4. Choosing a number from 0 to 9 and flipping a coin 20 5. Andrew is ordering shirts for the soccer team. He has 4 sizes to choose from (small, medium, large, and extra large), 3 colors (white, blue, and black) and 2 styles (short sleeve and long sleeve). Make a list of all possible outcomes. How many different shirts does Andrew have to choose from? Check students’ work; 24

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. There are 10 red and 10 blue marbles in the bag. Mikayla selects a marble, does not replace it, and selects another marble. Find P(red, not red).

Spiral Review Determine the number of outcomes for each compound event. 1. spinning a 3-section spinner and rolling a 6-sided number cube 2. flipping a coin and selecting a token from a bag of 15 different-color tokens 3. rolling a 6-sided number cube and choosing a month of the year 4. spinning an 8-section spinner and a 6-section spinner

Lesson Quiz For problems 1-4 below, write independent or dependent to describe the events. 1. Spin the pointer twice on a spinner divided equally into 9 sections.

© Harcourt

2. Select a marble from 20 colored marbles in a bag, do not replace it, and select a second marble. 3. Draw a card from a box of cards labeled 20 to 40, replace it, and draw a second card. 4. Roll two six-sided number cubes. For problem 5, find the probability. 5. Suppose the bag in Question 2 has 8 blue marbles, 6 pink marbles, and 6 green marbles. Find P(pink, pink).

Grade 6

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24.6

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. There are 10 red and 10 blue marbles in the bag. Mikayla selects a marble, does not replace it, and selects another marble. Find P(red, 5 not red). __ 19

Spiral Review Determine the number of outcomes for each compound event. 1. spinning a 3-section spinner and rolling a 6-sided number cube 18 2. flipping a coin and selecting a token from a bag of 15 different-color tokens 30 3. rolling a 6-sided number cube and choosing a month of the year 72 4. spinning an 8-section spinner and a 6-section spinner 48

Lesson Quiz For problems 1-4 below, write independent or dependent to describe the events.

© Harcourt

1. Spin the pointer twice on a spinner divided equally into 9 sections. independent 2. Select a marble from 20 colored marbles in a bag, do not replace it, and select a second marble. dependent 3. Draw a card from a box of cards labeled 20 to 40, replace it, and draw a second card. independent 4. Roll two six-sided number cubes. independent For problem 5, find the probability. 5. Suppose the bag in Question 2 has 8 blue marbles, 6 pink marbles, and 6 3 green marbles. Find P(pink, pink). __ 38

Grade 6

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24.7

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She plans to use one of these items to conduct a simulation. Each time she buys a pack of trading cards, she collects 1 of 8 bonus cards. She wants to know how many packs she can expect to buy to collect all 8 cards. How can Mikayla simulate this situation?

Spiral Review Hugh has a quarter and a number cube labeled 1–6. Find each probability. 1. P(heads, 3)

2. P(tails, odd)

3. P(tails, 1 or 6)

4. P(heads, greater than 2)

Lesson Quiz Describe a simulation that you could use to model the situation. 1. Collecting 7 randomly generated letters

© Harcourt

2. Finding 5 students who each received 5 different club assignments 3. Collecting 6 randomly generated number cards 4. Finding 14 randomly generated puzzle pieces 5. Name three simulations that can be used to find the experimental probability of randomly generating an 8?

Grade 6

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24.7

Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She plans to use one of these items to conduct a simulation. Each time she buys a pack of trading cards, she collects 1 of 8 bonus cards. She wants to know how many packs she can expect to buy to collect all 8 cards. How can Mikayla simulate this situation? Possible answer: Place 8 marbles of different colors in the bag. Select a marble, tally its color, and replace it. Repeat until each color has been selected once.

Spiral Review Hugh has a quarter and a number cube labeled 1–6. Find each probability. 1 1. P(heads, 3) __

2. P(tails, odd) 1_ 4

12

3. P(tails, 1 or 6) 1_ 6

4. P(heads, greater than 2) 1_ 3

Lesson Quiz Describe a simulation that you could use to model the situation. Possible answers are given. 1. Collecting 7 randomly generated letters spinner with 7 sections

© Harcourt

2. Finding 5 students who each received 5 different club assignments spinner with 5 sections 3. Collecting 6 randomly generated number cards number cube 4. Finding 14 randomly generated puzzle pieces bag of 14 tokens 5. Name three simulations that can be used to find the experimental probability of randomly generating an 8? Possible answers: spinner with 8 sections, spinner with 9 sections, and the bag of 14 tokens Grade 6

Daily Transparency DT24.7

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has 6 marbles in the bag, and she needs to take 4 of them out for her next experiment. Find the number of combinations of 4 marbles that she could remove.

Spiral Review Describe how you can simulate the situation.

1. collecting each letter of the word SIMULATION 2. collecting 30 trading cards 3. finding 3 students who each selected one of the 3 available lunch choices 4. finding 45 people who each opened cookies and received one of 45 different fortunes

Lesson Quiz Find the number of permutations for each situation. 1. There are 16 girls at cheerleading auditions. The director chooses the first 3 to audition. 2. Kirk bought 9 souvenirs on his vacation. He plays to display 4 of them from left to right on a shelf. Find the number of combinations for the situation.

© Harcourt

3. Mr. Martin writes out 5 monthly bills. He selects 3 to put stamps on. 4. Mrs. Amos has 6 paintings to show to her art class. She picks 4 to show today. 5. A cafeteria dietician offers 7 proposed meals for the upcoming school week. The cafeteria manager will select 5 meals and assign one to each day of the week. Is this a permutation or a combination? Find the number of ways the manager can select and assign the meals.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has 6 marbles in the bag, and she needs to take 4 of them out for her next experiment. Find the number of combinations of 4 marbles that she could remove. 15

Spiral Review Describe how you can simulate the situation. Answers will vary. Students should describe simulations that take into account the number of items in each situation. 1. collecting each letter of the word SIMULATION 2. collecting 30 trading cards 3. finding 3 students who each selected one of the 3 available lunch choices 4. finding 45 people who each opened cookies and received one of 45 different fortunes

Lesson Quiz Find the number of permutations for each situation. 1. There are 16 girls at cheerleading auditions. The director chooses the first 3 to audition. 3,360 2. Kirk bought 9 souvenirs on his vacation. He plays to display 4 of them from left to right on a shelf. Find the number of combinations for the situation. 3,024

© Harcourt

3. Mr. Martin writes out 5 monthly bills. He selects 3 to put stamps on. 10 4. Mrs. Amos has 6 paintings to show to her art class. She picks 4 to show today. 15 5. A cafeteria dietician offers 7 proposed meals for the upcoming school week. The cafeteria manager will select 5 meals and assign one to each day of the week. Is this a permutation or a combination? Find the number of ways the manager can select and assign the meals. permutation; 2,520

Grade 6

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1

The length of a modern-day marathon is about 138,435 feet. How should 138,435 be written in word form?

Pose the following problem to students.

2

Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.7 m wide.

© Harcourt

Rewrite the width as a decimal measurement to the hundredths place. Next, write an inequality using a less than symbol (,) and the measures from the problem.

Grade 6

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Unit 1 • Problem of the Day Trent’s class followed the story of the astronaut who “ran” a marathon while she was in space.

1

The length of a modern-day marathon is about 138,435 feet. How should 138,435 be written in word form? one hundred thirty-eight thousand, four hundred thirty-five

Pose the following problem to students.

2

Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.7 m wide.

© Harcourt

Rewrite the width as a decimal measurement to the hundredths place. Next, write an inequality using a less than symbol (,) and the measures from the problem. 1.70 m, 1.35 m , 1.70 m.

Grade 6

Daily Transparency DT • Unit 1

1.1

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a marathon is usually measured in miles or kilometers. Measured in feet, a marathon is about 138,435 feet. How would you write 138,435 in expanded form?

Spiral Review 1. Write three hundred thousand, four hundred seventeen in standard form. 2. Write 1,170,007 in word form.

Lesson Quiz Compare the numbers and use , or . for each d. 1. 5,289,200 d 5,279,200 2. 4,795,614 d 2,999,999,000 3. 12 trillion d 152 billion © Harcourt

4. one hundred thirty four thousand, one hundred twelve d. two hundred fifty three 5. In 2005 the U.S. census stated that San Antonio, Texas had a population of 1,256,509. San Diego, that same year, had a population of one million, two hundred fifty five thousand, five hundred and forty. Which city had the largest population?

Grade 6

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1.1

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a marathon is usually measured in miles or kilometers. Measured in feet, a marathon is about 138,435 feet. How would you write 138,435 in expanded form? (1 3 100,000) 1 (3 3 10,000) 1 (8 3 1,000) 1 (4 3 100) 1 (3 3 10) 1 (5 3 1)

Spiral Review 1. Write three hundred thousand, four hundred seventeen in standard form. 300,417 2. Write 1,170,007 in word form. one million, one hundred seventy thousand, seven

Lesson Quiz Compare the numbers and use , or . for each d. 1. 5,289,200 d 5,279,200 . 2. 4,795,614 d 2,999,999,000 , 3. 12 trillion d 152 billion . © Harcourt

4. one hundred thirty four thousand, one hundred twelve d. two hundred fifty . three 5. In 2005 the U.S. census stated that San Antonio, Texas had a population of 1,256,509. San Diego, that same year, had a population of one million, two hundred fifty five thousand, five hundred and forty. Which city had the largest population? San Antonio, Texas Grade 6

Daily Transparency DT1.1

1.2

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was 34.5 kilometers long, which converts to about 113,189 feet in customary measure. Estimate the difference, in feet, between the lengths of a modern-day marathon and the original marathon.

Spiral Review Compare, using ,, ., or 5. 1.

3,050,556 d 3,006,889

2.

7,009,889 d 7,010,889

Lesson Quiz Use an estimate to solve the problems. 1. 5,287 5 4,592 5 2. 7,394,002 2 4,709,287 5

© Harcourt

3. 453 3 605 5 4. 378qw 15,782 5 5. Max has a goal this year to save at least $400 for his college fund. He makes $4.50 for each hour he works. About how many hours would he need to work to save that much money? Should you underestimate or overestimate if he wants to be sure to make his goal?

Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was 34.5 kilometers long, which converts to about 113,189 feet in customary measure. Estimate the difference, in feet, between the lengths of a modern-day marathon and the original marathon. Possible estimate: about 30,000 ft

Spiral Review Compare, using ,, ., or 5. 1.

3,050,556 d 3,006,889 3,006,889 , 3,050,556

2.

7,009,889 d 7,010,889 7,010,889 . 7,009,889

Lesson Quiz Use an estimate to solve the problems. Possible answers given 1. 5,287 5 4,592 5 10,000 2. 7,394,002 2 4,709,287 5 2,600,000

© Harcourt

3. 453 3 605 5 300,000 4. 378qw 15,782 5 40 5. Max has a goal this year to save at least $400 for his college fund. He makes $4.50 for each hour he works. About how many hours would he need to work to save that much money? Should you underestimate or overestimate if he wants to be sure to make his goal? About 100 hours; 400 ÷ 4 = 100 I should overestimate. If I underestimate he might not make his goal. I can do that by rounding his pay down to $4 before I divide. Grade 6

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1.3

Problem of the Day Trent's class followed the story of an astronaut who "ran" a marathon while she was in space. The length of a modern-day marathon is a little more than 42.195 kilometers, or about 42,195 meters. In ancient Greece, the original race was about 34.5 kilometers, or 34,500 meters, long. Explain whether 7,695 meters is a reasonable answer for the difference between the length of a modern-day marathon and the original marathon.

Spiral Review 1. 2.

Estimate by rounding addends: 1,278 1 176. Use compatible numbers to estimate 1,549 4 29.

Lesson Quiz 1. Meg said that a car traveling 55 miles per hour, would take about 4,345 hours to travel the distance from the moon to Earth, which is 238,900 miles sway. Is this a reasonable answer? © Harcourt

2. In 2005, Pakistan, with a land area of 796,095 square kilometers, had a population of 157,935,100 people. Population density can be found by dividing the number of people by the area of the land they occupy. Is 1,984 people per square kilometer a reasonable number for the density?

Grade 6

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8/30/07 1:25:01 PM

1.3

Problem of the Day Trent's class followed the story of an astronaut who "ran" a marathon while she was in space. The length of a modern-day marathon is a little more than 42.195 kilometers, or about 42,195 meters. In ancient Greece, the original race was about 34.5 kilometers, or 34,500 meters, long. Explain whether 7,695 meters is a reasonable answer for the difference between the length of a modern-day marathon and the original marathon. Possible answer: it is a reasonable answer because it is close to my estimate of 7,000 meters (42,000 2 35,000).

Spiral Review 1. 2.

Estimate by rounding addends: 1,278 1 176. Possible answer: 1,500 Use compatible numbers to estimate 1,549 4 29. Possible answer: 50

Lesson Quiz 1. Meg said that a car traveling 55 miles per hour, would take about 4,345 hours to travel the distance from the moon to Earth, which is 238,900 miles sway. Is this a reasonable answer? Possible answer: Yes, because 240,000 4 60 5 4,000 © Harcourt

2. In 2005, Pakistan, with a land area of 796,095 square kilometers, had a population of 157,935,100 people. Population density can be found by dividing the number of people by the area of the land they occupy. Is 1,984 people per square kilometer a reasonable number for the density? No, the population is about 160,000,000 and the area about 800,000. 160,000,000 4 800,000 5 200 so 1,984 is not reasonable. Grade 6

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1.4

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was about 34.5 kilometers long, which converts to about 113,189 ft in customary measure. What is the difference, in feet, between the lengths of a modern-day marathon and the original marathon?

Spiral Review 1. 2.

Estimate by rounding the factors: 378 3 19. Why is 56 not a reasonable quotient for 6,899 4 67?

Lesson Quiz

© Harcourt

Find the sum or the difference. 1. 32 1 78 1 93 1 47 5

3. 4,499 1 298 5

2. 7,863 2 3,246 5

4. 647 2 228 5

5. The difference between the area of two parks is 23 square miles. If the smaller park is 370 square miles, what is the area of the bigger park? Explain how you found the answer.

Grade 6

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8/30/07 1:25:05 PM

1.4

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is a little more than 26 miles, or about 138,435 feet. In ancient Greece, the original race was about 34.5 kilometers long, which converts to about 113,189 ft in customary measure. What is the difference, in feet, between the lengths of a modern-day marathon and the original marathon? Possible answer: about 25,246 ft

Spiral Review 1. 2.

Estimate by rounding the factors: 378 3 19. Possible answer: 8,000 Why is 56 not a reasonable quotient for 6,899 4 67? Possible answer: It is not close enough to my estimate, about 100 (7000 4 70).

Lesson Quiz

© Harcourt

Find the sum or the difference. 1. 32 1 78 1 93 1 47 5 250

3. 4,499 1 298 5 4,797

2. 7,863 2 3,246 5 4,617

4. 647 2 228 5 419

5. The difference between the area of two parks is 23 square miles. If the smaller park is 370 square miles, what is the area of the bigger park? Explain how you found the answer. 393 sq miles: Addition is the inverse operation for subtraction. 23 1 370 5 393 Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 138,435 feet long. A runner covers the equivalent of a marathon in five days by running an equal distance each day. About how many feet does the runner travel each day?

Spiral Review 1. 2.

Subtract 6,899 from 34,500. Use an inverse operation to explain why 3,000 2 489 is not 2,521.

Lesson Quiz Find the product or quotient, then estimate to check. 1. 413 3 87 5 35,931; © Harcourt

2. 5,279 4 43 5 122 r33; 3. 547 3 698 5 381,806; 4. 7qw 556 5. The parking lot where Fred works pays him $0.75 for every car he parks. Each customer usually tips him $2.00 when he returns their car. If he parks 37 cars on Friday, how much will he make?

Grade 6

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8/30/07 1:25:08 PM

1.5

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 138,435 feet long. A runner covers the equivalent of a marathon in five days by running an equal distance each day. About how many feet does the runner travel each day? about 27,687 ft each day

Spiral Review 1. 2.

Subtract 6,899 from 34,500. 27,601 Use an inverse operation to explain why 3,000 2 489 is not 2,521. Possible answer: When 2,521 is added to 489, the sum is 3,010 instead of 3,000.

Lesson Quiz Find the product or quotient, then estimate to check. 1. 413 3 87 5 35,931; 400 3 90 5 36,000 © Harcourt

2. 5,279 4 43 5 122 r33; 5200 4 40 5 130 3. 547 3 698 5 381,806; 500 3 700 5 350,000 4. 7qw 556 79 r3; 560 4 7 5 80 5. The parking lot where Fred works pays him $0.75 for every car he parks. Each customer usually tips him $2.00 when he returns their car. If he parks 37 cars on Friday, how much will he make? (37 3 $0.75) 1 ( 37 3 $2.00) or 37 3 $2.75 5 $101.75 Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Trent divided 42,195 by 6 find out the number of meters his uncle ran each day for 6 days. What does the remainder to his division problem represent?

Spiral Review 1. Find the product of 478 and 15. 2. Use an inverse operation to explain why 4,272 4 48 is not 79.

Lesson Quiz © Harcourt

1. There are 52 pieces of candy in a bag. If Petra wants to give each of her 11 friends the same number of pieces of candy, how many pieces will each get and how many pieces will she have left over? 2. Each bus holds 32 students. How many buses will it take to get 102 students to the museum for a field trip? Every student must have a seat.

Grade 6

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8/30/07 1:25:11 PM

1.6

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Trent divided 42,195 by 6 find out the number of meters his uncle ran each day for 6 days. What does the remainder to his division problem represent? Possible answer: The remainder could represent the number of meters more his uncle needed to run a marathon.

Spiral Review 1. Find the product of 478 and 15. 7,170 2. Use an inverse operation to explain why 4,272 4 48 is not 79. Possible answer: When 79 is multiplied by 48, the product is 3,792 instead of 4,272.

Lesson Quiz © Harcourt

1. There are 52 pieces of candy in a bag. If Petra wants to give each of her 11 friends the same number of pieces of candy, how many pieces will each get and how many pieces will she have left over? 52 4 11 5 4 r8: Each will get 4 pieces and she will have 8 left over. 2. Each bus holds 32 students. How many buses will it take to get 102 students to the museum for a field trip? Every student must have a seat. 102 4 32 5 3 r6: They will need 4 buses. Grade 6

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1.7

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Write its length in expanded form with exponents in powers of 10.

Spiral Review 1.

What is the remainder of 3,789 4 23?

2.

What is the remainder of 789 4 23?

3.

What is the remainder of 6,423 4 23?

Lesson Quiz 1. Write 4,872 in expanded form using powers of 10 and exponents.

2. Write (5 3 104) 1 (7 3 103) 1 (8 3 102) 1 (4 3 100) in standard notation. © Harcourt

3. What is the exponent n needed to make this true; 7n 5 2,401 ? 4. Is 542,007 , or . 5 3 105 ? 5. Mercury is about 6 3 107 km from the sun, while Pluto is about 6 3 109 km from the sun. Write each distance in standard notation. Which planet is farther from the sun? How much farther?

Grade 6

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8/30/07 1:25:15 PM

1.7

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. A marathon is about 42,195 meters long. Write its length in expanded form with exponents in powers of 10. (4 3 104) 1 (2 3 103) 1 (1 3 102) 1 (9 3 101) 1 (5 3 100)

Spiral Review 1.

What is the remainder of 3,789 4 23? r 5 17

2.

What is the remainder of 789 4 23? r5 7 What is the remainder of 6,423 4 23? r5 6

3.

Lesson Quiz

© Harcourt

1. Write 4,872 in expanded form using powers of 10 and exponents. (4 3 1,000) 1 (8 3 100) 1 (7 3 10) 1 (2 3 1) 5 (4 3 103) 1 (8 3 102) 1 (7 3 101) 1 (2 3 100) 2. Write (5 3 104) 1 (7 3 103) 1 (8 3 102) 1 (4 3 100) in standard notation. 57,804 3. What is the exponent n needed to make this true; 7n 5 2,401 ? n5 4 4. Is 542,007 , or . 5 3 105 ? . 5. Mercury is about 6 3 107 km from the sun, while Pluto is about 6 3 109 km from the sun. Write each distance in standard notation. Which planet is farther from the sun? How much farther? 60,000,000; 6,000,000,000; Pluto is farther by 5,940,000,000 km.

Grade 6

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1.8

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 42 kilometers. Fill in the correct number in the numerical expression so that its value is 42: 18 4 j 3 3 1 42 1 52 2 23.

Spiral Review Write 63 find the 2. Write 25 find the 3. Write 33 find the

1.

as a product of factors. Then value. as a product of factors. Then value. as a product of factors. Then value.

Lesson Quiz © Harcourt

Evaluate the expression. 1. 42 2 3 3 2 5

3. 29 2 22 3 7 5

2. (42 2 3) 3 2 5

4. 42 4 7 3 3 5

5. There are 25 buses. Each bus will seat 32 students. 15 of the buses each have 3 empty seats, the rest have only 1 empty seat each. What is the total number of students on the buses? Grade 6

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8/31/07 9:15:05 AM

1.8

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 42 kilometers. Fill in the correct number in the numerical expression so that its value is 42: 18 4 j 3 3 1 42 1 52 2 23. 6

Spiral Review 1. 2. 3.

Write 63 find the Write 25 find the Write 33 find the

as a product of factors. Then value. 6 3 6 3 6 5 216 as a product of factors. Then value. 2 3 2 3 2 3 2 3 2 5 32 as a product of factors. Then value. 3 3 3 3 3 5 27

Lesson Quiz

© Harcourt

Evaluate the expression. 1. 42 2 3 3 2 5 10

3. 29 2 22 3 7 5 1

2. (42 2 3) 3 2 5 26

4. 42 4 7 3 3 5 18

5. There are 25 buses. Each bus will seat 32 students. 15 of the buses each have 3 empty seats, the rest have only 1 empty seat each. What is the total number of students on the buses? 15 3 (32 2 3) 1 10 3 (32 2 1) 5 745 Grade 6

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Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 26 miles. A runner ran the equivalent of seven marathon races last year during practice runs. Rewrite the expression 7 3 26 to show how the Distributive Property can help you multiply mentally.

Spiral Review 1. 12 1 2 3 33 4 9

2. 12 1 62 4 2 3 9

Lesson Quiz Find the value of n and name the property used. 1. n 1 23 5 23 1 72 2. 7(n 1 4) 5 (7 3 3) 1 (7 3 4) © Harcourt

3. 8 3 (9 × 4) 5 (8 3 n) 3 4 4. (42 3 92) 3 0 5 n 5. What property could you use to make the problem (7 3 87) 1 (7 3 13) easier to calculate? Explain.

Grade 6

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8/30/07 1:25:22 PM

1.9

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The approximate length of a marathon is 26 miles. A runner ran the equivalent of seven marathon races last year during practice runs. Rewrite the expression 7 3 26 to show how the Distributive Property can help you multiply mentally. 7 3 26 5 7 3 (20 1 6) 5 (7 3 20) 1 (7 3 6) 5 140 1 42 5 182

Spiral Review 1. 12 1 2 3 33 4 9 12 1 2 3 27 4 9 5 12 1 54 4 9 5 12 1 6 5 18

2. 12 1 62 4 2 3 9 12 1 36 4 2 3 9 5 12 1 18 3 9 5 12 1 162 5 174

Lesson Quiz Find the value of n and name the property used. 1. n 1 23 5 23 1 72 n 5 72, Commutative Property of addition 2. 7(n 1 4) 5 (7 3 3) 1 (7 3 4) n 5 3 Distributive Property © Harcourt

3. 8 3 (9 × 4) 5 (8 3 n) 3 4 n 5 9 Associative Property 4. (42 3 92) 3 0 5 n n 5 0 Zero Property of multiplication 5. What property could you use to make the problem (7 3 87) 1 (7 3 13) easier to calculate? Explain. The Distributive Property says that the expression is equivalent to 7 3 ( 87 1 13) 5 7 3 100. Grade 6

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Problem of the Day

1.10

Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is about 42,195 meters. In ancient Greece, the length of the original race was about 34,500 meters. Show how compensation can help you find the difference, in meters, between the length of a modern-day marathon and the original marathon.

Spiral Review 1. What property is illustrated by 3 3 (7 1 8) 5 (3 3 7) 1 (3 3 8)? 2. What property is illustrated by (8 1 7) 1 3 5 8 1 (7 1 3)

Lesson Quiz Name the property or strategy used to find the value. 1. 15 3 13 5 15 3 (10 1 3) 5 (15 3 10) 1 (15 3 3) 5 195 2. 25 3 15 3 4 5 25 3 4 3 15 5 1,500

3. Mary wrote out the following steps to solve the problem, 4 3 (23 3 2). Write the name of the property that justifies each step which is followed by a blank. © Harcourt

4 3 (23 3 2) 5 4 3 (2 3 23) ______________________ 5 (4 3 2) 3 23 _____________________ 5 8 3 23 5 8 3 (20 1 3) 5 (8 3 20) 1 (8 3 3) ____________________ 5 160 1 24 5 184

Grade 6

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8/30/07 1:25:26 PM

1.10

Problem of the Day Trent’s class followed the story of an astronaut who “ran” a marathon while she was in space. The length of a modern-day marathon is about 42,195 meters. In ancient Greece, the length of the original race was about 34,500 meters. Show how compensation can help you find the difference, in meters, between the length of a modern-day marathon and the original marathon. Possible answer: (42,195 1 500) 2 (34,500 1 500) 5 42,695 2 35,000 5 7,695

Spiral Review 1. What property is illustrated by 3 3 (7 1 8) 5 (3 3 7) 1 (3 3 8)? Distributive Property 2. What property is illustrated by (8 1 7) 1 3 5 8 1 (7 1 3) Associative Property

Lesson Quiz Name the property or strategy used to find the value. 1. 15 3 13 5 15 3 (10 1 3) 5 (15 3 10) 1 (15 3 3) 5 195 Distributive Property 2. 25 3 15 3 4 5 25 3 4 3 15 5 1,500 Commutative Property

3. Mary wrote out the following steps to solve the problem, 4 3 (23 3 2). Write the name of the property that justifies each step which is followed by a blank. Commutative Property 4 3 (23 3 2) 5 4 3 (2 3 23) ______________________ © Harcourt

Associative Property 5 (4 3 2) 3 23 _____________________

5 8 3 23 5 8 3 (20 1 3) Distributive Property 5 (8 3 20) 1 (8 3 3) ____________________

5 160 1 24 5 184

Grade 6

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2.1

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. Write each decimal in word form and expanded form. Which is greater, the height or the width?

Spiral Review Write in exponent form then simplify. 1. 5 3 5 3 5 2. 4 3 4 3. 3 3 3 3 3 3 3

Lesson Quiz 1. Write 1.628 in expanded form and in word form. 2. Compare these two numbers. Write ,, ., or 5 . 5.467 ___ 5.471 © Harcourt

3. Order from least to greatest: 86.541, 86.54, 86.411, 86.514 4. Order from greatest to least: 0.079, 0.81, 0.709, 0.081 5. For a game, David needs to find three decimals that are between 3.88 and 3.90. What could these three numbers be? List them in order from least to greatest.

Grade 6

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8/30/07 1:28:25 PM

2.1

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. Write each decimal in word form and expanded form. Which is greater, the height or the width? one and thirty-five hundredths; 1 1 0.3 1 0.05; one and seventy hundredths; 1 1 0.7 1 0.00; The width is greater.

Spiral Review Write in exponent form then simplify. 1. 5 3 5 3 5 53; 125 2. 4 3 4 42; 16 3. 3 3 3 3 3 3 3 34; 81

© Harcourt

Lesson Quiz 1. Write 1.628 in expanded form and in word form. 1 1 0.6 1 0.02 1 0.008; one and six hundred twenty-eight thousandths 2. Compare these two numbers. Write ,, ., or 5 . 5.467 ___ 5.471 , 3. Order from least to greatest: 86.541, 86.54, 86.411, 86.514 86.411, 86.514, 86.54, 86.541 4. Order from greatest to least: 0.079, 0.81, 0.709, 0.081 0.81, 0.709, 0.081, 0.079 5. For a game, David needs to find three decimals that are between 3.88 and 3.90. What could these three numbers be? List them in order from least to greatest. Possible Answer: 3.89, 3.891, 3.898 Grade 6

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Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. She wants to put a frame around it. Estimate the distance around the chalkboard.

Spiral Review 1. Write as a decimal number: twelve and twelve thousandths. 2. Write as a decimal number: one hundred five and five hundredths. 3. Write in words: 104.004.

Lesson Quiz Estimate and indicate your method of estimation. 1. 6.65 1 8.9 1 3.4

© Harcourt

2. 92.45 3 29.71 3. 236.8 ∏ 75.2 4. 88.12 2 71.3 5. Dylan is buying milk. A gallon of milk costs $2.89. Estimate the number of gallons of milk Dylan can buy if he has $15.25. Grade 6

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8/30/07 1:28:29 PM

2.2

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. She wants to put a frame around it. Estimate the distance around the chalkboard. 6 m

Spiral Review 1. Write as a decimal number: twelve and twelve thousandths. 12.012 2. Write as a decimal number: one hundred five and five hundredths. 105.05 3. Write in words: 104.004. one hundred four and four thousandths

Lesson Quiz Estimate and indicate your method of estimation. Sample answers are provided. 1. 6.65 1 8.9 1 3.4 19; rounded to the nearest ones place

© Harcourt

2. 92.45 3 29.71 2,700; used compatible numbers 3. 236.8 ∏ 75.2 3; used compatible numbers 4. 88.12 2 71.317; rounded to the nearest ones place 5. Dylan is buying milk. A gallon of milk costs $2.89. Estimate the number of gallons of milk Dylan can buy if he has $15.25.5 gallons; used compatible numbers Grade 6

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2.3

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. How much longer is the height of the chalkboard than the width?

Spiral Review Find the whole-number overestimation of the following sums: 1. $2.35 1 $3.90 5 about ____ 3. $1.76 1 $3.34 1 $4.45 5 about ____

2. $3.49 1 $12.75 5 about ____ 4. $2.76 1 $4.34 1 $5.45 5 about ____

Lesson Quiz Estimate. Then find the sum or difference.

© Harcourt

1. 4.8 2. 93.84 112 2 7.258 __ 0.61 86.582 __ 17.41

3. 21.06 0.273 1 9.2 __ 30.533

4. 13.059 2 0.92 __ 12.139

5. Jeremy bought 2.38 pounds of bananas and 0.907 pounds of cherries. How many more pounds of bananas did he buy than cherries?

Grade 6

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8/30/07 1:28:31 PM

2.3

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. How much longer is the height of the chalkboard than the width? 0.35 m

Spiral Review Find the whole-number overestimation of the following sums: 1. $2.35 1 $3.90 $7 5 about ____ 3. $1.76 1 $3.34 1 $4.45 5 about $11 ____

2. $3.49 1 $12.75 $17 5 about ____ 4. $2.76 1 $4.34 1 $5.45 5 about $14 ____

Lesson Quiz Estimate. Then find the sum or difference.

© Harcourt

1. 4.8 2. 93.84 3. 21.06 4. 13.059 112 0.273 2 7.258 2 0.92 __ __ 0.61 1 9.2 86.582 12.139 __ __ 87 17.41 12 30.533 18 30 5. Jeremy bought 2.38 pounds of bananas and 0.907 pounds of cherries. How many more pounds of bananas did he buy than cherries? 1 pound; 1.473 pounds Grade 6

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2.4

Problem of the Day Sarah is painting a chalkboard on her wall using chalkboard paint. The chalkboard will be 1.35 m tall and 1.70 m wide. What is the area of the chalkboard?

Spiral Review 1. 4.8 1 0.5 5 j

2. 4.8 1 5 5 j

3. 4.8 1 0.15 5 j

4. 4.8 1 1.5 5 j

Estimate. Then tell whether the given product is reasonable. 1. 0.821 3 19.3 5 1584.53

© Harcourt

2. 32.564 3 6.15 5 200.26860 Estimate. Then find the product. 3. 2.9 3 6.64

4. 0.67 3 3.29

5. Sharon worked 35.8 hours one week. If she makes $11.75 an hour, how much did she earn that week?

Grade 6

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8/30/07 1:28:33 PM

2.4

Problem of the Day Sarah is painting a chalkboard on her wall using chalkboard paint. The chalkboard will be 1.35 m tall and 1.70 m wide. What is the area of the chalkboard? 2.995 m2

Spiral Review 1. 4.8 1 0.5 5 j 5.3

2. 4.8 1 5 5 j 9.8

3. 4.8 1 0.15 5 j 4.95 4. 4.8 1 1.5 5 j 6.3

Lesson Quiz Estimate. Then tell whether the given product is reasonable.

© Harcourt

1. 0.821 3 19.3 5 1584.53 19; no, it is not reasonable, the correct answer is 15.8453 2. 32.564 3 6.15 5 200.26860 180; yes it is reasonable Estimate. Then find the product. 3. 2.9 3 6.64 21; 19.256

4. 0.67 3 3.29 3; 2.2043

5. Sharon worked 35.8 hours one week. If she makes $11.75 an hour, how much did she earn that week? Possible estimate: $400; $420.65

Grade 6

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2.5

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. She wants to buy color chalk for her chalkboard. A box of 6 pieces costs $1.25, a box of 10 pieces costs $1.60, and a box of 12 pieces costs $1.75. If she has $5.00 and wants to buy only one kind of box, what is the greatest number of boxes of each kind that she can buy?

Spiral Review Multiply. 1. 1.11 3 0.2

2. 0.05 3 0.255

3. $3.45 3 5

4. 1.7 3 1.7

Lesson Quiz Make a table to solve. A juice stand sells apple, cranberry, and orange juices. Apple juice costs $1.50, cranberry juice costs $2.00, and orange juice costs $1.75.

© Harcourt

1. Edward has $7.50. If he wants to buy only one type of juice, what is the greatest number of each type that he can buy?

2. Sam wants to buy orange or cranberry juice. He wants to buy as many juices as he can with $10.00. Will he be able to buy more cranberry or orange juices for $10.00? Explain.

Grade 6

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8/30/07 1:28:36 PM

2.5

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. She wants to buy color chalk for her chalkboard. A box of 6 pieces costs $1.25, a box of 10 pieces costs $1.60, and a box of 12 pieces costs $1.75. If she has $5.00 and wants to buy only one kind of box, what is the greatest number of boxes of each kind that she can buy? 4 boxes of 6 pieces or 3 boxes of 10 pieces or 2 boxes of 12 pieces

Spiral Review Multiply. 1. 1.11 3 0.2 0.222

2. 0.05 3 0.255 0.01275

3. $3.45 3 5 $17.25

4. 1.7 3 1.7 2.89

Lesson Quiz Make a table to solve. A juice stand sells apple, cranberry, and orange juices. Apple juice costs $1.50, cranberry juice costs $2.00, and orange juice costs $1.75. 1. Edward has $7.50. If he wants to buy only one type of juice, what is the greatest number of each type that he can buy? Juice Stand

© Harcourt

Number Apple Cranberry Orange 1 $1.50 $2.00 $1.75 2 $3.00 $4.00 $3.50 3 $4.50 $6.00 $5.25 4 $6.00 $8.00 $7.00 5 $7.50 $10.00 $8.75 5 apple juices, 3 strawberry juices, 4 orange juices

2. Sam wants to buy orange or cranberry juice. He wants to buy as many juices as he can with $10.00. Will he be able to buy more cranberry or orange juices for $10.00? Explain. He will be able to buy the same number of cranberry and orange juices for $10.00. Five cranberry juices cost exactly $10. Even though 5 orange juices cost $8.75, less than $10, he cannot buy 6 orange juices because that would cost more than $10.00. Grade 6

Daily Transparency DT2.5

2.6

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she divides the chalkboard into two equal sections, how wide will each section be?

Spiral Review Order the decimals from greatest to least. 1. 0.17, 0.071, 0.07, 0.007, 1.01 2. 0.45, 0.095, 0.4, 0.05, 0.5

Lesson Quiz

© Harcourt

Estimate. Then correctly place the decimal point in the quotient. 635 2009 50.8 28.126 1. 8qw 2. 14qw Estimate. Then find the quotient. 3. $234.16 ∏ 4

4. 15qw 4.005

5. Derek earned $99.45 for 13 hours of work. What was the average amount he earned per hour?

Grade 6

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2.6

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she divides the chalkboard into two equal sections, how wide will each section be? 0.85 m

Spiral Review Order the decimals from greatest to least. 1. 0.17, 0.071, 0.07, 0.007, 1.01 1.01, 0.17, 0.071, 0.07, 0.007 2. 0.45, 0.095, 0.4, 0.05, 0.5 0.5, 0.45, 0.4, 0.095, 0.05

Lesson Quiz

© Harcourt

Estimate. Then correctly place the decimal point in the quotient. Possible answers are given. 635 2009 50.8 6; 6.35 28.126 2; 2.009 1. 8qw 2. 14qw Estimate. Then find the quotient. Possible answers are given. 3. $234.16 ∏ 4 $60; $58.54

4. 15qw 4.005

0.3; 0.267

5. Derek earned $99.45 for 13 hours of work. What was the average amount he earned per hour? Estimate $10; exact answer $7.65 per hour Grade 6

Daily Transparency DT2.6

2.7

Problem of the Day Sarah painted a chalkboard on her wall. She spent a total of 5.25 hours working on the chalkboard. If she spent 1.75 hours painting the chalkboard each day, how many days did it take her?

Spiral Review 1. 22.8 4 3 5 j 3. 37.6 4 4 5 j

2. 57.26 4 7 5 j 4. 156.6 4 9 5 j

Lesson Quiz

© Harcourt

Use decimal squares to find the quotient. 1. 4.8 4 1.2

2. 1.68 4 0.56

3. 0.98 4 0.14

4. 5.16 4 0.86

5. A farmer sells peanuts in containers that hold 0.75 lb. How many containers are needed for 4.5 lb of peanuts?

Grade 6

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2.7

Problem of the Day Sarah painted a chalkboard on her wall. She spent a total of 5.25 hours working on the chalkboard. If she spent 1.75 hours painting the chalkboard each day, how many days did it take her? 3 days

Spiral Review 1. 22.8 4 3 5 j 7.6 2. 57.26 4 7 5 j 8.18 3. 37.6 4 4 5 j 9.4 4. 156.6 4 9 5 j 17.4

Lesson Quiz

© Harcourt

Use decimal squares to find the quotient. 1. 4.8 4 1.2 4

2. 1.68 4 0.56 3

3. 0.98 4 0.14 7

4. 5.16 4 0.86 6

5. A farmer sells peanuts in containers that hold 0.75 lb. How many containers are needed for 4.5 lb of peanuts? 6

Grade 6

Daily Transparency DT2.7

2.8

Problem of the Day Sarah painted a chalkboard on her wall. The chalkboard is 1.35 m tall and 1.70 m wide. She added a wood frame when it was finished. The total area of the frame and chalkboard is 2.52 m2. If the chalkboard and frame together are 1.8 m wide, what is their height?

Spiral Review 1. 3.2 4 0.8 5 j

2. 5.4 4 0.3 5 j

3. 4.5 4 0.3 5 j

4. 0.52 4 0.26 5 j

Lesson Quiz Place the decimal point in the quotient. 1. 14.78 4 0.5 = 2956 2. 3.048 4 6.35 = 48 © Harcourt

Find the quotient. 3. 6.8qw 2.04 4. 21.32 4 8.2 5. How long will it take a car traveling 67.8 miles

per hour to drive 162.72 miles? Grade 6

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8/30/07 1:28:44 PM

2.8

Problem of the Day Sarah painted a chalkboard on her wall. The chalkboard is 1.35 m tall and 1.70 m wide. She added a wood frame when it was finished. The total area of the frame and chalkboard is 2.52 m2. If the chalkboard and frame together are 1.8 m wide, what is their height? 1.4 m

Spiral Review 1. 3.2 4 0.8 5 j 4

2. 5.4 4 0.3 5 j 18

3. 4.5 4 0.3 5 j 15

4. 0.52 4 0.26 5 j 2

Lesson Quiz Place the decimal point in the quotient. 1. 14.78 4 0.5 = 2956 29.56 2. 3.048 4 6.35 = 48

0.48

© Harcourt

Find the quotient. 3. 6.8qw 2.04 0.3 4. 21.32 4 8.2 2.6 5. How long will it take a car traveling 67.8 miles

per hour to drive 162.72 miles? 2.4 hours Grade 6

Daily Transparency DT2.8

2.9

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If the can of paint will cover 5 m2, does she have enough paint? Explain.

Spiral Review Place the decimal point in the quotient. 1. 13.78 4 0.4 5 3445 2. 42.64 4 4.1 5 104

Lesson Quiz Determine whether an exact answer or an estimate is needed and solve.

© Harcourt

1. Alex runs marathons at about 4.8 miles per hour. About how many miles will he have run after 3 hours? 2. Talia cuts a piece of fabric that is 50 cm long into 4 smaller pieces. The lengths of 3 of the pieces are: 22.5 cm, 10.7 cm, and 6.7 cm. How long is the fourth piece? Grade 6

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8/30/07 1:28:46 PM

2.9

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If the can of paint will cover 5 m2, does she have enough paint? Explain. Yes; the area of the chalkboard is 2.295 m2, which is less than 5 m2.

Spiral Review Place the decimal point in the quotient. 1. 13.78 4 0.4 5 3445 34.45 2. 42.64 4 4.1 5 104 10.4

Lesson Quiz Determine whether an exact answer or an estimate is needed and solve.

© Harcourt

1. Alex runs marathons at about 4.8 miles per hour. About how many miles will he have run after 3 hours? Estimate; about 15 miles 2. Talia cuts a piece of fabric that is 50 cm long into 4 smaller pieces. The lengths of 3 of the pieces are: 22.5 cm, 10.7 cm, and 6.7 cm. How long is the fourth piece? Exact answer; 10.1 cm Grade 6

Daily Transparency DT2.9

Problem of the Day

2.10

Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she paid $15.00 for 0.5 gallon of paint, how much does 1 gallon of paint cost?

Spiral Review Is an estimate or an exact answer needed? 1. Arlina cut 3 kite strings each 3.8 m long from a 12 m piece of string. How much string does she have left over?

Lesson Quiz Solve using mental math, pencil and paper, or a calculator. 1. 25 3 8 3 10 © Harcourt

2. 12.5 2 1.25 3. 22.46 1 21.39 4. 0.8 4 0.32 5. Anna buys 3.25 yards of ribbon. The fabric costs $0.88 per yard. How much does Anna’s fabric cost?

Grade 6

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8/30/07 1:28:48 PM

2.10

Problem of the Day Sarah painted a chalkboard on her wall using chalkboard paint. The chalkboard is 1.35 m tall and 1.70 m wide. If she paid $15.00 for 0.5 gallon of paint, how much does 1 gallon of paint cost? $30.00

Spiral Review Is an estimate or an exact answer needed? 1. Arlina cut 3 kite strings each 3.8 m long from a 12 m piece of string. How much string does she have left over? exact answer

Lesson Quiz Solve using mental math, pencil and paper, or a calculator. 1. 25 3 8 3 10 2,000 © Harcourt

2. 12.5 2 1.25 11.25 3. 22.46 1 21.39 43.85 4. 0.8 4 0.32 2.5 5. Anna buys 3.25 yards of ribbon. The fabric costs $0.88 per yard. How much does Anna’s fabric cost? $2.86 Grade 6

Daily Transparency DT2.10

Unit 2 • Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged.

3

© Harcourt

A mantid egg case may contain as many as 400 eggs. Name 7 pairs of whole number factors of 400.

Sam is making bread. He will need to use 3 _ teaspoon of salt. Sam measured out the salt but 4 spilled 1_2 teaspoon of it. Draw a number line marked with 0 and 1 and place a point on the number line to indicate how much salt Sam has left.

4

The Delgados are fencing in a pasture on their farm. If the western and eastern borders are 1 7_8 mi long and southern and northern borders are 3_4 mi long. How many miles of fencing do they need? 1 7_8 1 1 7_8 1 3_4 1 3_4 5 5 1_4 miles.

5

Manny is preparing a dinner for his friends. He has 3 2_3 ice cream rolls and wants to be sure he has enough for everyone to receive 1_6 of a roll. He decides to express 3 2_3 as a fraction before he divides by 1_6 . What fraction can Manny use that is equivalent to 3 2_3 ?

6

Grade 6

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DT • Unit 2

8/30/07 2:42:58 PM

Unit 2 • Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged.

3

© Harcourt

A mantid egg case may contain as many as 400 eggs. Name 7 pairs of whole number factors of 400. Possible answer: 1 3 400, 2 3 200, 4 3 100, 5 3 80, 8 3 50, 10 3 40, 20 3 20

Sam is making bread. He will need to use 3 _ teaspoon of salt. Sam measured out the salt but 4 spilled 1_2 teaspoon of it. Draw a number line marked with 0 and 1 and place a point on the number line to indicate how much salt Sam has left. Check students’ number lines: 0 on left end; 1 on the right; line segment divided into fourths; point on 1_4 .

4

The Delgados are fencing in a pasture on their farm. If the western and eastern borders are 1 7_8 mi long and southern and northern borders are 3_4 mi long. How many miles of fencing do they need? 1 7_8 1 1 7_8 1 3_4 1 3_4 5 5 1_4 miles.

5

Manny is preparing a dinner for his friends. He has 3 2_3 ice cream rolls and wants to be sure he has enough for everyone to receive 1_6 of a roll. He decides to express 3 2_3 as a fraction before he divides by 1_6 . What fraction can Manny use that is equivalent __ to 3 2_3 ? 11 3

6

Grade 6

Daily Transparency DT • Unit 2

3.1

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The number 252 is divisible by which of the following: 2, 3, 4, 5, 6, 9, 10?

Spiral Review 1. 13.4 1 4.35 5 3. 3.3 3 0.2 5 5. 0.344 4 8 5

2. 3.4 2 2 5 4. 0.66 4 0.02 5 6. 0.03 3 0.02 5

Lesson Quiz

© Harcourt

Tell whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 or none of these. 1. 78

2. 288

3. 521

4. 745

5. A three-digit number is greater than 310, less than 370, a multiple of 7, and divisible by 2, 5, and 10. What is the number? Grade 6

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8/30/07 1:32:21 PM

3.1

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The number 252 is divisible by which of the following: 2, 3, 4, 5, 6, 9, 10? 2, 3, 4, 6, 9

Spiral Review 1. 13.4 1 4.35 5 17.75 2. 3.4 2 2 5 1.4 3. 3.3 3 0.2 5 0.66 4. 0.66 4 0.02 5 33 5. 0.344 4 8 5 0.043 6. 0.03 3 0.02 5 0.0006

Lesson Quiz

© Harcourt

Tell whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 or none of these. 1. 78 2, 3, 6

2. 288 2, 3, 4, 6, 8, 9

3. 521 none

4. 745 5

5. A three-digit number is greater than 310, less than 370, a multiple of 7, and divisible by 2, 5, and 10. What is the number? 350 Grade 6

Daily Transparency DT3.1

3.2

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. Is 252 a prime number, a composite number, or neither?

Spiral Review 1. How do the divisibility rules help you know that 1,484 is divisible by 4?

2. How do the divisibility rules help you know that 918 is divisible by 3?

Lesson Quiz

© Harcourt

Tell whether each number is prime, composite, or neither. 1. 37

2. 88

3. 1

4. 67

5. Of the numbers 29, 39, and 49, which one is not composite? Why?

Grade 6

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DT3.2

8/30/07 1:32:25 PM

3.2

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. Is 252 a prime number, a composite number, or neither? composite number

Spiral Review 1. How do the divisibility rules help you know that 1,484 is divisible by 4? The last two digits form the number 84 which is divisible by 4 (84 4 4 5 21). 2. How do the divisibility rules help you know that 918 is divisible by 3? The sum of the digits is divisible by 3 (9 1 1 1 8 5 18 and 1 1 8 5 9; 9 is divisible by 3.)

Lesson Quiz

© Harcourt

Tell whether each number is prime, composite, or neither. 1. 37 prime

2. 88 composite

3. 1 neither

4. 67 prime

5. Of the numbers 29, 39, and 49, which one is not composite? Why? 29 is the only prime number. Its only factors are 1 and 29. Grade 6

Daily Transparency DT3.2

3.3

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The product of which five prime numbers equals 252?

Spiral Review Tell whether each number is prime or composite. Then list the factors of the number. 1. 9 2. 17

Lesson Quiz © Harcourt

Write the prime factorization in exponent form. 1. 90

2. 75

3. 236

4. 588

5. What number has the prime factorization 2 x 3 x 5 x 72?

Grade 6

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8/30/07 1:32:27 PM

3.3

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. The product of which five prime numbers equals 252? 2, 2, 3, 3, 7

Spiral Review Tell whether each number is prime or composite. Then list the factors of the number. 1. 9 composite; 1, 3, 9 2. 17 prime; 1, 17

Lesson Quiz © Harcourt

Write the prime factorization in exponent form. 1. 90 2 x 32 x 5

2. 75 3 x 52

3. 236 22 x 59

4. 588 22 x 3 x 72

5. What number has the prime factorization 2 x 3 x 5 x 72? 1,470

Grade 6

Daily Transparency DT3.3

3.4

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. If another egg case hatched and 180 insects emerged, what is the greatest common factor of 252 and 180?

Spiral Review Write the prime factorization of each number, using exponents when possible. 1. 56 3. 51

2. 36 4. 100

Lesson Quiz Find the LCM.

© Harcourt

1. 10, 35

2. 6, 9, 27

Find the GCF. 3. 10, 45, 5

4. 14, 56, 112

5. The LCM of two numbers is 180. The GCF of the numbers is 9. What are the numbers?

Grade 6

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8/30/07 1:32:30 PM

3.4

Problem of the Day Amanda’s class is raising insects called mantids. One mantid egg case hatched and 252 insects emerged. If another egg case hatched and 180 insects emerged, what is the greatest common factor of 252 and 180? 36

Spiral Review Write the prime factorization of each number, using exponents when possible. 1. 56 23 3 7 3. 51 3 3 17

2. 36 22 3 32 4. 100 22 3 52

Lesson Quiz Find the LCM.

© Harcourt

1. 10, 35 70

2. 6, 9, 27 54

Find the GCF. 3. 10, 45, 5 5

4. 14, 56, 112 14

5. The LCM of two numbers is 180. The GCF of the numbers is 9. What are the numbers? Possible answers are 36 and 45. Grade 6

Daily Transparency DT3.4

3.5

Problem of the Day Amanda’s class is raising insects called mantids. The original number of eggs was a factor of 120. What might have been the original number of eggs?

Spiral Review Find the GCF and LCM of each set of numbers. 1. 6, 8, 18 2. 12, 20 GCF 5 __ GCF 5 __ LCM 5 __ LCM 5 __ 3. 7, 14, 56 4. 3, 6, 8 GCF 5 __ GCF 5 __ LCM 5 __ LCM 5 __

© Harcourt

Lesson Quiz 1. When Tyler was born, his grandfather gave him 15 classic baseball cards. For each birthday, his grandfather gave him 20 more cards. At what birthday did Tyler have more than 75 baseball cards? 2. Betty has 40¢ in collectible coins. None of the coins are pennies. How many different groups of coins totaling 40¢ can Betty have?

Grade 6

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Daily Transparency

DT3.5

8/30/07 1:32:33 PM

3.5

Problem of the Day Amanda’s class is raising insects called mantids. The original number of eggs was a factor of 120. What might have been the original number of eggs? 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Spiral Review Find the GCF and LCM of each set of numbers. 1. 6, 8, 18 2. 12, 20 2 4 GCF 5 __ GCF 5 __ 72 LCM 5 __ LCM 5 60 __ 3. 7, 14, 56 4. 3, 6, 8 7 1 GCF 5 __ GCF 5 __ 56 LCM 5 __ LCM 5 24 __

© Harcourt

Lesson Quiz 1. When Tyler was born, his grandfather gave him 15 classic baseball cards. For each birthday, his grandfather gave him 20 more cards. At what birthday did Tyler have more than 75 baseball cards? third 2. Betty has 40¢ in collectible coins. None of the coins are pennies. How many different groups of coins totaling 40¢ can Betty have? 7

Grade 6

Daily Transparency DT3.5

4.1

Problem of the Day Sam is making bread. He will need to use 3_4 teaspoon of salt. How could you represent 3_4 using a number line from 0 to 1? Draw a number line marked with 0 and 1.

Spiral Review Find the LCM and GCF for the following numbers: 1. 12, 6, 10 LCM 5 j

GCF 5 j

2. 6, 12, 18 LCM 5 j

GCF 5 j

Lesson Quiz

© Harcourt

Draw a model to represent the fraction. 1. 1_5

5 2. __ 10

3. _49

4. 68_

5. At an archaeological dig, 2_5 of the workers are volunteers and the remaining workers are professionals. What fraction of the workers are professionals?

Grade 6

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8/30/07 1:43:43 PM

4.1

Problem of the Day Sam is making bread. He will need to use 3_4 teaspoon of salt. How could you represent 3_4 using a number line from 0 to 1? Draw a number line marked with 0 and 1. 0

3 4

1

Spiral Review Find the LCM and GCF for the following numbers: 1. 12, 6, 10 LCM 5 j 60 GCF 5 j 2 2. 6, 12, 18 LCM 5 j 36 GCF 5 j 6

Lesson Quiz Draw a model to represent the fraction. Answers may vary. 5 2. __ 1. 1_5 10 © Harcourt

3. _49

4. _68

5. At an archaeological dig, 2_5 of the workers are volunteers and the remaining workers are professionals. What fraction of the workers are professionals? 3_5 Grade 6

Daily Transparency DT4.1

4.2

Problem of the Day Sam is making bread. Sam needs 2 _ teaspoon ground cinnamon. Sam 4 has a 1_4 teaspoon measure and a 1 _ teaspoon measure. How could he 2 use either measuring spoon?

Spiral Review 1. Is 27 prime or composite? 2. Is 53 prime or composite? 3. Is 51 prime or composite?

Lesson Quiz Complete. 4 28 __ 1. __ j 5 49

j 3 __ 2. ___ 160 5 20

© Harcourt

Write the fraction in simplest form. __ 3. 18 27

__ 4. 45 65

5. Tran has 6 heirloom tomato plants, 5 cherry tomato plants, and 7 yellow tomato plants. What fraction of his tomato plants are heirloom tomato plants? Write your answer in simplest form.

Grade 6

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8/30/07 1:43:47 PM

4.2

Problem of the Day Sam is making bread. Sam needs 2 _ teaspoon ground cinnamon. Sam 4 has a 1_4 teaspoon measure and a 1 _ teaspoon measure. How could he 2 use either measuring spoon? Two scoops with the 1_4 teaspoon measure or one scoop with the 21_ teaspoon measure because 2_4 5 21_ .

Spiral Review 1. Is 27 prime or composite? composite 2. Is 53 prime or composite? prime 3. Is 51 prime or composite? composite

Lesson Quiz Complete. 4 28 __ 1. __ j 5 49 7

j 3 __ 2. ___ 160 5 20 24

© Harcourt

Write the fraction in simplest form. 2 18 _ 3. __ 27 3

9 45 __ 4. __ 65 13

5. Tran has 6 heirloom tomato plants, 5 cherry tomato plants, and 7 yellow tomato plants. What fraction of his tomato plants are heirloom tomato plants? Write your answer in simplest form. 1_3 Grade 6

Daily Transparency DT4.2

4.3

Problem of the Day Sam is making bread. Sam will need 5_2 pounds of whole wheat flour. What is 52_ written as a mixed number?

Spiral Review Write the fraction in simplest form. __ 1. 21 27

__ 2. 35 14

16 3. __ 48

40 4. __ 16

Lesson Quiz Write the mixed number as a fraction. 1. 3 1_5

2. 2 7_8

© Harcourt

Write the fraction as a mixed number in simplest form. 21 3. __ 4

22 4. __ 6

5. A cheese wedge weighs 25 ounces. Write the weight in pounds as a fraction and as a mixed number. Note that 1 pound 5 16 ounces. Grade 6

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8/30/07 1:43:50 PM

4.3

Problem of the Day Sam is making bread. Sam will need 5_2 pounds of whole wheat flour. What is 5_2 written as a mixed number? 2 1_2

Spiral Review Write the fraction in simplest form. 21 __ 1. 27

7 _ 9

35 __ 2 1_ 2. 14 2

16 __ 3. 48

1 _ 3

40 __ 2 1_ 4. 16 2

Lesson Quiz Write the mixed number as a fraction. 16 1. 3 1_5 __ 5

23 2. 2 78_ __ 8

© Harcourt

Write the fraction as a mixed number in simplest form. __ 5 1_ 3. 21 4 4

__ 3 2_ 4. 22 3 6

5. A cheese wedge weighs 25 ounces. Write the weight in pounds as a fraction and as a mixed 9 __ ; 1 __ number. Note that 1 pound 5 16 ounces. 25 16 16 Grade 6

Daily Transparency DT4.3

4.4

Problem of the Day Sam is baking bread. He needs 3 _ pound of bread flour. Sam's 4 scale expresses weight in decimals. Rename the weight of the flour as a decimal.

Spiral Review Write each fraction as a mixed number in simplest form: 1. twenty-three fourths 2. thirty-two sixths

Lesson Quiz Write as a fraction or mixed number in simplest form. 1. 1.4

2. 0.675

Write as a decimal. Tell whether the decimal terminates or repeats.

© Harcourt

2 3. __ 11

5. During basketball practice, Francie made a basket on 0.6 of her free throws. Charmian made a 7 basket on __ 12 of her free throws. Which girl was more successful in making free throws? Explain.

Grade 6

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9 4. __ 40

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DT4.4

8/30/07 1:43:52 PM

4.4

Problem of the Day Sam is baking bread. He needs 3 _ pound of bread flour. Sam's 4 scale expresses weight in decimals. Rename the weight of the flour as a decimal. 0.75

Spiral Review Write each fraction as a mixed number in simplest form: 1. twenty-three fourths 5 3_4 2. thirty-two sixths 5 1_3

Lesson Quiz Write as a fraction or mixed number in simplest form. 1. 1.4 1 2_5

2. 0.675 _58

Write as a decimal. Tell whether the decimal terminates or repeats. 3. repeats 4. terminates

© Harcourt

2 3. __ 11 0.18181818…

9 0.225 4. __ 40

5. During basketball practice, Francie made a basket on 0.6 of her free throws. Charmian made a 7 basket on __ 12 of her free throws. Which girl was more successful in making free throws? Explain. 7 Francie; Charmian made __ 12 or about 0.583 of her free throws. 0.6 . 0.583 Grade 6

Daily Transparency DT4.4

4.5

Problem of the Day Sam is making bread. He has decided to give away 25% of the bread he makes. What is 25% written as a fraction?

Spiral Review Write each fraction as a terminating or repeating decimal. Does it terminate or repeat? 1. _78

2. _79

Lesson Quiz 1. Copy and complete the table. Write each fraction in simplest form.

© Harcourt

Fraction

Decimal 0.6

Percent

7 __ 50

2. Twelve percent of the students have more than one middle name. What fraction of students have more than one middle name?

Grade 6

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DT4.5

8/31/07 9:00:56 AM

4.5

Problem of the Day Sam is making bread. He has decided to give away 25% of the bread he makes. What is 25% written as a ? 5 ___ 25 1 ___ _ fraction? 25% 5 100 100 5 4

Spiral Review Write each fraction as a terminating or repeating decimal. Does it terminate or repeat? 1. 7_8 0.875; terminates 2. 7_9 0.7; repeats

Lesson Quiz 1. Copy and complete the table. Write each fraction in simplest form. Fraction © Harcourt

_3 5 7 __ 50

Decimal 0.6

Percent 60%

0.14

14%

2. Twelve percent of the students have more than one middle name. What fraction of students 3 have more than one middle name? __ 25 Grade 6

Daily Transparency DT4.5

4.6

Problem of the Day Sam is making bread. Which ingredient amount is greater, 3 _ teaspoon cinnamon or 0.5 4 teaspoon ground cloves? Locate the two amounts on the number line labeled 0 to 1. 0

1

Spiral Review Compare. Use ., ,, or 5. 1. 0.4 ____ 7%

2. 0.89 ____ 1

3. 20% ____ _15

4. 3_4 ____ _57

Lesson Quiz Compare. Write , or = for each ___. 1. 5_6 __ 85%

8 _2 2. __ 20 __ 5

Order from least to greatest. 1 3. 16%, __ 10 , 0.09

© Harcourt

Find all possible whole number values for x that make the statement true. __ 4. 8_x 5 16 36

5. Two farmers both plan to grow 100 acres of sunflowers. Farmer A has planted 80% of his 100 acres. Farmer B has __ of his 100 acres. Which farmer has planted planted 19 20 more acres? Show the comparison using symbols.

Grade 6

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4.6

Problem of the Day Sam is making bread. Which ingredient amount is greater, 3 _ teaspoon cinnamon or 0.5 4 teaspoon ground cloves? 3_4 teaspoon Locate the two amounts on the number line labeled 0 to 1. 0.5

0

3 4

1

Spiral Review Compare. Use ., ,, or 5. 1. 0.4 ____ 7% .

2. 0.89 ____ 1 ,

3. 20% ____ 15_ 5

4. 3_4 ____ 5_7 .

Lesson Quiz Compare. Write , or = for each ___. 1. 5_6 __ 85% ,

8 2 _ 2. __ 20 __ 5 5

Order from least to greatest. 1 , 0.09 1 , 16% __ __ 3. 16%, 10 0.09, 10

© Harcourt

Find all possible whole number values for x that make the statement true. __ x 5 18 4. 8_x 5 16 36

5. Two farmers both plan to grow 100 acres of sunflowers. Farmer A has planted 80% of his 100 acres. Farmer B has __ of his 100 acres. Which farmer has planted planted 19 20 more acres? Show the comparison using symbols. __ Farmer B; 80% , 19 20 Grade 6

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4.7

Problem of the Day Sam is making bread. He compares his recipe to one he found online. Which recipe uses more butter? Sam’s Recipe 5 eggs

Online Recipe 4 eggs

1 1_4 cups butter

1.375 cups butter

Spiral Review

Compare. Use ., ,, or 5. 1. 3_5 ___ 0.6

2. 5_8 ___ _46

3. 2_3 ___ 0.6

4. 2_3 ___ _25

Lesson Quiz For 1–2, use the table.

© Harcourt

Tree Height (meters) Year Tree A Tree B 1 1.5 1 1_3 2

1.8

1 7_8

1. Which tree was taller in Year 1? 2. Which tree grew more by Year 2? Grade 6

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4.7

Problem of the Day Sam is making bread. He compares his recipe to one he found online. Which recipe uses more butter? The online recipe Sam’s Recipe 5 eggs

Online Recipe 4 eggs

1 1_4 cups butter

1.375 cups butter

Spiral Review Compare. Use ., ,, or 5. 1. 3_5 ___ 0.6 5

2. 5_8 ___ 4_6 ,

3. 2_3 ___ 0.6 .

4. 2_3 ___ 2_5 .

Lesson Quiz For 1–2, use the table.

© Harcourt

Tree Height (meters) Year Tree A Tree B 1 1.5 1 1_3 2

1.8

1 7_8

1. Which tree was taller in Year 1? Tree A 2. Which tree grew more by Year 2? Tree B Grade 6

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5.1

Problem of the Day The Delgados are fencing in a pasture on their farm. A tree growing along the western border of the pasture is 1_8 mi 9 from one corner and __ 10 mi from the other corner. About how far is it from one corner to the other? Round the fractions to help you estimate 1 9 _ 1 __ 8 10 .

0

1

2

Spiral Review Compare. Replace ____ with ,, ., or 5. 1. 0.4 ___ 7%

2. 3_4 ___ _57

3. 0.89 ___ 1

4. 20% ___ _15

Lesson Quiz Estimate the sum or difference. 2 1 __ 1. __ 18 2 10

2. 3 6_8 1 2 _47

Estimate to compare. Write , or ..

© Harcourt

1 3. 7_8 1 4 __ 12 __ 6

8 4. 6 3_5 2 2 __ 15 __ 3

In problem 5 below, tell whether an overestimate or an underestimate is needed. Solve. 5. Jim needs 9 cups of apples for a mile-high apple pie recipe. He measures the sliced apples in four batches. The batches measure 3 1_8 c, 1 2_3 c, 2 1_4 c, and 3 1_3 c. Estimate the total amount of apples. Does Jim have enough for his recipe?

Grade 6

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5.1

Problem of the Day The Delgados are fencing in a pasture on their farm. A tree growing along the western border of the pasture is 1_8 mi 9 from one corner and __ 10 mi from the other corner. About how far is it from one corner to the other? Round the fractions to help you estimate 1 9 _ 1 __ 8 10 . 1 8

9 10

0

1

2

Spiral Review Compare. Replace ____ with ,, ., or 5. 1. 0.4 ___ 7% .

2. 3_4 ___ 5_7 ,

3. 0.89 ___ 1 ,

4. 20% ___ 1_5 5

Lesson Quiz Estimate the sum or difference. Possible answers are shown. 2 1 __ 1. __ 18 2 10 0

2. 3 6_8 1 2 4_7 6 1_2

Estimate to compare. Write , or ..

© Harcourt

1 __ 6 __ 3. 7_8 1 4 12 ,

8 . 4. 6 3_5 2 2 __ 15 __ 3

In problem 5 below, tell whether an overestimate or an underestimate is needed. Solve. 5. Jim needs 9 cups of apples for a mile-high apple pie recipe. He measures the sliced apples in four batches. The batches measure 3 1_8 c, 1 2_3 c, 2 1_4 c, and 3 1_3 c. Estimate the total amount of apples. Does Jim have enough for his recipe? underestimate; 9 c of apples; yes Grade 6

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Problem of the Day The Delgados are fencing in a pasture on their farm. The eastern border is 2_5 mi long. The western border is 1_3 mi long. How many miles of fencing do the Delgados need for the eastern and western borders of the pasture? Use fraction bars to solve.

Spiral Review 1. 8_9 1 _58

7 _3 2. __ 15 1 5

3. 3 7_8 2 1 4_9

4. 8_9 2 2_5

Lesson Quiz Use a common denominator to rewrite the problem using equivalent fractions. 1 1. 2_3 1 __ 10

__ 2 _1 2. 16 21 6

© Harcourt

Estimate. Then write the sum or difference in simplest form. 3.

1 _78

4. 6_7 2 _13

5. In a neighborhood, 1_8 of the houses have finished basements. Half of the houses have full, unfinished basements. Another 1 _ of the houses have partial, unfinished basements. The rest of 4 the houses have no basement at all. How many houses in the neighborhood do not have a basement?

Grade 6

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5.2

Problem of the Day The Delgados are fencing in a pasture on their farm. The eastern border is 2_5 mi long. The western border is 1_3 mi long. How many miles of fencing do the Delgados need for the eastern and western borders of the __ pasture? 11 15 Use fraction bars to solve.

Spiral Review 1. 8_9 1 5_8 1 1_2

7 3 _ 2. __ 15 1 5 1

3. 3 7_8 2 1 4_9 2 21_

4. 8_9 2 _25

_1 2

Lesson Quiz Use a common denominator to rewrite the problem using equivalent fractions. 1 1. 2_3 1 __ 10

20 __ 30

1

3 __ 30

__ 2 _1 2. 16 21 6

32 __ 42

2

7 __ 42

© Harcourt

Estimate. Then write the sum or difference in simplest form. 3.

3 _ 5

__ 1 7_8 1 1_2 ; 1 19 40

4. 6_7 2 1_3 1_2 ;

11 __ 21

5. In a neighborhood, 1_8 of the houses have finished basements. Half of the houses have full, unfinished basements. Another 1 _ of the houses have partial, unfinished basements. The rest of 4 the houses have no basement at all. How many houses in the neighborhood do not have a basement? 1_8 Grade 6

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Problem of the Day The Delgados are fencing in a pasture on their farm. The northern section of the fence will be 1 1_8 mi long. It will connect with a fence that measures 2 1_2 mi. What is the total length of the two sections of fence? 8

1 81 221

Spiral Review Write the sum or difference in simplest form. 1. 1_3 1 _16

7 _1 2. __ 10 2 5

3. 6_7 1 1_3

4. 5_9 2 _13

Lesson Quiz

© Harcourt

Write the sum or difference in simplest form. 1. 2 1_5 1 3 _12

__ 2 2 _3 2. 5 17 20 4

3. 14 7_8 2 11 1_3

4. 5 1_3 1 3 3_4

5. Sandi ran 6 1_3 miles on Saturday. Her friend Janelle ran 1 1_8 miles farther. How far did Janelle run?

Grade 6

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5.3

Problem of the Day The Delgados are fencing in a pasture on their farm. The northern section of the fence will be 1 1_8 mi long. It will connect with a fence that measures 2 1_2 mi. What is the total length of the two sections of fence? 3 5_8 mi 8

1 81 221

Spiral Review Write the sum or difference in simplest form. 1. 1_3 1 _16 _12

7 _1 _1 2. __ 10 2 5 2

4 3. 6_7 1 1_3 1 __ 21

4. 5_9 2 _13 2_9

Lesson Quiz

© Harcourt

Write the sum or difference in simplest form. 7 1. 2 1_5 1 3 1_2 5 __ 10

1 __ 2 2 3_ 3 __ 2. 5 17 10 20 4

13 __ 3. 14 7_8 2 11 1_3 3 24

1 __ 4. 5 1_3 1 3 34_ 9 12

5. Sandi ran 6 1_3 miles on Saturday. Her friend Janelle ran 1 1_8 miles farther. How far did __ mi Janelle run? 7 11 24

Grade 6

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5.4

Problem of the Day The Delgados are fencing in a pasture on their farm. When they are finished, 3 5_8 mi along the northern border of their farm will be fenced. The north side of their property is 5 mi long. How many miles will be unfenced? Use fraction bars to solve the problem.

Spiral Review 1. 7_8 2 _14

9 _2 2. __ 10 2 5

3. 3_4 2 _16

4. 5_8 2 _14

Lesson Quiz

© Harcourt

Use fraction bars to find the difference. Write the answer in simplest form. 1. 4 2 3 _14

2. 5 2 1 _45

3. 4 1_3 2 2 _23

4. 2 1_2 2 1 _78

5. 5 2 2 _13

Grade 6

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5.4

Problem of the Day The Delgados are fencing in a pasture on their farm. When they are finished, 3 58_ mi along the northern border of their farm will be fenced. The north side of their property is 5 mi long. How many miles will be unfenced? 1 3_8 Use fraction bars to solve the problem.

Spiral Review 1. 7_8 2 _14 _58

9 2 _ 2. __ 10 2 5

7 3. 3_4 2 _16 __ 12

4. 5_8 2

5 __ 10 1 _ 3_ 4 8

or

1 _ 2

Lesson Quiz

© Harcourt

Use fraction bars to find the difference. Write the answer in simplest form. 1. 4 2 3 _14 _34

2. 5 2 1 4_5 3 1_5

3. 4 1_3 2 2 2_3 1 2_3

4. 2 1_2 2 1 78_ _58

5. 5 2 2 1_3 2 2_3

Grade 6

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Problem of the Day The Delgados are fencing in a pasture on their farm. The total length of the fence will be 7 1_8 mi. The combined lengths of the northern, eastern, and western borders of the fence is 4 1_4 mi. How long, in miles, is the southern border of the fence?

Spiral Review What fraction bars can you use to rename 6 1_3 ?

Lesson Quiz

© Harcourt

Estimate. Then write the difference in simplest form. 1. 5 1_2 2 3 _78

2. 10 2_5 2 3 _23

3. 8 2 6 _47

3 _3 4. 6 __ 10 2 2 4

5. The door to Leo’s room is 32 1_8 inches wide. The door to his closet is 29 3_4 inches wide. How much wider is the door to his room?

Grade 6

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5.5

Problem of the Day The Delgados are fencing in a pasture on their farm. The total length of the fence will be 7 1_8 mi. The combined lengths of the northern, eastern, and western borders of the fence is 4 1_4 mi. How long, in miles, is the southern border of the fence? 2 7_8 mi

Spiral Review What fraction bars can you use to rename 6 1_3 ? Possible answers: five whole and four 1_3 bars or nineteen 13_ bars

Lesson Quiz Estimate. Then write the difference in simplest form. Possible estimates shown. © Harcourt

1. 5 1_2 2 3 7_8 1 1_2 ; 1 85_ 3. 8 2 6 _47

1 1_2 ; 1 3_7

__ 2. 10 2_5 2 3 2_3 7; 6 11 15 3 3 __ _ 3 1_ ; 3 11 4. 6 __ 2 20 10 2 2 4

5. The door to Leo’s room is 32 1_8 inches wide. The door to his closet is 29 3_4 inches wide. How much wider is the door to his room? 2 3_8 in. Grade 6

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5.6

Problem of the Day The Delgados are fencing in a pasture on their farm. They purchase 3 miles of fencing. The northern and southern borders of the pasture each measure 1 1_8 mi. The eastern border measures 2 _ mi; the western, 1_ mi. 5 3 After fencing the northern and southern borders, will the Delgados have enough fencing left over for both the eastern and western border? Explain.

Spiral Review 1. 3 1_3 2 11_4

2. 12 1_3 2 9 2_3

3. 5 2 1_14

4. 2 2 _23

Lesson Quiz © Harcourt

1. Mark has 1 5_8 lb flour. He needs 7_8 for muffins. Is there enough left for a second recipe that calls for 1_2 lb? Explain. 2. If 5_8 of a lot is occupied by the house and 1 driveway and __ 10 is occupied by a deck, how much is left for the yard?

Grade 6

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8/30/07 1:41:46 PM

5.6

Problem of the Day The Delgados are fencing in a pasture on their farm. They purchase 3 miles of fencing. The northern and southern borders of the pasture each measure 1 1_8 mi. The eastern border measures 2 _ mi; the western, 1_ mi. 5 3 After fencing the northern and southern borders, will the Delgados have enough fencing left over for both the eastern and western border? Explain. Yes. Possible 2 _ explanation: 3 2 2 1_4 5 2_4 and 2_4 . 5 1 1_3

Spiral Review 1 __ 1. 3 1_3 2 11_4 2 12

2. 12 1_3 2 9 2_3 2 2_3

3. 5 2 1_14 3 3_ 4

4. 2 2 2_3 1 1_3

Lesson Quiz © Harcourt

1. Mark has 1 5_8 lb flour. He needs 7_8 for muffins. Is there enough left for a second recipe that calls for 1_2 lb? Explain. Yes, there is 3_4 lb left and 3_4 . 1_2 . 2. If 5_8 of a lot is occupied by the house and 1 driveway and __ 10 is occupied by a deck, how much __ is left for the yard? 11 40

Grade 6

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5.7

Problem of the Day The Delgados are fencing in a pasture on their farm. The Masons’ farm is 3 3_4 mi down the road from the Delgados’ farm. The Bergens’ farm is 1 1_2 miles farther down the road. How far is the Bergens’ farm from the Delgados’ farm?

Spiral Review 1. 8 2 5 _13

2. 3 2_3 1 3 _14

Lesson Quiz Write the sum or difference in simplest form. __ 1 _3 1. 11 20 5

1 2. 85_ 2 __ 12

3. 2 2_3 1 3 5_6 1 _12

4. 8 2 (2 1_5 1 1 3_4 )

© Harcourt

Solve. Then explain how you solved the problem. 5. On Saturday, Parker drove 2 41_ hours to the ski park. Then he skied for 4 1_2 hours. His drive back took 2 3_4 hours because of traffic. Did Parker spend more time driving or skiing on Saturday? Explain.

Grade 6

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8/30/07 1:41:49 PM

5.7

Problem of the Day The Delgados are fencing in a pasture on their farm. The Masons’ farm is 3 3_4 mi down the road from the Delgados’ farm. The Bergens’ farm is 1 1_2 miles farther down the road. How far is the Bergens’ farm from the Delgados’ farm? 5 1_4 mi

Spiral Review 1. 8 2 5 1_3 2 2_3

__ 2. 3 2_3 1 3 1_4 6 11 12

Lesson Quiz Write the sum or difference in simplest form. __ 1 3_ 1 __ 3 1. 11 20 5 20

__ 1 13 __ 2. 5_8 2 12 24

3. 2 2_3 1 3 5_6 1 1_2 7

1 __ 4. 8 2 (2 1_5 1 1 3_4 ) 4 20

© Harcourt

Solve. Then explain how you solved the problem. 5. On Saturday, Parker drove 2 1_4 hours to the ski park. Then he skied for 4 1_2 hours. His drive back took 2 3_4 hours because of traffic. Did Parker spend more time driving or skiing on Saturday? Explain. He spent more time driving on Saturday. Parker’s total driving time was 2 1_4 1 2 3_4 5 4 44_ or 5 hours and 5 . 4 1_2 . Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He has 8 cups of rice. If one serving of rice is 7_8 cup, about how many servings of rice does he have?

Spiral Review Round each fraction to 0, 1_2 , or 1. 1 1. __ 16

7 __ 4. 12

2. _38

5. 7_1

3. _79

6. 5_4

Lesson Quiz

© Harcourt

Estimate the product or quotient. 1. 7 3_7 4 _49

2. 4 2_3 3 5 _14

3. 17 7_8 4 6 _16

4. 3_5 3 10

5. A bike trail is 3 3_4 miles long. Mariah rode around the trail 4 times. About how many miles did Mariah ride?

Grade 6

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6.1

Problem of the Day Manny is preparing a dinner for his friends. He has 8 cups of rice. If one serving of rice is 7_8 cup, about how many servings of rice does he have? Round 7_8 to 1. Manny has about 8 4 1, or 8 servings.

Spiral Review Round each fraction to 0, 12_ , or 1. 1 1. __ 16

0

7 __ 4. 12

2. 3_8

1 _ 2

5. 7_1 0

3. 7_9

1

6. 54_ 1

1 _ 2

Lesson Quiz

© Harcourt

Estimate the product or quotient. Possible estimates shown. 1. 7 3_7 4 4_9 14

2. 4 2_3 3 5 14_ 25

3. 17 7_8 4 6 1_6 3

4. 53_ 3 10 5

5. A bike trail is 3 3_4 miles long. Mariah rode around the trail 4 times. About how many miles did Mariah ride? 16

Grade 6

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6.2

Problem of the Day Manny is preparing a dinner for his friends. He buys 3_4 lb of cheese. He serves 1_2 of the cheese with crackers. How much cheese did he serve with crackers?

Spiral Review Estimate the product or quotient. 1. 4_7 3 12

4. 23 7_8 4 5 _56

2. 10 4 _38

5. 3 1_3 3 3 _13

9 3 _ 3. 22 __ 10 4 8 8

6. 3_8 3 _58

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 1. 1_2 3 _37

2. 3_5 3 _14

3. 21 3 _23

3 4. 8_9 3 __ 16

5. Lanny rode 7_8 of a bike trail. Nelida rode 1_3 of Lanny’s distance. What fraction of the bike trail did Nelida ride?

Grade 6

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6.2

Problem of the Day Manny is preparing a dinner for his friends. He buys 3_4 lb of cheese. He serves 1_2 of the cheese with crackers. How much cheese did he serve with crackers? 1_2 3 3_4 5 3_8 ; He served 3_8 lb of cheese with crackers.

Spiral Review Estimate the product or quotient. 1. 4_7 3 12 ¯ 6

4. 23 7_8 4 5 5_6 ¯ 4

2. 10 4 3_8 ¯ 20

5. 3 1_3 3 3 1_3 ¯ 9

9 3 _ 3. 22 __ 10 4 8 8 ¯ 3

6. 3_8 3 5_8 ¯ _14

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 3 1. 1_2 3 3_7 __ 14

3 2. 53_ 3 _14 __ 20

3. 21 3 2_3 14

1 3 _ __ 4. 8_9 3 16 6

5. Lanny rode 7_8 of a bike trail. Nelida rode 1_3 of Lanny’s distance. What fraction of the bike trail 7 did Nelida ride? __ 24 Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He made 3 1_2 bowls of spaghetti sauce. If each bowl holds 1 1_4 quarts, how much sauce did Manny make?

Spiral Review Find the product. Write it in simplest form. 1. 5_7 3 _12

4. 2_9 3 _23

2. 1_5 3 3

5. 39 3 _23

3 3. 5_6 3 __ 10

6. 1_5 3 _58

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 1. 1 1_4 3 2 2_3

2. 5 3 2 1_3

3. 4_5 3 4 _38

4. 3 6_7 3 3 _19

5. Kelly drank 1 7_8 pints of juice. Ralph drank 2 1_5 times as much juice as Kelly. How much juice did Ralph drink?

Grade 6

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6.3

Problem of the Day Manny is preparing a dinner for his friends. He made 3 1_2 bowls of spaghetti sauce. If each bowl holds 1 1_4 quarts, how much sauce did Manny make? Multiply 3 1__2 3 1 1__4 5 7 __ 5 35 3 __ ___ __ 2 3 4 5 8 5 4 8 . Manny made 4 3_8 quarts of spaghetti sauce.

Spiral Review Find the product. Write it in simplest form. 1. 5_7 3 1_2

4. 2_9 3 _23

2. 1_5 3 3

5 __ 14 3 _ 5

3 3. 5_6 3 __ 10

1 _ 4

6. 1_5 3 5_8

4 __ 27

5. 39 3 2_3 26 1 _ 8

Lesson Quiz

© Harcourt

Find the product. Write it in simplest form. 1. 1 1_4 3 2 2_3 3 1_3

2. 5 3 2 13_ 11 2_3

3. 4_5 3 4 3_8 3 1_2

4. 3 67_ 3 3 1_9 12

5. Kelly drank 1 78_ pints of juice. Ralph drank 2 1_5 times as much juice as Kelly. How much juice did Ralph drink? 4 1_8 pints Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He makes 2 cups of vegetable dip for an appetizer. Each serving is 1_2 cup. Use a model to find the total number of servings.

Spiral Review 1. 2_5 3 _57

3 2. 5_6 3 __ 10

3. 1 1_2 3 1_3

4. 1 1_2 3 1 1_2

5. 9 3 2 1_4

6. 1_3 3 16

Lesson Quiz

© Harcourt

Find the quotient. Write it in simplest form. 2. 2_5 4 _13

3. 3_8 4 _45

4. 6 4 _19

__ lb of sunflower seeds 5. Vivian wants to divide 15 16 into bags that each contain 1_8 lb of sunflower seeds. How many 1_8 -lb bags can she make?

Grade 6

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1. 7 4 _37

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6.4

Problem of the Day Manny is preparing a dinner for his friends. He makes 2 cups of vegetable dip for an appetizer. Each serving is 1_2 cup. Use a model to find the total number of servings. 4 servings

Spiral Review 1. 2_5 3 5_7 3. 1 1_2 3 _13

3 2. 5_6 3 __ 10

2 _ 7

1 _ 4

4. 1 1_2 3 1 1_2 2 1_4

1 _ 2

5. 9 3 2 1_4 20 1_4

6. 1_3 3 16 5 1_3

Lesson Quiz

© Harcourt

Find the quotient. Write it in simplest form. 1. 7 4 3_7 16 1_3

2. 2_5 4 13_ 1 1_5

15 __ 3. 3_8 4 _45 32

4. 6 4 1_9 54

__ lb of sunflower seeds 5. Vivian wants to divide 15 16 into bags that each contain 81_ lb of sunflower seeds. How many 1_8 -lb bags can she make? 7 1_2 bags

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He makes 6 2_3 cups of squash. How many bowls can he fill if each bowl holds 2 2_3 cups?

Spiral Review Multiply. 1. 4_5 4 4_5 5 ___ 1 16 __ 2. 3_8 4 __ 16 5 ___ 3 1

3. 7_8 4 1_4 5 ___ 4. 3_5 4 1_5 5 ___ 3 4 _ 5. 4_5 4 __ 10 5 5 3 ___

6. 1_4 4 1_8 5 ___

Lesson Quiz 2. 3 3_4 4 1 _14

3. 9_4 4 _47

4. 7_8 4 1 _78

© Harcourt

5. Greta is making pillow covers with 9 3_8 yards of fabric. If each pillow cover requires 1 7_8 yards of fabric, how many pillow covers can she make? Write and solve a division problem to find the answer.

Grade 6

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1. 1 2_3 4 2_5

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6.5

Problem of the Day Manny is preparing a dinner for his friends. He makes 6 23_ cups of squash. How many bowls can he fill if each bowl holds 2 32_ cups? 2 1_2 bowls

Spiral Review Multiply. 1 1. 4_5 4 4_5 5 ___

3 _ 1 5 ___ __ __ 8 3 16 2. 3_8 4 16 1

3 1_2 3. 7_8 4 1_4 5 ___ 3 4. 3_5 4 1_5 5 ___

10 __ 3 5 4 _ 3 ___ 3 5. 4_5 4 __ 10 5

2 6. 1_4 4 1_8 5 ___

Lesson Quiz 1. 1 2_3 4 2_5 4 1_6

2. 3 34_ 4 1 1_4 3

__ 3. 9_4 4 4_7 3 15 16

7 4. 87_ 4 1 78_ __ 15

© Harcourt

5. Greta is making pillow covers with 9 3_8 yards of fabric. If each pillow cover requires 1 7_8 yards of fabric, how many pillow covers can she make? Write and solve a division problem to find the 8 __ 5 75 __ 3 __ answer. 9 3_8 4 1 7_8 5 7 5_8 4 15 8 8 15 5 5; Greta can make 5 pillow covers. Grade 6

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6.6

Problem of the Day Manny is preparing a dinner for his friends. He wants to find out how many pints of sherbet he will need for 4 servings, if each serving is 5_8 pint. Choose the operation and solve the problem.

Spiral Review Rewrite each division problem as a multiplication problem. 1. 3_4 4 _23

2. 5_6 4 4

3. 1 3_4 4 1 _23

4. 4 4 1 _12

Lesson Quiz Solve.

1. Kyle worked 3 1_3 hours on Monday and 2 3_4 hours on © Harcourt

Tuesday. Choose the operation to find how many more hours he worked on Monday than on Tuesday. Then solve.

2. Inez has 4 quarts of lemonade. Choose the

operation to find how many 1 1_2 -quart pitchers she can fill. Then solve.

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He wants to find out how many pints of sherbet he will need for 4 servings, if each serving is 5_8 pint. Choose the operation and solve the problem. Multiply; 1

4

@ 5 3 _58 5 4_1 3 _ 5 5_2 , or @ 8

2

2 1_2 pt

Spiral Review Rewrite each division problem as a multiplication problem. 5 _ 6

1 _ 4

1. 3_4 4 2_3 3_4 3 _32

2. 65_ 4 4

3. 1 3_4 4 1 _23 7_4 3 _35

4. 4 4 1 _12 4_1 3 _23

3

Lesson Quiz Solve.

1. Kyle worked 3 1_3 hours on Monday and 2 3_4 hours on © Harcourt

Tuesday. Choose the operation to find how many more hours he worked on Monday than on Tuesday. 7 hour Then solve. Subtraction; 3 1_3 2 2 3_4 5 __ 12

2. Inez has 4 quarts of lemonade. Choose the

operation to find how many 1 1_2 -quart pitchers she can fill. Then solve. Division; 4 4 1 1_2 5 2 2_3 pitchers

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He buys 4 pounds of salmon. Use mental math to find how many servings of salmon Manny can make if each serving is 1_2 pound.

1. 11 3

_1 7

Spiral Review 2. 8 3 _23

4 3. 3_8 3 __ 15

4. 7_8 4 _12

5 8 __ 5. __ 12 3 15

6. 7 1_3 4 5 _12

Lesson Quiz

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Solve. Choose mental math, paper and pencil, or a calculator. 1. 4_9 2 _12

2. 15 4 _12

5 3. 1 5_8 2 __ 12

4. 7_8 4 12_

5. Linda makes 9 tuna sandwiches. She uses 5_6 oz of tuna for each sandwich. How much tuna does Linda use for all 9 sandwiches?

Grade 6

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Problem of the Day Manny is preparing a dinner for his friends. He buys 4 pounds of salmon. Use mental math to find how many servings of salmon Manny can make if each serving is 1_2 pound. Think: 4 5 8 3 12_ . So, 4 4 1_2 5 8. Manny can make 8 servings of salmon.

Spiral Review

1. 11 3 1_7 77

2. 8 3 2_3 5 1_3

4 3. 3_8 3 __ 15

1 __ 10

4. 7_8 4 1_2 1 3_4

5 8 __ 5. __ 12 3 15

2 _ 9

6. 7 1_3 4 5 1_2 1 1_3

Lesson Quiz

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Solve. Choose mental math, paper and pencil, or a calculator. 1. 4_9 2 _12

1 _ 9

5 5 __ 3. 1 5_8 2 __ 12 1 24

2. 15 4 1_2 30 4. 87_ 4 1_2 1 3_4

5. Linda makes 9 tuna sandwiches. She uses 5_6 oz of tuna for each sandwich. How much tuna does Linda use for all 9 sandwiches? 7 1_2 oz

Grade 6

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Unit 3 • Problem of the Day

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Tyler and Ana each toss a fair number cube ten times. What are some comparisons you can make about their tosses?

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Mrs. Parker’s class is collecting data about sixth graders’ computer usage. In her class, 5 students used the computer 22 minutes a day, 3 used it 15 minutes a day, 7 used it 25 minutes a day, and 2 used it 45 minutes a day. If 3 of the students who originally used the computer 25 minutes started to increase their usage to 45 minutes a day, would the mean, median, mode, and range increase, decrease, or remain unchanged?

Grade 6

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Unit 3 • Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. In her class, 5 students used the computer 22 minutes a day, 3 used it 15 minutes a day, 7 used it 25 minutes a day, and 2 used it 45 minutes a day. If 3 of the students who originally used the computer 25 minutes started to increase their usage to 45 minutes a day, would the mean, median, mode, and range increase, decrease, or remain unchanged? The mean would increase, the median and the range would remain unchanged, and the mode would have two values, one higher and one lower.

7

Tyler and Ana each toss a fair number cube ten times. What are some comparisons you can make about their tosses? Possible answer: the actual numbers showing on the number cubes; the number of times each student tossed an even number, the number of times each tossed an odd number, or the number of times each tossed a prime number.

8

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Antonio said that he used the computer every day. The number of hours he spent on the computer last week were 3, 2, 4, 3, 1, 5, and 3. What is the average time, or mean time, that Antonio spent on the computer last week?

Spiral Review Solve. Use mental math, paper and pencil, or a calculator. 1. 3 3 1 _23

5 3. 5_6 4 __ 12

2. 4 3_5 4 _15 4. 4 2_3 3 _67

Lesson Quiz The table below shows the number of minutes Sonia exercised during a two-week training period. Use the table to answer 1–4.

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NUMBER OF MINUTES EXERCISING Week 1 25 20 29 30 30 30 29 Week 2 35 30 35 40 40 35 40 1. What is the mode?

2. What is the mean?

3. What is the median?

4. What is the range?

5. Sonia wanted to exercise an average of 35 minutes daily. How many more total minutes should she have exercised to reach this mean goal? Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Antonio said that he used the computer every day. The number of hours he spent on the computer last week were 3, 2, 4, 3, 1, 5, and 3. What is the average time, or mean time, that Antonio spent on the computer last week? 3 hours

Spiral Review Solve. Use mental math, paper and pencil, or a calculator. 1. 3 3 1 _23 5

2. 4 3_5 4 _15 23 4. 4 2_3 3 6_7 4

5 3. 5_6 4 __ 12 2

Lesson Quiz The table below shows the number of minutes Sonia exercised during a two-week training period. Use the table to answer 1–4.

© Harcourt

NUMBER OF MINUTES EXERCISING Week 1 25 20 29 30 30 30 29 Week 2 35 30 35 40 40 35 40 1. What is the mode? 30 minutes

2. What is the mean? 32 minutes

3. What is the median? 30 minutes 4. What is the range? 40 minutes 2 20 minutes = 20 minutes 5. Sonia wanted to exercise an average of 35 minutes daily. How many more total minutes should she have exercised to reach this mean goal? 42 minutes Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Anna is a sixth grader who was surveyed. Over the past 10 days, she was on the computer for the following number of hours: 3, 4, 2, 3, 3, 5, 3, 1, 2, 3. On how many days did Anna spend fewer than 4 hours on the computer?

Spiral Review Find the mean, median, mode, and range. 1. 8, 6, 7, 7, 4, 10, 7

2. 12, 16, 10, 17, 18, 10, 15

3. 30, 31, 36, 31, 42

4. 100, 98, 94, 100, 89, 93, 98

Lesson Quiz A survey asked 20 people how many different websites they visit in a day. Use the table to answer 1–4.

Number of Web Sites Visited in a Day 2 12

6 0

4 1

6 7

8 5

1 6

9 2

8 3

7 6

6 9

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1. Make a line plot for the data. 2. Complete the frequency table. and identify any outliers in Number of Websites Visited in a Day the plot. Number of Visited Websites

Frequency

Cumulative Frequency

0–4 5–9 10–12

7

10–14 19

1

3. If the survey were extended to include 20 more people, what do you predict the results would be? Explain.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Anna is a sixth grader who was surveyed. Over the past 10 days, she was on the computer for the following number of hours: 3, 4, 2, 3, 3, 5, 3, 1, 2, 3. On how many days did Anna spend fewer than 4 hours on the computer? 8 days

Spiral Review Find the mean, median, mode, and range. 1. 8, 6, 7, 7, 4, 10, 7 mean 57; median 5 7; mode 57; range 5 6

2. 12, 16, 10, 17, 18, 10, 15 mean 5 14; median 5 15; mode 5 10; range 5 8

3. 30, 31, 36, 31, 42 4. 100, 98, 94, 100, 89, 93, 98 mean 5 34; median 5 31; mean 5 96; median 5 98; mode 5 31; range 5 12 mode 5 98 and 100; range 5 11

Lesson Quiz A survey asked 20 people how many different websites they visit in a day. Use the table to answer 1–4.

Number of Web Sites Visited in a Day 2 12

6 0

4 1

6 7

8 5

1 6

9 2

8 3

7 6

6 9

1. Make a line plot for the data. 2. Complete the frequency table. and identify any outliers in Number of Websites Visited in a Day the plot. © Harcourt

X X X XX XXXX XXX X X X XXXX X 0 1 2 3 4 5 6 7 8 9 10 11 12

Number of Visited Websites

Frequency

Cumulative Frequency

0–4 5–9 10–12

7

10–14 19

12 1

20

3. If the survey were extended to include 20 more people, what do you predict the results would be? Explain. Possible answer: Most people would visit between 5 and 9 Web sites a day. This category had the largest frequency and the data seems to cluster around 5–9. Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Ted wants to survey a sixth-grade class. Elana wants to survey every tenth student from a list of sixth graders at the school. If the survey needs to be completed within two hours, which method should they choose?

Spiral Review Free Throws Made During Tournament 0–5 6–11 12–17

Frequency 4 3

Cumulative Frequency 4 14

Refer to the frequency table above. 1. What is the total cumulative frequency? 2. How many times were more than 11 free throws made?

Lesson Quiz For 1–4, tell the best sampling method to use. 1. Mrs. Townson wants to know if her middle school students prefer having time in the morning to do homework or time in the afternoon. She wants to survey every third student from her class attendance list.

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2. The guidance department wants to know which elective classes sixth graders enjoy most. They want each sixth-grade student to have an equal chance of being selected. 3. Candidate Simmons wants to know if the planned community center is a popular idea with the voters. They plan to survey shoppers at the local mall. 4. The sixth-grade class is allowed to choose the destination for their class trip. Students will be surveyed at the school library. 5. The drama teacher wants to know what type of movies her students enjoy most. There are a total of 95 students in her classes. Describe how she could perform a systematic sample.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. Ted wants to survey a sixth-grade class. Elana wants to survey every tenth student from a list of sixth graders at the school. If the survey needs to be completed within two hours, which method should they choose? They should survey a sixth-grade class. This will take less time than surveying every tenth student from the list of sixth-grade students.

Spiral Review Free Throws Made During Tournament 0–5 6–11 12–17

Frequency 4

Cumulative Frequency 4 14

3

Refer to the frequency table above. 1. What is the total cumulative frequency? 17 2. How many times were more than 11 free throws made? 3

Lesson Quiz For 1–4, tell the best sampling method to use. 1. Mrs. Townson wants to know if her middle school students prefer having time in the morning to do homework or time in the afternoon. She wants to survey every third student from her class attendance list. systematic sampling

© Harcourt

2. The guidance department wants to know which elective classes sixth graders enjoy most. They want each sixth-grade student to have an equal chance of being selected. random sampling 3. Candidate Simmons wants to know if the planned community center is a popular idea with the voters. They plan to survey shoppers at the local mall. convenience sampling

4. The sixth-grade class is allowed to choose the destination for their class trip. Students will be surveyed at the school library. convenience sampling 5. The drama teacher wants to know what type of movies her students enjoy most. There are a total of 95 students in her classes. Describe how she could perform a systematic sample. Possible answer: She could combine her class lists and survey every fifth student on the new list.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. The class has a topic, but needs a good survey question. What question might work for this survey?

Spiral Review Given the following survey guidelines, what is the best sampling method to use for a survey of 6th graders? 1. First fifty 6th graders entering the cafeteria are surveyed.

2. Every fifth student on the 6th-grade enrollment list is surveyed.

3. 6th graders' names are 4. All 6th graders are surveyed. placed in a bag and thirty are selected for the survey.

Lesson Quiz Use the following survey information to answer questions 1–5. Mr. Balsom’s 6th-grade class has 24 students. Every third student on his class list is asked to complete a survey in which students are asked if they walk to school or ride a bus. Six of the students say that they ride a bus. 1. What is the topic of the survey?

© Harcourt

2. What population is surveyed? 3. What is the survey question? 4. Can you make a prediction based on the information in the survey? 5. How can you check the information in the survey to see if it is reasonable?

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. The class has a topic, but needs a good survey question. What question might work for this survey? Answers will vary. Possible answer: When do you use a computer the most—before school, during school, or after school?

Spiral Review Given the following survey guidelines, what is the best sampling method to use for a survey of 6th graders? 1. First fifty 6th graders entering the cafeteria are surveyed. convenience sampling

2. Every fifth student on the 6th-grade enrollment list is surveyed. systemic sampling

3. 6th graders' names are 4. All 6th graders are surveyed. No sampling; the entire placed in a bag and population of 6th graders thirty are selected for the is surveyed. survey. random sampling

Lesson Quiz Use the following survey information to answer questions 1–5. Mr. Balsom’s 6th-grade class has 24 students. Every third student on his class list is asked to complete a survey in which students are asked if they walk to school or ride a bus. Six of the students say that they ride a bus. 1. What is the topic of the survey? Transportation to school

© Harcourt

2. What population is surveyed? A sampling of 6th graders. 3. What is the survey question? Do you walk or ride a bus to school? 4. Can you make a prediction based on the information in the survey? Possible answer: Most 6th-grade students ride a bus to school. 5. How can you check the information in the survey to see if it is reasonable? Possible answer: Repeat the survey using a larger number of students by either using random or systematic sampling method to survey the entire 6th grade. You can also research the number of 6th-grade students who walk or ride the bus to school.

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. A survey showed that 60 students use the computer in the morning, 90 students use the computer in the afternoon, and 30 students use the computer at both times. How many students use the computer in the morning only? In the afternoon only?

Spiral Review Suppose you are designing a survey about music. 1. List two topics that you could use.

2. Describe the population you will use in your survey. 3. Write two survey questions.

4. Develop a prediction.

Lesson Quiz

© Harcourt

Draw a diagram to solve. 1. To get to soccer practice, Kate’s mom drives 2 1_2 mi north, 3 mi east, 3 mi south to Kate’s school. Then she drives east to the soccer field. If she drives 10 mi altogether, how far east does she drive from the school to the soccer field? 2. Aaron wants to frame his rectangular painting. Two sides of his painting are 18 in. long and two sides are 12 in. long. How many inches of framing material does Aaron need?

Grade 6

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Problem of the Day Mrs. Parker’s class is collecting data about sixth graders’ computer usage. A survey showed that 60 students use the computer in the morning, 90 students use the computer in the afternoon, and 30 students use the computer at both times. How many students use the computer in the morning only? In the afternoon only? Thirty students use the computer in the morning only; 60 students use the computer in the afternoon only.

Spiral Review Suppose you are designing a survey about music. 1. List two topics that you could use. Possible answers: favorite artist, favorite type of music

2. Describe the population you will use in your survey. Possible answers: all students in your school, all sixth-grade students in your school 3. Write two survey questions. Possible answers: Who is your favorite musical artist? What is your favorite type of music? 4. Develop a prediction. Answers will vary.

Lesson Quiz

© Harcourt

Draw a diagram to solve. 1. To get to soccer practice, Kate’s mom drives 2 1_2 mi north, 3 mi east, 3 mi south to Kate’s school. Then she drives east to the soccer field. If she drives 10 mi altogether, how far east does she drive from the school to the soccer field? 1 1_2 mi – see diagram 2. Aaron wants to frame his rectangular painting. Two sides of his painting are 18 in. long and two sides are 12 in. long. How many inches of framing material does Aaron need? 60 inches; see diagram

Grade 6

3 mi 2 1 mi 2

3 mi ? mi

12 in. 18 in.

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Problem of theof Day the Problem

8.1

Day

Tyler and Ana each toss a number cube ten times. What is the best way to show how the results of their tosses compare?

Spiral Review A tile pattern uses 3-inch-long red tiles and 7-inch-long black tiles. The space between each tile and the next is 1 inch. Solve by drawing a diagram. 1. How long is a pattern row with 2 red tiles and 1 black tile? 3. How long is a pattern row with 5 red tiles and 3 black tiles?

2. How long is a pattern row with 4 red tiles and 6 black tiles? 4. A pattern row is 27 in. long. If there are 3 black tiles, how many red tiles are there?

Lesson Quiz Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. The boys’ and girls’ favorite kind of zoo animal.

© Harcourt

2. The number of mp3 players purchased in Illinois and New York in the last four years. 3. The number of students in the school who ride the bus compared to the number of students who walk. 4. Amount of rain over a period of a month in Cleveland and Philadelphia. 5. During a school election, one candidate polled the students to find which of five issues they felt was most important.

Grade 6

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Problem of theof Day the Problem

8.1

Day

Tyler and Ana each toss a number cube ten times. What is the best way to show how the results of their tosses compare? A double-bar graph can be used to compare two sets of data.

Spiral Review A tile pattern uses 3-inch-long red tiles and 7-inch-long black tiles. The space between each tile and the next is 1 inch. Solve by drawing a diagram. 1. How long is a pattern row with 2 red tiles and 1 black tile? 15 in. 3. How long is a pattern row with 5 red tiles and 3 black tiles? 43 in.

2. How long is a pattern row with 4 red tiles and 6 black tiles? 63 in. 4. A pattern row is 27 in. long. If there are 3 black tiles, how many red tiles are there? 1 red tile

Lesson Quiz Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. The boys’ and girls’ favorite kind of zoo animal. double-bar graph

© Harcourt

2. The number of mp3 players purchased in Illinois and New York in the last four years. double-line graph 3. The number of students in the school who ride the bus compared to the number of students who walk. circle graph 4. Amount of rain over a period of a month in Cleveland and Philadelphia. double-line graph 5. During a school election, one candidate polled the students to find which of five issues they felt was most important. circle graph Grade 6

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Problem of the Day Tyler and Ana each toss a number cube ten times. Tyler’s tosses represent the tens digit in a number and Ana’s represent the ones digit. How could they organize their tosses in a stemand-leaf plot?

Spiral Review Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. Favorite music of sixth-graders 2. Out of 5 color choices, the compared to the favorite music number of students in a class of their parents who prefer red over blue 3. Compare the length of daylight 4. Compare the percents of in each day in December to the students who like English length of daylight in each day best and students who like in July. mathematics best.

Lesson Quiz The data in the table represents the results of a survey of 12 people. Use the data to answer the questions.

Ounces of water consumed per day 16 20

48 24

30 48

8 36

48 32

64 54

© Harcourt

1. Make a stem-and-leaf plot of the data in the table.

2. Using your plot, find the median and the mode of the data. 3. Make a histogram of the data in the table using intervals starting at 0–20 ounces. 4. How many people consumed less than 64 ounces of water daily? 5. Ema redrew the histogram using intervals starting at 0–9. What frequencies

were represented by the bars? Grade 6

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Problem of the Day Tyler and Ana each toss a number cube ten times. Tyler’s tosses represent the tens digit in a number and Ana’s represent the ones digit. How could they organize their tosses in a stemand-leaf plot? Tyler’s tosses are the stems and Ana’s are the leaves in the plot.

Spiral Review Choose the most appropriate type of graph for each data set: a double-bar graph, a double-line graph, or a circle graph. 1. Favorite music of sixth-graders 2. Out of 5 color choices, the compared to the favorite music number of students in a class of their parents who prefer red over blue double-bar graph circle graph 3. Compare the length of daylight 4. Compare the percents of in each day in December to the students who like English length of daylight in each day best and students who like in July. double-line graph mathematics best. circle graph

Lesson Quiz Use the data to answer the questions. 1. Make a stem-and-leaf plot of the data in the table.

© Harcourt

Stems 0 1 2 3 4 5 6

Leaves 8 6 0 4 0 2 6 8 8 8 4 4

Ounces of water consumed per day 16 20

48 24

30 48

8 36

48 32

64 54

Ounces of Water Consumed Per Day Frequency (number of responses)

The data in the table represents the results of a survey of 12 people.

5 4 3 2 1 0

0–19 20–39 40–59 60–79

Ounces

2. Using your plot, find the median and the mode of the data. median: 34, mode: 48 3. Make a histogram of the data in the table using intervals starting at 0–20 ounces. 4. How many people consumed less than 64 ounces of water daily? 11 5. Ema redrew the histogram using intervals starting at 0–9. What frequencies were represented by the bars? 1, 1, 2, 3, 3, 1, 1 Grade 6

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Problem of the Day Tyler and Ana each toss a fair number cube ten times. How could the data showing the totals for each number tossed be graphed?

Spiral Review Choose a histogram or stem-and-leaf plot to best represent each set of data. 1. Number of minutes Josh spends on math homework each day for two weeks

2. Weights of wrestlers grouped by weight class

3. Level of baseball players based on ranges of runs scored during a season

4. Joanne’s top 15 scores on her favorite computer game

Lesson Quiz Compare the graphs. 1. Which graph shows when most students buy lunch?

40

2. Which graph tells you if more students prefer to buy lunch or

30

bring lunch? 3. What is the average number of students who buy lunch? Which graph did you use to find your answer? © Harcourt

Students Buying Lunch

4. Do more students buy lunch at the end of the week or the beginning? Which graph shows this? 5. The manager of the school cafeteria needs to decide how

20 10 0 Mon

Thurs

Fri

40 30 20

to find this information?

10 0

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Average Student Lunch Habits

much food to prepare each day. Which graph should he use

Grade 6

Tues

Buy Lunch

Bring Lunch

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8.3

Problem of the Day Tyler and Ana each toss a fair number cube ten times. How could the data showing the totals for each number tossed be graphed? A circle graph could compare the percent of times a number is tossed out of the total number of tosses. A bar graph could show the number of occurrences for each number tossed.

Spiral Review Choose a histogram or stem-and-leaf plot to best represent each set of data. 1. Number of minutes Josh spends on math homework each day for two weeks stem-and-leaf plot

2. Weights of wrestlers grouped by weight class histogram

3. Level of baseball players based on ranges of runs scored during a season histogram

4. Joanne’s top 15 scores on her favorite computer game stem-and-leaf plot

Lesson Quiz Compare the graphs.

Students Buying Lunch

1. Which graph shows when most students buy lunch? line graph 2. Which graph tells you if more students prefer to buy lunch or bring lunch? bar graph 3. What is the average number of students who buy lunch? © Harcourt

Which graph did you use to find your answer? 15; bar graph 4. Do more students buy lunch at the end of the week or the beginning? Which graph shows this? at the end of the week; line graph 5. The manager of the school cafeteria needs to decide how

40 30 20 10 0 Mon

Wed

Thurs

Fri

Average Student Lunch Habits 40 30

much food to prepare each day. Which graph should he use

20

to find this information? line graph

10 0

Grade 6

Tues

Buy Lunch

Bring Lunch

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Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler wants to show the results of their tosses using a line graph and Ana wants to use a bar graph. Whose graph would be the best to use? Explain.

Spiral Review The day and night temperatures for a week are graphed using a double-line graph and a double-bar graph. Choose the better graph to analyze each situation. 1. the trend in temperatures for the week

2. the difference in Wednesday’s temperatures

3. the time when the temperatures varied the most

4. the exact information for each day

Lesson Quiz Choose the most appropriate type of graph to make for each data set: a bar or double-bar graph, a line or double line-graph, a circle graph, a pictograph, or a histogram. 1. Your height measured once each month for a year

© Harcourt

2. The amount of time spent on homework for each subject 3. The number of hours practiced in one week by five dance teams 4. The number of wins and losses for six soccer teams 5. A science experiment tracked the monthly growth of two plants—one in the sun and one in the shade. Which graph would best show how to compare the plant growth?

Grade 6

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Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler wants to show the results of their tosses using a line graph and Ana wants to use a bar graph. Whose graph would be the best to use? Explain. A line graph shows how data changes over time. Since tosses are not affected by time, a bar graph would be the better choice.

Spiral Review The day and night temperatures for a week are graphed using a double-line graph and a double-bar graph. Choose the better graph to analyze each situation. 1. the trend in temperatures for the week double-line graph 3. the time when the temperatures varied the most double-line graph

2. the difference in Wednesday’s temperatures double-bar graph 4. the exact information for each day double-bar graph

Lesson Quiz Choose the most appropriate type of graph to make for each data set: a bar or double-bar graph, a line or double line-graph, a circle graph, a pictograph, or a histogram. Possible answers are given. 1. Your height measured once each month for a year line graph

© Harcourt

2. The amount of time spent on homework for each subject circle graph 3. The number of hours practiced in one week by five dance teams 4. The number of wins and losses for six soccer teams double-bar graph pictograph 5. A science experiment tracked the monthly growth of two plants—one in the sun and one in the shade. Which graph would best show how to compare the plant growth? double-line graph

Grade 6

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Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler tosses twice as many even numbers as Ana. What conclusion could you make from the results of the tosses? Explain.

Spiral Review Choose the most appropriate type of graph for each data set based on a sixth-grade student survey about sports. 1. boys’ favorite sports compared to girls’ favorite sports

2. increase or decrease in sport activity every week for 3 months

3. a comparison of the number of students who chose a specific sport to the total number of students surveyed.

4. totals for type of favorite sport displayed using symbols

Lesson Quiz Average Hours of Sleep

Use the graph to answer the questions.

© Harcourt

1. A group of sixth-graders was surveyed to find out how many hours of sleep they averaged during May, June, and July. Using the data in the graph, what conclusion can you make about their sleep patterns during these months?

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Jun

Jul

2. What do you think would happen if the graph were extended three more months?

Grade 6

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Problem of the Day Tyler and Ana each toss a fair number cube ten times. Tyler tosses twice as many even numbers as Ana. What conclusion could you make from the results of the tosses? Explain. Possible answer: Tyler and Ana have different cubes. Tyler’s cube had more even numbers or is weighted.

Spiral Review Choose the most appropriate type of graph for each data set based on a sixth-grade student survey about sports. 1. boys’ favorite sports compared to girls’ favorite sports double-bar graph 3. a comparison of the number of students who chose a specific sport to the total number of students surveyed. circle graph

2. increase or decrease in sport activity every week for 3 months line graph 4. totals for type of favorite sport displayed using symbols pictograph

Lesson Quiz Average Hours of Sleep

© Harcourt

Use the graph to answer the questions. 1. A group of sixth-graders was surveyed to find out how many hours of sleep they averaged during May, June, and July. Using the data in the graph, what conclusion can you make about their sleep patterns during these months? Possible answer: The students sleep for longer periods of time with each month.

10 8 6 4 2 0

May

Jun

Jul

2. What do you think would happen if the graph were extended three more months? Possible answer: You might predict that the number of hours of sleep would continue to increase. However, the conclusion would be wrong if students are out of school during the summer months and can sleep longer in June and July. When they are back in school in September, the number of hours of sleep would decrease after school starts.

Grade 6

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Unit 4 • Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers.

9

Keisha makes a deposit of $50 and a withdrawal of $18. Write an integer to represent each situation.

Natalie enjoys playing basketball with her friends. Every week, they compete to see who shoots the most successful baskets in 20 throws.

10

© Harcourt

This week, Natalie made 12 baskets. What fraction of her throws were successful?

Grade 6

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Unit 4 • Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers.

9

Keisha makes a deposit of $50 and a withdrawal of $18. Write an integer to represent each situation. 1 50, 218

Natalie enjoys playing basketball with her friends. Every week, they compete to see who shoots the most successful baskets in 20 throws.

10

© Harcourt

This week, Natalie made 12 baskets. What fraction of her throws were successful? 3_5

Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes deposits of $50, $25, and $10. She makes withdrawals of $15, $10, $23, and $12. Write an integer to represent each situation and order them from least to greatest.

Spiral Review 1. What type of graph examines change over time? 2. How would you represent 25% of a circle graph? 3. What type of graph represents percentages of a whole? 4. Determine 20% of 420.

Lesson Quiz 1. Write an integer to represent a weight gain of 10 pounds

© Harcourt

2. Write an integer to represent a $25 discount 3. What is the absolute value of 4? 4. Use , or = to compare 27 and 6 5. Average temperatures for five days in December were 21°F, 25°F, 1°F, 24°F, and 4°F. Place the temperatures in order from least to greatest.

Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes deposits of $50, $25, and $10. She makes withdrawals of $15, $10, $23, and $12. Write an integer to represent each situation and order them from least to greatest. 2 23, 2 15, 2 12, 2 10, 10, 25, 1 50

Spiral Review 1. What type of graph examines change over time? Line graph 2. How would you represent 25% of a circle graph? Shade in 1_4 of the graph. 3. What type of graph represents percentages of a whole? Circle graph 4. Determine 20% of 420. 84

Lesson Quiz 1. Write an integer to represent a weight gain of 10 pounds 10

© Harcourt

2. Write an integer to represent a $25 discount 2 25 3. What is the absolute value of 4? 4 4. Use , or = to compare 27 and 6 2 7 , 6 5. Average temperatures for five days in December were 21°F, 25°F, 1°F, 24°F, and 4°F. Place the temperatures in order from least to greatest. 2 5°F, 2 4°F, 2 1°F, 1°F, 4°F

Grade 6

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9.2

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Explain how to use a number line to model a withdrawal of $20.

Spiral Review 1. Place in order from least to greatest: 1 _ , 0.01, 3_ 4 8 2. Place in order from greatest to least: 2 , 2.10 1.02, 1 __ 10

© Harcourt

Lesson Quiz Use counters to find each sum. 1. 6 1 26

2. 22 1 27

3. 3 1 28

4. 21 1 9

5. 23 1 22 Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Explain how to use a number line to model a withdrawal of $20. Start at the current balance, move 20 units to the left.

Spiral Review 1. Place in order from least to greatest: 1 _ , 0.01, 3_ 0.01, 1_ , 3_ 4 8 4 8 2. Place in order from greatest to least: 2 , 1.02 2 , 2.10 2.10, 1 __ __ 1.02, 1 10 10

© Harcourt

Lesson Quiz Use counters to find each sum. 1. 6 1 26 0

2. 22 1 27 2 9

3. 3 1 28 2 5

4. 21 1 9 8

5. 23 1 22 2 5 Grade 6

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9.3

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the sum of a withdrawal of $10 and a deposit of $15.

Spiral Review Use a model to find each sum. 1. 4 1 1 3. 3 1 27

2. 6 1 22 4. 23 1 25

Lesson Quiz

© Harcourt

Find the sum. 1. 7 1 29

2. 13 1 28

3. 4 1 16

4. 26 1 6

5. A business had a profit of $40 in March and a loss of $50 in April. What was the total profit or loss for both months?

Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the sum of a withdrawal of $10 and a deposit of $15. 2 10 1 15

Spiral Review Use a model to find each sum. Check students’ models. 1. 4 1 1 5 2. 6 1 22 4 3. 3 1 27 24 4. 23 1 25 28

Lesson Quiz

© Harcourt

Find the sum. 1. 7 1 29 2 2

2. 13 1 28 5

3. 4 1 16 20

4. 26 1 6 0

5. A business had a profit of $40 in March and a loss of $50 in April. What was the total profit or loss for both months? 2 $10

Grade 6

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9.4

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use a number line to represent a deposit of $10 that is cancelled.

Spiral Review 1. 8 1 7 2. 23 1 211 3. 12 1 –5 4. 28 1 13 5. 217 1 9 6. 12 1 222

© Harcourt

Lesson Quiz Find the difference using counters. 1. 6 2 7 5 3. 8 2 24 5

2. 23 2 25 5 4. 2 2 21 5

5. 6 2 4 5

Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use a number line to represent a deposit of $10 that is cancelled. Move 10 units to the right, then 10 units to the left.

Spiral Review 1. 8 1 7 15 2. 23 1 211 2 14 3. 12 1 –5 7 4. 28 1 13 2 5 5. 217 1 9 2 8 6. 12 1 222 2 10

© Harcourt

Lesson Quiz Find the difference using counters. 1. 6 2 7 5 2 1 3. 8 2 24 5 12

2. 23 2 25 5 2 4. 2 2 21 5 3

5. 6 2 4 5 2

Grade 6

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9.5

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write two expressions to represent a deposit of $100 and a withdrawal of $50.

Spiral Review Use counters to find each difference. 1. 4 2 3 3. 27 2 2

2. 5 2 6 4. 25 2 28

Lesson Quiz

© Harcourt

Find the difference by rewriting each subtraction problem as an addition problem. 2. 12 2 211

3. 4 2 9

4. 0 2 7

5. Paul’s dog’s weight was 3 lb below its normal weight. One month later its weight was 2 lb above its normal weight. Write and solve a subtraction problem to find how much weight Paul’s dog gained. Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write two expressions to represent a deposit of $100 and a withdrawal of $50. 100 1 2 50; 100 2 50

Spiral Review Use counters to find each difference. Check students’ models. 1. 4 2 3 1 2. 5 2 6 2 1 3. 27 2 2 2 9 4. 25 2 28 3

Lesson Quiz

© Harcourt

Find the difference by rewriting each subtraction problem as an addition problem. 1. 6 2 25 6 1 5 5 11

2. 12 2 211 12 1 11 5 1

3. 4 2 9 4 1 2 9 5 2 5

4. 0 2 7 0 1 2 7 5 2 7

5. Paul’s dog’s weight was 3 lb below its normal weight. One month later its weight was 2 lb above its normal weight. Write and solve a subtraction problem to find how much weight Paul’s dog gained. 2 2 2 3 5 5 Grade 6

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9.6

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the product of 5 withdrawals of $25 each.

Spiral Review Find the sum or difference. 1. 3 1 25 2. 36 1 215 3. 27 2 8 4. 76 2 (223)

Lesson Quiz © Harcourt

Find the product. 1. 28 3 2

2. 24 3 21

3. 5 3 3

4. 11 3 27

5. The temperature on Monday was 3°F. If the temperature on Tuesday was 3 times as cold, what was the temperature on Tuesday? Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Write an expression to represent the product of 5 withdrawals of $25 each. 5 3 2 25

Spiral Review Find the sum or difference. 1. 3 1 25

2

2

2. 36 1 215 12 3. 27 2 8 2 15 4. 76 2 (223) 99

Lesson Quiz © Harcourt

Find the product. 1. 28 3 2 2 16

2. 24 3 21 4

3. 5 3 3 15

4. 11 3 27 2 77

5. The temperature on Monday was 3°F. If the temperature on Tuesday was 3 times as cold, what was the temperature on Tuesday? 2 9˚F Grade 6

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9.7

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. The total of 5 equal withdrawals is $45. Write an expression to represent the amount of 1 withdrawal.

Spiral Review Find the sum or product. 1. 18 1 25 2. 4 3 26 3. 221 1 27 4. 22 323

Lesson Quiz

© Harcourt

Find the quotient. 1. 25 4 25

2. 32 4 8

3. 218 4 22

4. 2100 4 10

5. A plane’s altitude changed by 8,000 ft over 4 hr. What was the average change per hour?

Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. The total of 5 equal withdrawals is $45. Write an expression to represent the amount of 1 withdrawal. 2 45 4 5

Spiral Review Find the sum or product. 1. 18 1 25 13 2. 4 3 26 2 24 3. 221 1 27 2 28 4. 22 323 6

Lesson Quiz

© Harcourt

Find the quotient. 1. 25 4 25 2 5

2. 32 4 8 4

3. 218 4 22 9

4. 2100 4 10 2 10

5. A plane’s altitude changed by 8,000 ft over 4 hr. What was the average change per hour? 2,000 ft

Grade 6

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9.8

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes one withdrawal that is $10 greater than another withdrawal. Write two integers that could represent the amount of each withdrawal.

Spiral Review 1. 4 1 2 2 8 5

2. 8 2 9 1 3 5

3. 7 2 4 2 11 5

4. 6 1 24 2 3 5

5. 212 2 16 1 28 5

5. 5 2 210 1 2 2 28 5

Lesson Quiz

© Harcourt

1. The sum of two negative integers is 29. When the lesser integer is subtracted from the greater integer, the difference is 5. What are the two integers? 2. The perimeter of a rectangle is 20 ft. The length is 4 times as long as the width. What is the length and width of the rectangle?

Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Keisha makes one withdrawal that is $10 greater than another withdrawal. Write two integers that could represent the amount of each withdrawal. Possible answer: 2 50, 2 60

Spiral Review 1. 4 1 2 2 8 52 2

2. 8 2 9 1 3 5 2

2 4. 6 1 24 2 3 5 1 2 5. 212 2 16 1 28 5 36 5. 5 2 210 1 2 2 28 525

3. 7 2 4 2 11 52 8

Lesson Quiz

© Harcourt

1. The sum of two negative integers is 29. When the lesser integer is subtracted from the greater integer, the difference is 5. What are the two integers? 2 2, 2 7 2. The perimeter of a rectangle is 20 ft. The length is 4 times as long as the width. What is the length and width of the rectangle? 8 ft, 2 ft Grade 6

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9.9

Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use addition and multiplication to write an expression representing three deposits, each of which includes a check for $10 and a check for $15.

Spiral Review 1. (4 3 5) 3 8 5

2. 7 3 (50 4 5) 5

3. 4 1 ( 1_2 3 24) 5

4. ( 3_4 3 1_2 ) 1 3_4 5

Lesson Quiz Find the value of the expression. 1. 2(6 2 26) 1 28 © Harcourt

2. 27 3 23 1 4 3. (9 1 25)2 4. 1 1 24 3 24 1 1 5. Find the missing integers in the pattern 2, 22, 26, __ , __ , Grade 6

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Problem of the Day Keisha has opened a savings account. She records her deposits as positive integers and her withdrawals as negative integers. Use addition and multiplication to write an expression representing three deposits, each of which includes a check for $10 and a check for $15. 3 3 (10 1 15)

Spiral Review 1. (4 3 5) 3 8 5 160 2. 7 3 (50 4 5) 5 70 3. 4 1 ( 1_2 3 24) 5 16 4. ( 3_4 3 1_2 ) 1 3_4 5 1 1_8

Lesson Quiz Find the value of the expression. 1. 2(6 2 26) 1 28 16 © Harcourt

2. 27 3 23 1 4 25 3. (9 1 25)2 16 4. 1 1 24 3 24 1 1 18 5. Find the missing integers in the pattern 2, 22, 26, __ , __ , 2 10, 2 14 Grade 6

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Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie misses 6 baskets. What fraction of the throws were baskets?

Spiral Review 1. (3 1 12) 2 (24 1 5)

2. (4 3 6) 3 (22 3 4)

3. (12 2 18) 1 (4 2 6)

4. 27 3 (6 2 11)

Lesson Quiz Write the rational number in the form _ba . 1. 3.74 2.

2

2 4_7

Find a rational number between the two given rational numbers.

© Harcourt

__ 3. 28 and 2 30 4 __ 4. 3.1 and 33 10

5. Andrew collected 31 3_5 pounds of canned goods for his school’s charity drive. Marcus collected 31 5_6 pounds of canned goods for the charity drive. If Leslie collected an amount between what Andrew and Marcus collected, how many pounds of canned goods could she have collected?

Grade 6

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Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie misses 6 baskets. What fraction of the throws were baskets? 14 7 __ , or __ 20

10

Spiral Review 1. (3 1 12) 2 (24 1 5) 15 2 1 5 14 3. (12 2 18) 1 (4 2 6) 6 1 22 5 28

2

2. (4 3 6) 3 (22 3 4) 24 3 28 5 2192 4. 27 3 (6 2 11) 7 3 25 5 35

2

Lesson Quiz Write the rational number in the form _ba . 187 1. 3.74 ___ 50

2.

__ 2 4_7 2 18 7

2

Find a rational number between the two given rational numbers.

© Harcourt

__ 2 31 __ 3. 28 and 2 30 4 4 33 16 __ 4. 3.1 and __ 10 5

5. Andrew collected 31 3_5 pounds of canned goods for his school’s charity drive. Marcus collected 31 5_6 pounds of canned goods for the charity drive. If Leslie collected an amount between what Andrew and Marcus collected, how many pounds of canned goods could she have collected? Possible answer: 31 2_3 pounds of canned goods

Grade 6

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10.2

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie makes 14 baskets and her friend Tasha makes 12 baskets. Express the fraction of baskets Natalie makes and the fraction of baskets Tasha makes as decimals. Then compare these numbers using . or ,.

Spiral Review 7 7 1. Order 23 1_8 , 23.2, 23.14 2. Order 1.8, _4 , 1 _8 from least to greatest. from least to greatest.

3. Write 24 1_3 in the form _ba .

3 4. Write 7 __ 16 in the form _ba .

Lesson Quiz Compare. Write >, < or = for each d. 1. 23 d 22.5 2. 4.82 d 4.812 © Harcourt

__ 3. 25.45 d 25 17 20

4. 6.3 1 3.2 d 5.7 1 3.8 5. Arrange the following numbers in order from least to greatest: 22 87_ , 22 81_ , 22 41_ , 23 21_ .

Grade 6

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Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. This week, Natalie makes 14 baskets and her friend Tasha makes 12 baskets. Express the fraction of baskets Natalie makes and the fraction of baskets Tasha makes as decimals. Then compare these numbers __ , is 0.7 and 12 __ 0.6; Possible using . or ,. 14 20 20 comparisons: 0.7 . 0.6, or 0.6 , 0.7.

Spiral Review 7 7 1. Order 23 1_8 , 23.2, 23.14 2. Order 1.8, _4 , 1 _8 from least to greatest. from least to greatest. _ 2 2 2 1 7 _ , 1.8, 1 7_ 3.2, 3.14, 3 8 4 8 3 in the __ 4. Write 7 16 3. Write 24 1_3 in the 115 __ form _ba . ___ form _ba . 2 13 16 3

Lesson Quiz Compare. Write >, < or = for each d. 1. 23 d 22.5 , 2. 4.82 d 4.812 . © Harcourt

__ 3. 25.45 d 25 17 20

.

4. 6.3 1 3.2 d 5.7 1 3.8 5 5. Arrange the following numbers in order from least to greatest: 22 87_ , 22 81_ , 22 41_ , 23 21_ . 2 1 3 _2 , 22 7_8 , 22 1_4 , 22 1_8

Grade 6

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10.3

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. Over the course of three weeks, Natalie made 13, 16, and 17 baskets, while Danielle made 16, 13, and 14 baskets. What fraction of her throws did Natalie make? Danielle?

Spiral Review Compare the rational numbers using ., ,, or 5. 1. 3.65 ___ 3 5_8 2. 22.23 ___ 22.228 __ ___ 2.74 3. 2 39 50

__ ___ 249 ___ 4. 83 8 24

Lesson Quiz For 1–4, evaluate each expression. 1. 3 1_4 3 (1.4 1 3.2 1 22.4) © Harcourt

2. 6 3 3.2 1 22 4 8 3. 4 2_3 3 (2 1_5 1 4) 1 8 _23 4. (4.75 1 1 1_4 ) 4 (3 3_4 3 22.5) 5. Change Exercise 4 to make the answer an integer

Grade 6

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Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. Over the course of three weeks, Natalie made 13, 16, and 17 baskets, while Danielle made 16, 13, and 14 baskets. What fraction of her throws did Natalie make? Danielle? __ 5 23 __ ; Danielle 43 __ Natalie, 46 60 30 60

Spiral Review Compare the rational numbers using ., ,, or 5. 1. 3.65 ___ 3 5_8 . 2. 22.23 ___ 22.228 , 39 __ ___ 2.74 . 3. 2 50

__ ___ 249 ___ 5 4. 83 8 24

Lesson Quiz For 1–4, evaluate each expression. 3 1. 3 1_4 3 (1.4 1 3.2 1 22.4) 7.15 or 7 __ 20 © Harcourt

__ 2. 6 3 3.2 1 22 4 8 18.95 or 18 19 20

3. 4 2_3 3 (2 1_5 1 4) 1 8 23_

4 20 __ 15

2

2 16 4. (4.75 1 1 1_4 ) 4 (3 34_ 3 22.5) ___ 25

5. Change Exercise 4 to make the answer an integer Possible answer: ((4.75 1 1 1_4 ) 4 3 34_ ) 3 22.5 5 24 Grade 6

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10.4

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. During this week’s competition, Natalie makes 14 baskets, Danielle misses 8 shots, and Lisa makes 75% of her shots. What is the difference between the number of baskets made by Danielle and Lisa?

Spiral Review 1. 1.2 1 23.7 1 4.8

2. 0.5 3 (28 3 4.6)

3. 3_4 1 2 1_4 1 2 _18

4. 24.1 1 3.6 3 1.6 4 23

Lesson Quiz

© Harcourt

1. The Nile River is about 4,160 miles long, which makes it the longest river in the world. The Amazon River is approximately 4,000 miles long. The Mississippi-Missouri-Red Rock River is the longest river in the United States, at about 3,710 miles. What is the difference in length between the Nile and the Mississippi-Missouri-Red Rock rivers? 2. Sean works in a shoe store where he earns commission on every pair of shoes that he sells. On Monday, he sold 15 pairs of shoes. On Wednesday, he sold 22 pairs of shoes. On Friday, he sold twice as many pairs of shoes as he did on Monday. On Saturday, he sold twice as many pairs of shoes as he sold on Monday and Wednesday combined. How many pairs of shoes did he sell on Saturday?

Grade 6

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10.4

Problem of the Day Natalie enjoys playing basketball with her friends. Every week, they compete to see who makes the most baskets in 20 throws. During this week’s competition, Natalie makes 14 baskets, Danielle misses 8 shots, and Lisa makes 75% of her shots. What is the difference between the number of baskets made by Danielle and Lisa? 3

Spiral Review 1. 1.2 1 23.7 1 4.8 2.3

2. 0.5 3 (28 3 4.6) 2 18.4

3. 3_4 1 2 1_4 1 2 1_8 2 5_8

4. 24.1 1 3.6 3 1.6 4 23 2 3.38

Lesson Quiz

© Harcourt

1. The Nile River is about 4,160 miles long, which makes it the longest river in the world. The Amazon River is approximately 4,000 miles long. The Mississippi-Missouri-Red Rock River is the longest river in the United States, at about 3,710 miles. What is the difference in length between the Nile and the Mississippi-Missouri-Red Rock rivers? 450 miles 2. Sean works in a shoe store where he earns commission on every pair of shoes that he sells. On Monday, he sold 15 pairs of shoes. On Wednesday, he sold 22 pairs of shoes. On Friday, he sold twice as many pairs of shoes as he did on Monday. On Saturday, he sold twice as many pairs of shoes as he sold on Monday and Wednesday combined. How many pairs of shoes did he sell on Saturday? 74 pairs of shoes

Grade 6

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Unit 5 • Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join.

11

© Harcourt

If the variable m represents the price of renting one movie, what might the expression 5 1 m mean?

Alex and Sasha are making a quilt. They use the pattern shown. What will be the next shape in their pattern?

12

Morgan decorates scarves to sell at festivals. She sells cotton scarves for $12 and wool scarves for $18. She would like to make at least $180 at each fair. What are some different combinations of cotton and wool scarves that she can sell in order to make $180?

13

Grade 6

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Unit 5 • Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join.

11

© Harcourt

If the variable m represents the price of renting one movie, what might the expression 5 1 m mean? Possible answer: The expression might represent a $5.00 fee to join plus the cost, m, of renting one movie.

Alex and Sasha are making a quilt. They use the pattern shown. What will be the next shape in their pattern?

12

Morgan decorates scarves to sell at festivals. She sells cotton scarves for $12 and wool scarves for $18. She would like to make at least $180 at each fair. What are some different combinations of cotton and wool scarves that she can sell in order to make $180? Possible answers: (0,10), (3,8), (6,6), (9,4), (12,2), (15,0)

13

Grade 6

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Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. One video store has no fee to join, but it charges $6 for each movie. What is an algebraic expression for the total cost of renting m movies?

Spiral Review 1. 4 1 8 2 16 5

2. 4 2 8 3 16 5

3. (4 2 8) 3 16 5

4. (4 2 8)2 3 16 5

5. 4 2 8 3 162 1 8 5

6. (4 1 8) 2 16 3 82 5

Lesson Quiz For exercises 1–3, write an algebraic expression for each word expression. 1. the product of 48 and a number 2. 6 less than the product of a number and 9 © Harcourt

3. the square of a number decreased by 17 4. Write a word expression for the following algebraic expression: 8(n 2 7). 5. Jake has d dollars in his pocket. He also has $5.10 in his wallet. Write an algebraic expression for the total amount of money Jake has.

Grade 6

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11.1

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. One video store has no fee to join, but it charges $6 for each movie. What is an algebraic expression for the total cost of renting m movies? 6m

Spiral Review 1. 4 1 8 2 16 5 2 4 3. (4 2 8) 3 16 5 2 64

2. 4 2 8 3 16 5 2 124 4. (4 2 8)2 3 16 5 256

5. 4 2 8 3 162 1 8 52 2,036 6. (4 1 8) 2 16 3 82 5 2 1,012

Lesson Quiz For exercises 1–3, write an algebraic expression for each word expression. 1. the product of 48 and a number 48n 2. 6 less than the product of a number and 9 9n 2 6 © Harcourt

3. the square of a number decreased by 17 n2 2 17 4. Write a word expression for the following algebraic expression: 8(n 2 7). a number decreased by 7 which is then multiplied by 8 5. Jake has d dollars in his pocket. He also has $5.10 in his wallet. Write an algebraic expression for the total amount of money Jake has. 5.10 1 d

Grade 6

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11.2

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 10 1 4m shows the total cost at a store that charges $10 to join and $4 per movie. What is the total cost if Carla joins and rents 5 movies?

Spiral Review 1. Write an algebraic expression for seven more than twice a number n. 2. Write an algebraic expression for seven less than a number n.

Lesson Quiz Simplify each expression. Then evaluate each expression for the given value of the variable. 1. 5r 1 6r 2 2 for r 5 3 2. 7n 2 4n 1 5 for n 5 2

© Harcourt

3. 15 2 2d for d 5 6 4. 2 3 2 1 3x 1 12 for x 5 2 5. Fran plants a garden in the shape of a triangle in a corner of her back yard. The area of the garden is given by the expression 1_2 bh, where b is the base of the triangle and h is the height. If the base is 3 meters and the height is 4 meters, what is the area of the garden in square meters? Grade 6

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11.2

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 10 1 4m shows the total cost at a store that charges $10 to join and $4 per movie. What is the total cost if Carla joins and rents 5 movies? $30

Spiral Review 1. Write an algebraic expression for seven more than twice a number n. 2n 1 7 2. Write an algebraic expression for seven less than a number n. 2n 2 7

Lesson Quiz Simplify each expression. Then evaluate each expression for the given value of the variable. 1. 5r 1 6r 2 2 for r 5 3 11r 2 2 5 11 3 3 2 2 5 31 2. 7n 2 4n 1 5 for n 5 2 3n 1 5 5 3 3 2 1 5 5 11

© Harcourt

3. 15 2 2d for d 5 6 15 1 d 5 15 1 6 5 21 4. 2 3 2 1 3x 1 12 for x 5 2 4 1 3x 1 12 5 3x 1 16 5 3(2) 1 16 5 22 5. Fran plants a garden in the shape of a triangle in a corner of her back yard. The area of the garden is given by the expression 1_2 bh, where b is the base of the triangle and h is the height. If the base is 3 meters and the height is 4 meters, what is the area of the garden in square meters? 1_2 bh 5 1_2 3 3 3 4 5 6 square meters Grade 6

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11.3

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents.Some stores also charge a fee to join. The expression 25 1 3m shows the total cost at a store. What equation could you use to find the number of movies rented if Carla spends $34 at the store?

Spiral Review 1. Write an expression. 5 more than 3 times a number 2. Evaluate 3x 1 4 for x 5 4. 3. Evaluate 3x 1 4 for x 5 6.

Lesson Quiz Write an equation for the word sentence. © Harcourt

1. 30 fewer than x is 10. 2. Three-fourths of y is 15. 3. 10 more than twice a number is 18.

Grade 6

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8/30/07 2:49:59 PM

11.3

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents.Some stores also charge a fee to join. The expression 25 1 3m shows the total cost at a store. What equation could you use to find the number of movies rented if Carla spends $34 at the store? 25 1 3m 5 34

Spiral Review 1. Write an expression. 5 more than 3 times a number 3x 1 5 2. Evaluate 3x 1 4 for x 5 4. 3 3 4 1 4 5 16 3. Evaluate 3x 1 4 for x 5 6. 3 3 6 1 4 5 22

Lesson Quiz Write an equation for the word sentence. © Harcourt

1. 30 fewer than x is 10. x 2 30 5 10 2. Three-fourths of y is 15. 3 _ y 5 15 4 3. 10 more than twice a number is 18. 2n 1 10 5 18

Grade 6

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11.4

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 5 1 m represents the total cost to rent the first movie at a discount video store. Use algebra tiles to model this expression.

Spiral Review Write an algebraic expression for the word expression. 1. 23 more than a number

2. four times the sum of six and a number

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a model. 1. x 1 5 5 14

2. x 1 4 5 12

3. x 2 3 5 7

4. x 2 6 5 15

5. x 1 2 5 2

Grade 6

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11.4

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The expression 5 1 m represents the total cost to rent the first movie at a discount video store. Use algebra tiles to model this expression. one green rectangle and five yellow square tiles

Spiral Review Write an algebraic expression for the word expression. 1. 23 more than a number x 1 23

2. four times the sum of six and a number 4 3 (6 1 n)

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a model. Check students’ models. 1. x 1 5 5 14 9

2. x 1 4 5 12 8

3. x 2 3 5 7 10

4. x 2 6 5 15 21

5. x 1 2 5 2 0

Grade 6

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11.5

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Let f be the joining fee. After two months, Carla has spent $12 on movies. What expression shows the total she has spent on fees and movies? If she has spent $27 total, what equation could you use to find the fee?

Spiral Review 1. Use algebra tiles to model 8 2 4 5 x.

2. Use algebra tiles to model 7 1 x 5 12.

Lesson Quiz © Harcourt

Solve and check. 1. m 1 8 5 27

2. 3 1_2 5 x 1 1

3. 7.2 1 n 5 31

4. d 1 4 5 –11

5. During the last week of August, 1 3_4 inches of rain fell in an area. This made the monthly total 4 inches. How much rain had already fallen?

Grade 6

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11.5

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Let f be the joining fee. After two months, Carla has spent $12 on movies. What expression shows the total she has spent on fees and movies? f 1 12 If she has spent $27 total, what equation could you use to find the fee? f 1 12 5 27

Spiral Review 1. Use algebra tiles to model 8 2 4 5 x. Check students’ models.

2. Use algebra tiles to model 7 1 x 5 12. Check students’ models.

Lesson Quiz © Harcourt

Solve and check. 1. m 1 8 5 27 19

2. 3 1_2 5 x 1 1 2 1_2

3. 7.2 1 n 5 31 23.8

4. d 1 4 5 –11 –15

5. During the last week of August, 1 3_4 inches of rain fell in an area. This made the monthly total 4 inches. How much rain had already fallen? 2 1_4 inches

Grade 6

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11.6

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Since joining the local video store, Carla has spent $18 total and $14 on renting movies. What equation could represent this situation if j represents the joining fee?

Spiral Review If you have one green variable tile and five red tiles on one side of the equation, what do you do to both sides of the equal sign to solve the equation?

Lesson Quiz © Harcourt

Solve and check. 1. n 2 8 5 20

2. 31 5 s 2 8.6

3. p 2 2 5 7

4. d 2 2.4 5 –7.4

5. Kim estimated the hours of homework she has. After completing 1 5_8 hours, she still has 1 _58 hours left. What was her estimate? Grade 6

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11.6

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. Since joining the local video store, Carla has spent $18 total and $14 on renting movies. What equation could represent this situation if j represents the joining fee? Possible answer: 18 5 j 1 14

Spiral Review If you have one green variable tile and five red tiles on one side of the equation, what do you do to both sides of the equal sign to solve the equation? You place five yellow tiles on both sides of the equation.

Lesson Quiz © Harcourt

Solve and check. 1. n 2 8 5 20 28

2. 31 5 s 2 8.6 39.6

3. p 2 2 5 7 9

4. d 2 2.4 5 –7.4

2

5

5. Kim estimated the hours of homework she has. After completing 1 58_ hours, she still has 1 5_8 hours left. What was her estimate? 3 1_4 hours Grade 6

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11.7

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The most Carla can spend the first two months is $45. The equation 25 1 4m shows the total cost for a $25 joining fee and m movies at $4 each. Predict how many movies she will be able to rent, and then test your prediction.

Spiral Review Solve and check. 1. t 2 14 5 10

2. 9 1 x 5 22

3. z 2 5.5 5 12

4. j 1 34.3 5 54.2

Lesson Quiz

© Harcourt

1. During the summer, Rafa read 36 books. She read twice as many nonfiction books as fiction books. How many of each did she read? 2. Some children and parents went to a movie. Each child ticket cost $2.75, and each adult ticket cost $3.50. The total cost was $24.25. How many children and how many adults went to the movie?

Grade 6

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11.7

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The most Carla can spend the first two months is $45. The equation 25 1 4m shows the total cost for a $25 joining fee and m movies at $4 each. Predict how many movies she will be able to rent, and then test your prediction. 5 movies; 25 1 4 3 5 5 45

Spiral Review Solve and check. 1. t 2 14 5 10 t 5 24

2. 9 1 x 5 22 x 5 13

3. z 2 5.5 5 12 z 5 17.5

4. j 1 34.3 5 54.2 j 5 19.9

Lesson Quiz

© Harcourt

1. During the summer, Rafa read 36 books. She read twice as many nonfiction books as fiction books. How many of each did she read? 12 fiction books; 24 nonfiction books 2. Some children and parents went to a movie. Each child ticket cost $2.75, and each adult ticket cost $3.50. The total cost was $24.25. How many children and how many adults went to the movie? 5 children and 3 adults

Grade 6

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11.8

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. If one movie rental costs $5.00 and her purchase total is $40, how many movies did Carla rent? Use algebra tiles to model this equation.

Spiral Review Solve and check. 1. x 1 2.5 5 4; x 5

2. 9 5 3.4 1 y ; y 5

3. 4 5 c 2 4; c 5

4. x 2 4.5 5 5; x 5

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a picture. 1. 4m 5 8

2. 7p 5 28

3. 4x 5 40

4. 6r 5 24

5. 42 5 6y Grade 6

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11.8

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. If one movie rental costs $5.00 and her purchase total is $40, how many movies did Carla rent? Use algebra tiles to model this equation. Check students' models of 5r 5 40, r 5 8; 8 movies

Spiral Review Solve and check. 1. x 1 2.5 5 4; x 5 1.5

2. 9 5 3.4 1 y ; y 5 5.6

3. 4 5 c 2 4; c 5 8

4. x 2 4.5 5 5; x 5 9.5

Lesson Quiz © Harcourt

Solve each equation by using algebra tiles or by drawing a picture. Check students’ models. 1. 4m 5 8 m 5 2

2. 7p 5 28 p 5 4

3. 4x 5 40 x 5 10

4. 6r 5 24 r 5 4

5. 42 5 6y y 5 7 Grade 6

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11.9

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The total cost at Store A with no joining fee is given by the expression 8m. Store B also has no joining fee, but it charges half the price of Store A to rent a video. What expression shows the price at Store B?

Spiral Review How do you solve each equation? 1. 10 5 2.5 1 x

2. a 1 3.1 5 8

3. y 2 3 5 2

4. 5 5 c 2 2.4

Lesson Quiz © Harcourt

Solve and check. 1. 7r 5 56

2. 9h_ 5 18

n __ 3. 8 5 21

4. 9.5 5 3.8x

5. Fiona bought 8 notebooks for school. The total cost of the notebooks before tax was $7.84. How much did each notebook cost?

Grade 6

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11.9

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some stores also charge a fee to join. The total cost at Store A with no joining fee is given by the expression 8m. Store B also has no joining fee, but it charges half the price of Store A to rent a video. What expression shows the price at Store B? 8m 4 2, or 4m

Spiral Review How do you solve each equation? 1. 10 5 2.5 1 x Subtract 2.5 from both sides 3. y 2 3 5 2 Add 3 to both sides

2. a 1 3.1 5 8 Subtract 3.1 from both sides 4. 5 5 c 2 2.4 Add 2.4 to both sides

Lesson Quiz © Harcourt

Solve and check. 1. 7r 5 56 r 5 8

2. 9h_ 5 18 h 5 162

n n 5 168 __ 3. 8 5 21

4. 9.5 5 3.8x x 5 2.5

5. Fiona bought 8 notebooks for school. The total cost of the notebooks before tax was $7.84. How much did each notebook cost? $0.98

Grade 6

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Problem of the Day

11.10

Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some charge a fee to join. Carla is charged a fee and the cost of 5 movies. If each movie costs $5 and the total purchase is $29.50, what is the amount of the fee?

Spiral Review Solve and check. y 1. _2 5 18: y 5 ?

2. 32 5 _4c : c 5 ?

3. _2x 5 4.8: x 5 ?

4. 45 5 d 2 15: d 5 ?

© Harcourt

Lesson Quiz 1. Kenny has to leave his house for a soccer game at 4 p.m. Before he leaves he needs to spend 30 minutes doing chores and 1 1_2 hours doing homework. What time should Kenny start his homework or chores? 2. The current temperature outside is 75° F. When Tom woke up the temperature was 25° F less than the current temperature. When Tom went to bed the night before, the temperature was 35° F. How much did the temperature change while Tom was asleep?

Grade 6

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8/30/07 2:50:24 PM

11.10

Problem of the Day Carla wants to rent movies at a video store. All of the stores charge a fee for each movie she rents. Some charge a fee to join. Carla is charged a fee and the cost of 5 movies. If each movie costs $5 and the total purchase is $29.50, what is the amount of the fee? $4.50

Spiral Review Solve and check. y 1. _2 5 18: y 5 ? 36

2. 32 5 _4c : c 5 ? 128

3. _2x 5 4.8: x 5 ? 9.6

4. 45 5 d 2 15: d 5 ? 60

© Harcourt

Lesson Quiz 1. Kenny has to leave his house for a soccer game at 4 p.m. Before he leaves he needs to spend 30 minutes doing chores and 1 1_2 hours doing homework. What time should Kenny start his homework or chores? 2 p.m. 2. The current temperature outside is 75° F. When Tom woke up the temperature was 25° F less than the current temperature. When Tom went to bed the night before, the temperature was 35° F. How much did the temperature change while Tom was asleep? 15° F

Grade 6

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12.1

Problem of the Day Alex and Sasha are making a quilt. The first row has 1 blue square, the second row has 3 blue squares, the third row has 5 blue squares, and the fourth row has 7 blue squares. How many more blue squares does each row have compared to the previous row?

27 1 6 5 28 3 2 5 25 3 6 5

Spiral Review

7 2 25 5 224 4 8 5 215 2 3 5

Lesson Quiz Write a rule for the sequence using a variable. Use the rule to find the next term. 1. 1_2 , 1 1_2 , 4 1_2 , 13 1_2 , . . . 2. 500, 100, 20, 4, . . .

© Harcourt

3. 22, 18, 14, 10, . . . 4. 1_2 , 3_4 , 1, 1 1_4 , . . . 5. Justin is training for a triathlon. On Monday he biked 10 miles and on Tuesday he biked 18 miles. On Wednesday, he biked 26 miles and on Thursday he biked 34 miles. If this pattern continues, how many miles will he bike on Saturday? Grade 6

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12.1

Problem of the Day Alex and Sasha are making a quilt. The first row has 1 blue square, the second row has 3 blue squares, the third row has 5 blue squares, and the fourth row has 7 blue squares. How many more blue squares does each row have compared to the previous row? Each row has 2 more blue squares than the previous row.

Spiral Review 27 1 6 5 2 1 28 3 2 5 2 16 25 3 6 5 2 30

7 2 25 5 12 224 4 8 5 2 3 215 2 3 5 2 18

Lesson Quiz Write a rule for the sequence using a variable. Use the rule to find the next term. Rules and terms are given. 1. 1_2 , 1 1_2 , 4 1_2 , 13 1_2 , . . . 3n; 40 1_2 2. 500, 100, 20, 4, . . . n_5 ; _45

© Harcourt

3. 22, 18, 14, 10, . . . n 2 4; 6 4. 1_2 , 3_4 , 1, 1 1_4 , . . . n 1 1_ ; 1 1_ 4 2 5. Justin is training for a triathlon. On Monday he biked 10 miles and on Tuesday he biked 18 miles. On Wednesday, he biked 26 miles and on Thursday he biked 34 miles. If this pattern continues, how many miles will he bike on Saturday? 50 miles Grade 6

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12.2

Problem of the Day Alex and Sasha are making a quilt. The table shows the fabric needed for different numbers of Number of Amount of Quilt Fabric squares. How much fabric is needed to make 6 squares?

Squares

(square inches)

1

4

2

8

3

12

Explain.

Spiral Review 1. Write a rule for the pattern: 2, 4, 6, ... 2. Write a rule for the pattern: 1, 1, 2, 3, 5, 8, ... 3. Write a rule for the nth term: 2, 4, 6, ... 4. Find the next three possible numbers in the pattern: 3, 26, 12, ...

Lesson Quiz Write an equation to represent the function. Then use the equation to find the unknown term.

© Harcourt

1.

3.

j

14

16

k

7

8

f

15

20

25

g

12

17

22

18

20

22

10

11

30

35 32

2.

4.

p

1

2

q

4

6

x

30

50

y

70

3

4

5

10

12

70

90

110

150

190

230

5. It costs $22 per ticket, plus $15 per group of tickets ordered, to attend a play. Write an equation that represents the cost for a group of s people to attend the play. If Melinda purchases 6 tickets at one time, what is the cost? Grade 6

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12.2

Problem of the Day Alex and Sasha are making a quilt. The table shows the fabric needed for different numbers of Number of Amount of Quilt Fabric squares. Squares

(square inches)

1 4 How much fabric 2 8 is needed to 3 12 make 6 squares? Explain. Each square has 4 square inches of fabric. So they will need 4 3 6 5 24 square inches of fabric.

Spiral Review 1. Write a rule for the pattern: 2, 4, 6, ... Add 2 to previous term. 2. Write a rule for the pattern: 1, 1, 2, 3, 5, 8, ... Add the two previous terms to get the term. 3. Write a rule for the nth term: 2, 4, 6, ... n 3 2 4. Find the next three possible numbers in the pattern: 3, 26, 12, ... 2 24, 48, 2 96

Lesson Quiz Write an equation to represent the function. Then use the equation to find the unknown term. Equations and terms are given. 1.

j

14

16

18

20

22

k

7

8

9

10

11

2.

© Harcourt

1

2

3

4

5

q

4

6

8

10

12

50 110

70

90

110

150

190

230

2p + 2 = q

0.5j 5 k 3.

p

f

15

20

25

g

12

17

22

f 2 3 5 g; 27

30 27

35 32

4.

x

30

y

70

2x 1 10 5 y; 110

5. It costs $22 per ticket, plus $15 per group of tickets ordered, to attend a play. Write an equation that represents the cost for a group of s people to attend the play. If Melinda purchases 6 tickets at one time, what is the cost? 15 1 22s 5 t; $147 Grade 6

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12.3

Problem of the Day Alex and Sasha are making a quilt. Four quilt squares in the first row are shown below. Assuming there is a pattern, draw the next two possible squares in the row.

Spiral Review Make a function table to represent the equation. 1. y 5 5x

2. d 5 3 1 r

Lesson Quiz Draw the next two possible figures. 1.

2.

© Harcourt

3. Draw the next possible figure. 4. 5. Alex is designing a wallpaper border for his room. The first 3 squares for the border are shown. Draw the next two squares.

Grade 6

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12.3

Problem of the Day Alex and Sasha are making a quilt. Four quilt squares in the first row are shown below. Assuming there is a pattern, draw the next two possible squares in the row. Possible answer: red

Spiral Review Make a function table to represent the equation. Answers will vary. 1. y 5 5x

2. d 5 3 1 r

Lesson Quiz Draw the next two possible figures. Possible answers are shown. 1.

2.

© Harcourt

3. Draw the next possible figure. 4. 5. Alex is designing a wallpaper border for his room. The first 3 squares for the border are shown. Draw the next two squares.

Grade 6

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12.4

Problem of the Day Alex and Sasha are making a quilt. They have 3 red squares in the first row, 5 red squares in the second row, 7 red squares in the third row, and 9 red squares in the fourth row. If this pattern continues, how many red squares will be in the eight row?

Spiral Review 1.

What is the next possible shape in the pattern?

2.

What are the next two possible shapes in the pattern?

© Harcourt

Lesson Quiz 1. Kira has a set of six bookshelves in her room. She arranged her books so there are 6 books on the top shelf, 11 on the second shelf, 16 on the third, and 21 on the fourth. If the pattern continues, how many books are on the sixth shelf? 2. Find the area of the figure below. 8 ft 19 ft

6 ft

14 ft 19 ft

Grade 6

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12.4

Problem of the Day Alex and Sasha are making a quilt. They have 3 red squares in the first row, 5 red squares in the second row, 7 red squares in the third row, and 9 red squares in the fourth row. If this pattern continues, how many red squares will be in the eight row? 17 red squares

Spiral Review 1.

What is the next possible shape in the pattern?

2.

What are the next two possible shapes in the pattern?

© Harcourt

Lesson Quiz 1. Kira has a set of six bookshelves in her room. She arranged her books so there are 6 books on the top shelf, 11 on the second shelf, 16 on the third, and 21 on the fourth. If the pattern continues, how many books are on the sixth shelf? 31

2. Find the area of the figure below. 262 ft2 8 ft 19 ft

6 ft

14 ft 19 ft

Grade 6

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13.1

Problem of the Day Morgan decorates scarves to sell at festivals. She can finish 10 scarves in one week. Morgan spends at most 40 hours each week decorating scarves. If h represents the number of hours it takes Morgan to finish one scarf, write an inequality to represent this situation.

Spiral Review Marge is designing a pattern for one of her scarves. The first row of knitting is red. The second row is green. The next 2 rows are red. The next 2 rows are green, the next 3 rows are red, and the next 3 rows are green. If she continues alternating red and green, what color will the 25th row of knitting be?

Lesson Quiz 1. Solve and graph the inequality on a number line: 2k $ 36.

2. Solve and graph the inequality on a number line: r 1 15 . 3.

© Harcourt

3. Which of the numerical values, 4, 5, or 6, are solutions to the inequality 7x , 42? 4. Write an inequality for the following word sentence. The value of 6 less than f is more than 20. 5. The sum of the ages of three friends, Casey, Rene, and Ford, is at least 39. Casey is 13 and Rene is 14. Write an inequality that relates the age of Ford, f, to the sum of the ages of the three friends. Then solve the inequality.

Grade 6

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8/30/07 2:52:32 PM

13.1

Problem of the Day Morgan decorates scarves to sell at festivals. She can finish 10 scarves in one week. Morgan spends at most 40 hours each week decorating scarves. If h represents the number of hours it takes Morgan to finish one scarf, write an inequality to represent this situation. 10h # 40; h # 4

Spiral Review Marge is designing a pattern for one of her scarves. The first row of knitting is red. The second row is green. The next 2 rows are red. The next 2 rows are green, the next 3 rows are red, and the next 3 rows are green. If she continues alternating red and green, what color will the 25th row of knitting be? The 25th row will be red.

Lesson Quiz 1. Solve and graph the inequality on a number line: 2k $ 36. k $ 18

17

2. Solve and graph the inequality on a number line: r 1 15 . 3. r . 212

–

© Harcourt

3. Which of the numerical values, 4, 5, or 6, are solutions to the inequality 7x , 42? 4 and 5

13

1

18

19

12

–

2

11

–

3

20 21

8

23

10

–

–

–

4

5

6

7

–

9

22

7

4. Write an inequality for the following word sentence. The value of 6 less than f is more than 20. f 2 6 . 20 5. The sum of the ages of three friends, Casey, Rene, and Ford, is at least 39. Casey is 13 and Rene is 14. Write an inequality that relates the age of Ford, f, to the sum of the ages of the three friends. Then solve the inequality. Possible inequalities: f 1 14 1 13 $ 39 or f 1 27 $ 39; f $ 12

Grade 6

Daily Transparency DT13.1

13.2

Problem of the Day Morgan decorates scarves to sell at y festivals. She embroiders 4 A 2 flowers on the scarves C x B 4 2 0 2 4 in the pattern shown on E 2 D the coordinate plane. 4 Write the ordered pair for each point. –

–

– –

Spiral Review 1. Solve and graph the inequality on a number line. x 1 7 # 13

2. Solve and graph the inequality on a number line. y 2 5 $ 14

Lesson Quiz Write the ordered pair for each point and the quadrant where it is located. y

© Harcourt

2. point B 3. point C 4. point D

A

4

1. point A

B

2 4

–

2

C

0

–

2

4

x

2

–

4

–

D

5. Find the distance between point A and point C. Grade 6

M09ATE6_C013DT.indd 2

Daily Transparency

DT13.2

8/31/07 9:40:04 AM

13.2

Problem of the Day Morgan decorates scarves to sell at y festivals. She embroiders 4 A 2 flowers on the scarves C x B 4 2 0 2 4 in the pattern shown on E 2 D the coordinate plane. 4 Write the ordered pair for each point. A (2 2,2), B (0,0), C (2,2), D (2,2 2), E (2 2,2 2) –

–

– –

Spiral Review 1. Solve and graph 2. Solve and graph the inequality on the inequality on a number line. a number line. x 1 7 # 13 x # 6; y 2 5 $ 14 y $ 19; 1 2 3 4 5 6 7

18 19 20 21 22 23 24

Lesson Quiz Write the ordered pair for each point and the quadrant where it is located. y

© Harcourt

2. point B (4,2) quadrant I 3. point C (2,0); x-axis 4. point D (1,25); quadrant IV

A

4

1. point A (2,4) quadrant I

B

2

x

C 4

–

2

0

–

2

4

2

–

4

–

D

5. Find the distance between point A and point C. 4 units Grade 6

Daily Transparency DT13.2

13.3

Problem of the Day Morgan decorates scarves to sell at festivals. It takes her 5 hours to decorate one scarf. Write ordered pairs to show how many hours it takes her to decorate 1, 2, 3, 4, and 5 of these scarves.

Spiral Review Solve. 1. 3_x 5 3; x 5 j

3. 2x 1 4 5 16; x 5 j

3. 24 5 _3x ; x 5 j

4. 3 5 3x; x 5 j

Lesson Quiz Use the table for questions 1–4. x y

2

2 4

2

1 2

0 0

1 j

2 1

2

1. Write the data as ordered pairs. 2. Graph the function on a coordinate plane. 3. Write an equation relating y to x.

© Harcourt

4. Find the missing value of y. 5. Jim earns $5.00 for each car he washes. Graph his earnings for 1, 2, 3, 4, and 5 cars. Then write a rule for the function.

Grade 6

M09ATE6_C013DT.indd 3

Daily Transparency

DT13.3

8/30/07 2:52:51 PM

13.3

Problem of the Day Morgan decorates scarves to sell at festivals. It takes her 5 hours to decorate one scarf. Write ordered pairs to show how many hours it takes her to decorate 1, 2, 3, 4, and 5 of these scarves. (1,5), (2,10), (3,15), (4,20), (5,25)

Spiral Review Solve. 1. 3_x 5 3; x 5 j 9

3. 2x 1 4 5 16; x 5 j 6

3. 24 5 _3x ; x 5 j 72

4. 3 5 3x; x 5 j 1

Lesson Quiz Use the table for questions 1–4. x y

2 4

2

1 2

2

0 0

1 j

y

2 1

4

2

2

x

1. Write the data as ordered pairs. (–2, 4), (–1,2), (0,0), (1, 2), (2, –1) 2. Graph the function on a coordinate plane.

4

2

–

0

–

2

4

2

–

4

–

3. Write an equation relating y to x. y 5 22x 5. Jim earns $5.00 for each car he washes. Graph his earnings for 1, 2, 3, 4, and 5 cars. Then write a rule for the function. y 5 5x

Amount Earned

© Harcourt

4. Find the missing value of y. 22 $25 $20 $15 $10 $5 0

1

2 3 4

5

Cars Washed

Grade 6

Daily Transparency DT13.3

13.4

Problem of the Day Morgan decorates scarves to sell at festivals. One of her expenses is driving to and from the festivals. The equation d 5 0.25m relates her miles (m) to her driving cost in dollars (d ). Find three ordered pairs that are solutions to this equation.

Spiral Review Solve. 1. 3x 5 18; x 5 ?

2. x_3 5 21; x 5 ?

3. 7 5 x_7 ; x 5 ?

4. 9x 5 27; x 5 ?

Lesson Quiz 1. Which table represents the graph on the coordinate plane? y

A

B x y

0 2 1

1 0

2 1

4

x y

0 2 2

1 0

2 2

2 –

4

–

2

0

2

4

x

2

–

4

–

Graph the equation on a coordinate plane. 3. y 5 23x

4. y = 2x 1 2

© Harcourt

2. y 5 x 2 3

5. The cost for renting a canoe can be shown using the equation c 5 15h 1 10, where h represents the number hours the canoe is rented and c represents the total cost. Graph the equation on a coordinate plane.

Grade 6

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Daily Transparency

DT13.4

8/31/07 9:41:04 AM

13.4

Problem of the Day Morgan decorates scarves to sell at festivals. One of her expenses is driving to and from the festivals. The equation d 5 0.25m relates her miles (m) to her driving cost in dollars (d ). Find three ordered pairs that are solutions to this equation. Possible answers: (10, 2.50), (20, 5.00), (30, 7.50)

Spiral Review Solve. 1. 3x 5 18; x 5 ? 6

2. x_3 5 21; x 5 ? 63

3. 7 5 x_7 ; x 5 ? 49

4. 9x 5 27; x 5 ? 3

Lesson Quiz 1. Which table represents the graph on the coordinate plane? B y

A

B 0 2 1

x y

1 0

2 1

4

0 2 2

x y

1 0

2

2 2

x –

4

–

2

0 –

–

Graph the equation on a coordinate plane. 2. y 5 x 2 3

3. y 5 23x

8

6

8 6

4

2 6 –4

2 0 – 2

–

© Harcourt

–

4

–

6

–

8

–

2

4

6

x

6 –4

2 0 – 2

–

2

4

6

2

x 6 –4

–

2 0 – 2

–

4

–

6

–

8

–

– –

–

2

4

6

x

4

6 8

5. The cost for renting a canoe can be shown using the equation c 5 15h 1 10, where h represents the number hours the canoe is rented and c represents the total cost. Graph the equation on a coordinate plane.

Grade 6

4

4

2 –

2

y

8 6

4

4

4. y = 2x 1 2

y

y

2

y 40 20

x –

40

–

20

0 –

–

20

40

20

40

Daily Transparency DT13.4

13.5

Problem of the Day Morgan decorates scarves to sell at festivals. One day a week she drives to various stores, picking up supplies at each store. Which graph could be used to represent this situation?

A

B

Spiral Review Graph the equation on a coordinate plane. 1. y 5 3x

2. y 5 24x 2 2

3. y 5 22x 1 1

4. y 5 25x

Lesson Quiz Speed

For 1-3, interpret the graph on the right. 1. Describe the graph.

Time

2. Tell a story about what the graph could possibly show.

© Harcourt

3. Suppose the vertical axis were labeled Altitude. Given this new information, tell a story about what the graph could possibly show.

4. Sketch a graph that could be used to represent the speed of a race car at the beginning of a race, over time, as it travels around an oval track. 5. Ask a question about your graph.

Grade 6

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Daily Transparency

DT13.5

8/30/07 2:53:02 PM

13.5

Problem of the Day Morgan decorates scarves to sell at festivals. One day a week she drives to various stores, picking up supplies at each store. Which graph could be used to represent this situation? Graph B

A

B

Spiral Review Graph the equation on a coordinate plane. y

y

1. y 5 3x

3

3

1 3

–

2

–

1 0 – 1

–

2. y 5 4x 2 2

2

2

2

x 1

2

3

1 –3 –2 –1 0 – 1

x 1

2

3

2

–

2

–

3

–

3

–

y

3. y 5 22x 1 1

1 3

–

2

–

1 0 – 1

–

y

4. y 5 25x

3 2

3 2 1

x 1

2

3

3

–

2

–

1 0 – 1

–

2

–

3

–

–

–

x 1

2

3

2 3

Lesson Quiz 1. Describe the graph. As time passes, speed remains constant. Then speed rapidly decreases over time to zero. Speed remains at zero for some time and then rapidly increases before Time returning to the previous constant rate. 2. Tell a story about what the graph could possibly show. The graph could show a car trip. The car is traveling at a constant rate of speed until it slows down and comes to a complete stop at a stop light, and then rapidly accelerates from zero back to the same constant speed. 3. Suppose the vertical axis were labeled Altitude. Given this new information, tell a story about what the graph could possibly show. The graph could show a helicopter at a constant altitude, and then descending to ground level while time passes. After sitting on the ground for a time, the helicopter takes off again, gaining altitude, until it levels off to the same constant altitude again. Racing on an Oval Track 4. Sketch a graph that could be used to represent the speed of a race car at the beginning of a race, over time, as it travels around an oval track. 5. Ask a question about your graph. Check students’ work

Grade 6

Speed

© Harcourt

Speed

For 1-3, interpret the graph on the right.

Time

Daily Transparency DT13.5

13.6

Problem of the Day Morgan decorates scarves to sell at festivals. Due to bad weather, she offers a discount today. She will sell each cotton scarf for $10 and each wool scarf for $15. She would like to collect $150 today. Use ordered pairs to show all the possible combinations of scarves she could sell to collect $150 (# of cotton scarves, # of wool scarves).

Spiral Review 1. A bicyclist rides slowly up a hill, stops at the top for a drink of water, and then races down the hill as fast as he can. Draw a line graph to represent his speed.

2. Tell a story about what the graph below could possibly show.

Lesson Quiz 1. What type of graph could you use to help you compare the number of DVRs in homes in Ohio and Missouri over a 5-year period?

© Harcourt

2. The PTSA needs to raise $7,000 to help buy new band uniforms. They are having a plant sale. The plan is to sell pansies for $15 a flat and shrubs for $20 each. What are some different combinations of pansies and flats that they can sell in order to raise $7,000? Make a graph to solve.

Grade 6

M09ATE6_C013DT.indd 6

Daily Transparency

DT13.6

8/31/07 9:42:58 AM

13.6

Problem of the Day Morgan decorates scarves to sell at festivals. Due to bad weather, she offers a discount today. She will sell each cotton scarf for $10 and each wool scarf for $15. She would like to collect $150 today. Use ordered pairs to show all the possible combinations of scarves she could sell to collect $150 (# of cotton scarves, # of wool scarves). Possible answers: (0,10), (3,8), (6,6), (9,4), (12,2), (15,0)

Spiral Review 1. A bicyclist rides slowly up a hill, stops at the top for a drink of water, and then races down the hill as fast as he can. Draw a line graph to represent his speed.

2. Tell a story about what the graph below could possibly show. Possible answer: bicyclist is slowing down from a high speed, he speeds up while going down a hill, then slows down and stops.

Lesson Quiz

Shrubs

© Harcourt

1. What type of graph could you use to help you compare the number of DVRs in homes in Ohio and Missouri over a 5-year period? Possible Answer: A double line graph. 2. The PTSA needs to raise $7,000 to help buy new band uniforms. They are having a plant sale. The plan is to Plant Sale sell pansies for $15 a flat and shrubs for 500 $20 each. What are some different 400 combinations of pansies and flats that 300 they can sell in order to raise $7,000? 200 Make a graph to solve. 100 Possible answers: (0,350), (4,347), (8,344), (12,341), (16,338), (20,335), (24,332), (28,329)….(464,2)

Grade 6

0 100 200 300 400 500

Pansies

Daily Transparency DT13.6

© Harcourt

Unit 6 • Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. How many angles are formed from this intersection?

14

Van wants to add a rock garden to his front yard. While he is sketching triangular designs, he notices that the longest side of a triangle always seems to be opposite the greatest angle in the triangle. Draw a diagram to test Van’s conjecture and explain why you agree or disagree with him.

15

Sam has a colored ink pad and some rubber stamps. If his stamp had the figure of a circle on it, how many lines of symmetry would it have?

16

Mrs. Justice has the students in her class work with different types of solid figures. Ginger records the number of faces of three different pyramids. She counts each base as a face.

17

Triangular Base 4 faces

Square Base 5 faces

Pentagonal Base 6 faces

How many faces can she expect to count on a pyramid with an octagonal base?

Grade 6

MXENl09ATE6_U06UDT.indd 1

Daily Transparency

DT • Unit 6

8/30/07 2:46:16 PM

© Harcourt

Unit 6 • Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. How many angles are formed from this intersection? Possible answer: 4 angles

14

Van wants to add a rock garden to his front yard. While he is sketching triangular designs, he notices that the longest side of a triangle always seems to be opposite the greatest angle in the triangle. Draw a diagram to test Van’s conjecture and explain why you agree or disagree with him. Students’ diagrams will vary but should support Van’s conjecture.

15

Sam has a colored ink pad and some rubber stamps. If his stamp had the figure of a circle on it, how many lines of symmetry would it have? Endless; any diameter would be a line of symmetry.

16

Mrs. Justice has the students in her class work with different types of solid figures. Ginger records the number of faces of three different pyramids. She counts each base as a face.

17

Triangular Base 4 faces

Square Base 5 faces

Pentagonal Base 6 faces

How many faces can she expect to count on a pyramid with an octagonal base? 9 faces Grade 6

Daily Transparency DT • Unit 6

14.1

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. His friends Brandon, Cally, Danielle, and Ethan each live at a point on one of the two streets. According to the map, which points are NOT on A E the same line as point A, which represents C B where Alvin lives? D

Spiral Review Find the next two figures or terms in the pattern. 1. 2. 2, 4, 8, 16,

Lesson Quiz Name the geometric figure. 1.

J

2.

F

G

K

O

For 3 and 4, use the figure at the right.

© Harcourt

3. Name the figure. 4. Name the line segment.

M P L N

5. Draw a line with points A and B that intersects a line with points C and D at point E.

Grade 6

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Daily Transparency

DT14.1

8/30/07 2:55:27 PM

14.1

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. His friends Brandon, Cally, Danielle, and Ethan each live at a point on one of the two streets. According to the map, which points are NOT on A E the same line as point A, which represents C B where Alvin lives? D B and E

Spiral Review Find the next two figures or terms in the pattern. 1. 2. 2, 4, 8, 16, 32, 64

Lesson Quiz Name the geometric figure. 1.

J

ray KJ

2.

F

G

K

O

For 3 and 4, use the figure at the right.

© Harcourt

3. Name the figure. plane LMN

M P L

4. Name the line segment. OP or PO 5. Draw a line with points A and B that intersects a line with points C and D at point E.

N D A

E C

Grade 6

line segment FG

B

Daily Transparency DT14.1

14.2

Problem of the Day Alvin draws a map of A the street on which E he lives, as well as an intersecting street. He C B knows that the streets intersect at right angles. D How can he make sure that the streets on his drawing intersect at right angles?

Spiral Review 1. What is the geometric term for an exact location in space? 2. What is the geometric figure that is a part of a line that has one endpoint and extends without end in one direction?

Lesson Quiz Name each angle. Measure it with a protractor. 1.

© Harcourt

B

3.

2. D

A E

C

F

K L

M

Identify the angle as acute, right, obtuse, or straight. 4. 1808

Grade 6

M09ATE6_C014DT.indd 2

5. 958

Daily Transparency

DT14.2

8/30/07 2:55:46 PM

14.2

Problem of the Day Alvin draws a map of A the street on which E he lives, as well as an intersecting street. He C B knows that the streets intersect at right angles. D How can he make sure that the streets on his drawing intersect at right angles? He can use a protractor to measure the angle where the streets intersect on the diagram.

Spiral Review 1. What is the geometric term for an exact location in space? point 2. What is the geometric figure that is a part of a line that has one endpoint and extends without end in one direction? ray

Lesson Quiz Name each angle. Measure it with a protractor. 1.

© Harcourt

B

3.

2. D

A C

/ABC, 908

E

F

/ DEF, 408

K L

M

/ KLM, 1458

Identify the angle as acute, right, obtuse, or straight. 4. 1808 straight

Grade 6

5. 958 obtuse

Daily Transparency DT14.2

14.3

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street.

Wilson St. 1 2 Charles St. 4 3

He wants to compare the angles created by the intersection of the streets. Which pairs of angles are congruent?

Spiral Review Identify the angle as acute, right, obtuse, or straight. 1.

2. 42˚

90˚

3.

4. (.'ñ 109˚

Lesson Quiz Use the figure at the right. 1. Name a pair of vertical angles.

2

2. Name two pairs of adjacent angles.

1

5

© Harcourt

3. Name two pairs of supplementary angles. Find the unknown angle measure. 4. 498

Grade 6

M09ATE6_C014DT.indd 3

3 4

5. Two lines intersect so that one angle measure is 73°. What is the measure of the supplementary angle?

Daily Transparency

DT14.3

8/30/07 2:56:01 PM

14.3

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street.

Wilson St.

Charles St.

1 2 4 3

He wants to compare the angles created by the intersection of the streets. Which pairs of angles are congruent? /1 and /3 are congruent, and /2 and /4 are congruent.

Spiral Review Identify the angle as acute, right, obtuse, or straight. 1.

2. 42˚

acute

3.

90˚

right

4. (.'ñ 109˚

obtuse

obtuse

Lesson Quiz Use the figure at the right.

© Harcourt

1. Name a pair of vertical angles. / 2 and /5 2. Name two pairs of adjacent angles. /1 and /5, /1 and / 2 3. Name two pairs of supplementary angles. Possible answers: /1 and / 2, / 1 and / 5 Find the unknown angle measure. 4. 498

Grade 6

41°

3 4 2

1

5

5. Two lines intersect so that one angle measure is 73°. What is the measure of the supplementary angle? 107° Daily Transparency DT14.3

14.4

Problem of the Day Alvin draws a map of A C the street on which he lives, as well as an S intersecting street. He wants to make sure that his house is located the same distance from the stop sign at the intersection as his friend Charlie’s house. How can he make sure that AS > CS

Spiral Review Find the missing angle measure. 1.

115˚

3.

2. ?

?

50˚

4. ? 72˚ ?

60˚

Lesson Quiz

© Harcourt

For 1–3, use a compass or protractor to determine if the figures are congruent.

1.

2.

3.

4. Find the measure of angle m. m 758

5. A golf ball hits a wall at a 50°angle. At what angle will the golf ball bounce off the wall? Grade 6

M09ATE6_C014DT.indd 4

Daily Transparency

DT14.4

8/30/07 2:56:24 PM

14.4

Problem of the Day Alvin draws a map of A C the street on which he lives, as well as an S intersecting street. He wants to make sure that his house is located the same distance from the stop sign at the intersection as his friend Charlie’s house. How can he make sure that AS > CS Use___ a compass to measure the length of AS; then use the same compass ___ opening to compare it to CS.

Spiral Review Find the missing angle measure. 1.

115˚

2. ?

65˚ 3.

?

50˚

50˚ 4.

? 60˚

72˚ ?

30˚

108˚

Lesson Quiz

© Harcourt

For 1–3, use a compass or protractor to determine if the figures are congruent. 1. 3.

congruent

2.

not congruent

4. Find the measure of angle m. m

308 congruent 5. A golf ball hits a wall at a 50°angle. At what angle will the golf ball bounce off the wall? 50° 758

Grade 6

Daily Transparency DT14.4

14.5

Problem of the Day Alvin draws a map of A the street on which C he lives, as well as an E intersecting street. He then draws another set of intersecting streets. Which two streets are parallel?

G D F H

B

Spiral Review Trace and bisect the figures below. 1.

A

B

2. E

3.

4.

D

F C

Lesson Quiz Trace the figure and bisect it. X

1.

Y

2.

L M

© Harcourt

3.

4.

A

B

C

C

5. Draw a line segment that is 8 cm long, and then bisect it.

Grade 6

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Daily Transparency

DT14.5

8/30/07 2:56:52 PM

14.5

Problem of the Day Alvin draws a map of A the street on which C he lives, as well as an E intersecting street. He then draws another set of intersecting streets. Which streets are parallel? ___ two ___ 4 CD and EF are parallel

G D F B

H

Spiral Review Trace and bisect the figures below. 1.

A

B

A

B

3.

2. E

E

4.

D D

F

C C

F

Lesson Quiz Trace the figure and bisect it. 1.

X

Y

X

Y

© Harcourt

3.

2.

L M

M

4.

A

B

L

A

C

C B

C

5. Draw a line segment that is 8 cm long, and then bisect it. H

Grade 6

C

J

Daily Transparency DT14.5

14.6

Problem of the Day Alvin draws a map of the street on which he lives, as A well as an intersecting street. B

C

D His friends Brandon, Carla, S and Denise live on his street. Which friend’s house is located halfway between Alvin’s house and the stop sign at the intersection?If she divides the chalkboard into two equal sections, how wide will each section be?

Spiral Review Use a compass or protractor to determine whether the figures are congruent. 1.

2.

3.

4.

Lesson Quiz

© Harcourt

Identify each pair of lines or planes as intersecting, parallel, or perpendicular, or some combination of the three. 1.

2.

3.

4.

5. Draw AB perpendicular to CD. Draw EF parallel to AB. Describe the relationship between CD and EF.

Grade 6

M09ATE6_C014DT.indd 6

Daily Transparency

DT14.6

8/30/07 2:57:25 PM

14.6

Problem of the Day Alvin draws a map of the street on which he lives, as A well as an intersecting street. B

C

D His friends Brandon, Carla, S and Denise live on his street. Which friend’s house is located halfway between Alvin’s house and the stop sign at the intersection?If she divides the chalkboard into two equal sections, how wide will each section be? Carla’s house

Spiral Review Use a compass or protractor to determine whether the figures are congruent. 1.

2. congruent

not congruent 3.

4. congruent

not congruent

Lesson Quiz Identify each pair of lines or planes as intersecting, parallel, or perpendicular, or some combination of the three. 1.

2.

© Harcourt

parallel 3.

perpendicular and intersecting 4. parallel

intersecting 5. Draw AB perpendicular to CD. Draw EF parallel to AB. Describe the relationship between CD and EF. They are perpendicular.

Grade 6

Daily Transparency DT14.6

14.7

Problem of the Day A

Alvin draws a map of the street on which he lives, as well as an intersecting street.

D S B

His friend Danielle lives on the corner of the intersecting street and a street parallel to the one Alvin lives on. He wants to draw a line to represent the street parallel to his. What would his drawing look like?

Spiral Review Identify each pair as parallel, perpendicular, intersecting, or perpendicular and intersecting. 1.

2.

3.

4.

Lesson Quiz Use a compass and straightedge to perform the construction. 1. Construct a line parallel to AB. 2. Construct a line perpendicular to CD.

© Harcourt

A

C

B

D

3. Construct two lines parallel to EF. 4. Construct two lines perpendicular to GH. E

H F

G

5. If you construct a line LM that is perpendicular to the line NO, and then construct a line PQ that is parallel to the line NO, what is the relationship between LM and PQ? Grade 6

M09ATE6_C014DT.indd 7

Daily Transparency

DT14.7

8/30/07 2:57:57 PM

14.7

Problem of the Day A

Alvin draws a map of the street on which he lives, as well as an intersecting street. His friend Danielle lives on the corner of the intersecting street and a street parallel to the one Alvin lives on. He wants to draw a line to represent the street parallel to his. What would his drawing look like?

D S B A D O S B

Spiral Review Identify each pair as parallel, perpendicular, intersecting, or perpendicular and intersecting. 1.

parallel

2.

intersecting

perpendicular 4. intersecting

3.

parallel

Lesson7.6Quiz Use a compass and straightedge to perform the construction. 1. Construct a line parallel to AB. 2. Construct a line perpendicular to CD.

© Harcourt

A

B

A

B

C

X

Y

D

C

O X Y D

3. Construct two lines parallel to EF. 4. Construct two lines perpendicular to GH. E

E F

S F

X T

Y

H G

X

S G T

H Y

5. If you construct a line LM that is perpendicular to the line NO, and then construct a line PQ that is parallel to the line NO, what is the relationship between LM and PQ? LM is perpendicular to NO. Grade 6

Daily Transparency DT14.7

14.8

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. Each point represents a house. He wants to show where his friends live. They all live on his street. Charlie’s house is not the closest or farthest from the intersection. Ethan lives to the left of Danielle. Alvin lives next door to Brandon, who lives in the second house from the intersection. Danielle does not live in the fourth house. Where does everyone live?

Spiral Review Use a compass and a straightedge to make the following constructions. _ ‹

›

1. line parallel to AB A

B

‹_›

2. line perpendicular to EF E F

© Harcourt

Lesson Quiz 1. A class survey was taken about what pets each student had. 13 students had dogs, 11 students had cats, and 8 students had birds. 5 students had dogs and cats, 3 students had dogs and birds, and 4 students had cats and birds. 7 students only had dogs, 4 students only had cats, and 3 students only had birds. 2 students had dogs, cats, and birds. How many students were surveyed? 2. Karin, Monica, Bobby, and Carl participated in a community walkathon to raise money for the chess club. They walked 1.5 mi, 3 mi, 7 mi, and 10 mi. Carl walked twice as far as Karin, and Monica walked 4 more miles than Carl. Who walked the farthest? Grade 6

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14.8

Problem of the Day Alvin draws a map of the street on which he lives, as well as an intersecting street. Each point represents A B C E a house. He wants to show where his friends live. They all live on his street. Charlie’s house is not the closest or farthest from the intersection. Ethan lives to the left of Danielle. Alvin lives next door to Brandon, who lives in the second house from the intersection. Danielle does not live in the fourth house. Where does everyone live?

D

Spiral Review Use a compass and a straightedge to make the following constructions. _ ‹

›

1. line parallel to AB A A

BB

X

Y

‹_›

2. line perpendicular to EF E

E F

X

F

Y

© Harcourt

Lesson Quiz 1. A class survey was taken about what pets each student had. 13 students had dogs, 11 students had cats, and 8 students had birds. 5 students had dogs and cats, 3 students had dogs and birds, and 4 students had cats and birds. 7 students only had dogs, 4 students only had cats, and 3 students only had birds. 2 students had dogs, cats, and birds. How many students were surveyed? 22 students 2. Karin, Monica, Bobby, and Carl participated in a community walkathon to raise money for the chess club. They walked 1.5 mi, 3 mi, 7 mi, and 10 mi. Carl walked twice as far as Karin, and Monica walked 4 more miles than Carl. Who walked the farthest? Bobby Grade 6

Daily Transparency DT14.8

15.1

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several polygons. He would like it to have four sides (a quadrilateral). Name four polygons from which he can choose.

Spiral Review 1. /1 and /2 are supplementary, and /1 and /3 are complementary. If m/1 5 25°, what are the measures of the other angles? 2. /1 is complementary to /3, and /2 and /5 are obtuse. /4 is acute, and m/5 is 6 times m/3. Match the angles to their measures: 60°, 18°, 102°, 108°, 72°.

Lesson Quiz For 1–4, use the figure to name and identify a polygon with the given number of sides. 1. 6 sides © Harcourt

2. 7 sides

K J

3. 9 sides 4. 10 sides

B

A

C L

Q

E

M F

N O

P I

D

G

H

5. Hal draws two polygons. They do not have the same number of sides. He counts 16 vertices. What polygons did Hal draw?

Grade 6

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15.1

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several polygons. He would like it to have four sides (a quadrilateral). Name four polygons from which he can choose. Possible answers: square, rectangle, parallelogram, trapezoid

Spiral Review 1. /1 and /2 are supplementary, and /1 and /3 are complementary. If m/1 5 25°, what are the measures of the other angles? m/2 5 155°, m/3 5 65° 2. /1 is complementary to /3, and /2 and /5 are obtuse. /4 is acute, and m/5 is 6 times m/3. Match the angles to their measures: 60°, 18°, 102°, 108°, 72°. m/1 5 72°, m/2 5 102°, m/3 5 18°, m/4 5 60°, m/5 5 108°

Lesson Quiz For 1–4, use the figure to name and identify a polygon with the given number of sides. Possible answers are given. 1. 6 sides KLMNHQ, hexagon © Harcourt

2. 7 sides DEGNOLM, heptagon

K J

3. 9 sides AEGNOLPQI, nonagon 4. 10 sides AKBDMEFOLI, decagon

B

A

C L

Q

E

M N

F

O

P I

D

H

G

5. Hal draws two polygons. They do not have the same number of sides. He counts 16 vertices. What polygons did Hal draw? Possible answers: heptagon and nonagon; hexagon and decagon

Grade 6

Daily Transparency DT15.1

15.2

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. One shape is a triangle. 978 8 ft

8 ft

Classify the triangle in Van’s sketch. 12 ft

Spiral Review 1. What is the name of a polygon with 7 sides? 2. What is the name of a polygon with 10 sides? 3. What type of polygon has all sides congruent and all angles congruent? 4. What term names a closed plane figure with straight sides that are connected line segments? 5. What is the name of a polygon with 9 sides? 6. What is the name for the point where line segments in a polygon meet?

Lesson Quiz Classify each triangle by its angles and sides. K 8 mm

© Harcourt

J

368

1088

13 mm

2.

8 mm 368

10.3 ft 298

L

3. Find the measure of /B and classify ∆ABC by its angles.

B

618

5 ft

1.

9 ft

?

A

1188

258

C

4. Could the measures 7 cm, 8 cm, and 5 cm be the side lengths of a triangle? Write yes or no. 5. A right triangle has one angle that measures 33°. What are all the angle measures in the triangle. Grade 6

M09ATE6_C015DT.indd 2

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15.2

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. One shape is a triangle. 978 8 ft

Classify the triangle in Van’s sketch. isosceles obtuse

8 ft

12 ft

Spiral Review 1. What is the name of a polygon with 7 sides? heptagon 2. What is the name of a polygon with 10 sides? decagon 3. What type of polygon has all sides congruent and all angles congruent? regular polygon 4. What term names a closed plane figure with straight sides that are connected line segments? polygongon 5. What is the name of a polygon with 9 sides? nonagon 6. What is the name for the point where line segments in a polygon meet? vertex

Lesson Quiz Classify each triangle by its angles and sides. K

1.

© Harcourt

J

1088

2. 368

368 13 mm

10.3 ft

8 mm

618

5 ft

8 mm

298 9 ft

L

obtuse, isosceles 3. Find the measure of /B and classify ∆ABC by its angles. 37°, obtuse, scalene

right, scalene

B ?

A

1188

258

C

4. Could the measures 7 cm, 8 cm, and 5 cm be the side lengths of a triangle? Write yes or no. yes 5. A right triangle has one angle that measures 33°. What are all the angle measures in the triangle. 33°, 90°, and 57° Grade 6

Daily Transparency DT15.2

15.3

Problem of the Day Van wants to add a rock garden to his front yard. He designs a four-sided garden with exactly two parallel sides. One of the parallel sides is 10 feet long and the other is 12 feet long. Draw a figure that matches the description of Van’s design.

Spiral Review What is true about the angles of an isosceles right triangle?

Lesson Quiz Give the most exact name for each figure. 1.

2.

Find the unknown angle measure. © Harcourt

3.

(',

o

.,

(',

4.

.)

o

5. When a diagonal is drawn in a quadrilateral, two congruent right triangles are formed. What shape is the quadrilateral?

Grade 6

M09ATE6_C015DT.indd 3

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15.3

Problem of the Day Van wants to add a rock garden to his front yard. He designs a four-sided garden with exactly two parallel sides. One of the parallel sides is 10 feet long and the other is 12 feet long. Draw a figure that matches the description of Van’s design. Possible solution: this trapezoid 10 ft has two right angles, but student’s diagram may not 12 ft have right angles.

Spiral Review What is true about the angles of an isosceles right triangle? One angle is a right angle, and the other two angles are congruent to each other.

Lesson Quiz Give the most exact name for each figure. 1.

2. square

trapezoid

Find the unknown angle measure. © Harcourt

3.

(',

o

.,

(',

4.

.)

o

108º 75º 5. When a diagonal is drawn in a quadrilateral, two congruent right triangles are formed. What shape is the quadrilateral? rectangle Grade 6

Daily Transparency DT15.3

15.4

Problem of the Day Van wants to add a rock garden to his front yard. He plans to use cacti in the garden. Van has round, square, and hexagonal containers. He arranges the containers in a pattern. Which shape should the base of the next container have?

Spiral Review 1. Draw an isosceles triangle with one obtuse angle. 2. Draw an isosceles triangle with 3 acute angles.

Lesson Quiz Find a pattern to solve.

© Harcourt

1. Ted shaded all of a triangle. Then he shaded 1_2 of a square and 1_4 of a pentagon. How much of an octagon will he shade? Write a rule for the pattern.

2. If the pattern continues, how many non-square tiles will be painted by the sixth batch? Batch No. No. of tiles painted No. of square tiles

Grade 6

M09ATE6_C015DT.indd 4

1 10 8

2 20 16

3 30 24

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DT15.4

8/30/07 3:01:00 PM

15.4

Problem of the Day Van wants to add a rock garden to his front yard. He plans to use cacti in the garden. Van has round, square, and hexagonal containers. He arranges the containers in a pattern. Which shape should the base of the next container have? hexagonal

Spiral Review 1. Draw an isosceles triangle with one obtuse angle. Check students’ work. 2. Draw an isosceles triangle with 3 acute angles. Check students’ work.

Lesson Quiz

© Harcourt

Find a pattern to solve. 1. Ted shaded all of a triangle. Then he shaded 1_2 of a square and 1_4 of a pentagon. How much of an octagon will he 1 shade? Write a rule for the pattern. Possible answer: __ 32 ; the fraction used to determine how much to shade is half of the previous shape’s fraction. 2. If the pattern continues, how many non-square tiles will be painted by the sixth batch? 12 Batch No. No. of tiles painted No. of square tiles

Grade 6

1 10 8

2 20 16

3 30 24

Daily Transparency DT15.4

15.5

Problem of the Day Van wants to add a rock garden to his front yard. One of his design sketches shows a scalene right triangle, with the shortest side measuring 7 ft. Use square dot paper to draw a triangle that fits this description.

Spiral Review 1. Jan draws an octagon with 20 diagonals. In the next row he draws 2 octagons, each with 16 diagonals. How many octagons will be in the fourth row? How many diagonals will each octagon have? 2. What is the rule for determining the next brick?

3. What is the rule for the pattern? 8, 3, 7, 2, 6, 1, 5, 0, 4 4. What are the next 2 figures in the pattern? ∆I#0#I∆I#0#

Lesson Quiz Draw the figure. Use square or isometric dot paper.

© Harcourt

1. a quadrilateral with no right angles

2. a right scalene triangle

Complete each statement. 3. An acute scalene triangle must have ______. 4. A regular nonagon must have _______. 5. Ja’Nila drew a polygon. She drew 3 diagonals in the polygon. The diagonals formed 6 equilateral triangles inside the polygon. What polygon did Ja’Nila draw?

Grade 6

M09ATE6_C015DT.indd 5

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DT15.5

8/31/07 9:58:43 AM

15.5

Problem of the Day Van wants to add a rock garden to his front yard. One of his design sketches shows a scalene right triangle, with the shortest side measuring 7 ft. Use square dot paper to draw a triangle that fits this description.

Spiral Review 1. Jan draws an octagon with 20 diagonals. In the next row he draws 2 octagons, each with 16 diagonals. How many octagons will be in the fourth row? How many diagonals will each octagon have? 4; 8 diagonals 2. What is the rule for determining the next brick? Possible answer:every other square brick is black; every third rectangular brick is gray. Bricks alternate in size. 3. What is the rule for the pattern? 8, 3, 7, 2, 6, 1, 5, 0, 4 Possible answer: subtract 5, add 4. 4. What are the next 2 figures in the pattern? ∆ I # 0 # I ∆ I # 0 # star, triangle

Lesson Quiz Draw the figure. Use square or isometric dot paper.

© Harcourt

1. a quadrilateral with no right angles

2. a right scalene triangle

Complete each statement. 3. An acute scalene triangle must have ______. all acute angles and no congruent sides 4. A regular nonagon must have _______. 9 congruent sides and 9 congruent angles 5. Ja’Nila drew a polygon. She drew 3 diagonals in the polygon. The diagonals formed 6 equilateral triangles inside the polygon. What polygon did Ja’Nila draw? regular hexagon

Grade 6

Daily Transparency DT15.5

15.6

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. Van sketches a circle with a diameter of 11 1_2 ft. What is the radius of the circle?

Spiral Review Draw each polygon. 1. regular octagon 2. equilateral triangle 3. nonagon with no congruent sides 4. quadrilateral with one right angle

Lesson Quiz For 1–3, use the circle. Name the given parts of the circle.

F

1. AB

A

2. EF 3. CAD

E

D

B C

4. Find the unknown angle measure.

© Harcourt

1038 618 1248 ? 5. Fabian baked a round birthday cake. He cut it into 10 equal slices. Each slice formed a congruent central angle. What was the measure of each central angle?

Grade 6

M09ATE6_C015DT.indd 6

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8/30/07 3:01:16 PM

15.6

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. Van sketches a circle with a diameter of 11 1_2 ft. What is the radius of the circle? 5 3_4 ft; 5.75 ft

Spiral Review Draw each polygon. Check students’ drawings. 1. regular octagon 2. equilateral triangle 3. nonagon with no congruent sides 4. quadrilateral with one right angle

Lesson Quiz For 1–3, use the circle. Name the given parts of the circle.

F

1. AB radius

A

2. EF chord 3. CAD central angle

E

D

B C

4. Find the unknown angle measure. 72˚

© Harcourt

1038 618 1248 ? 5. Fabian baked a round birthday cake. He cut it into 10 equal slices. Each slice formed a congruent central angle. What was the measure of each central angle? 360˚ 4 10 5 36˚

Grade 6

Daily Transparency DT15.6

15.7

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. He decides to install a circular garden with a 8 ft regular hexagon inside it. What is the length of one side of the hexagon?

Spiral Review 1. What is the radius of a circle with a diameter of 10 in.? 3. What is the name of a line segment with endpoints on the circle?

2. What is the diameter of a circle with a radius of 7 mi? 4. A circle has 4 central angles that measure 130°, 75°, 115°, and m. Find m.

Lesson Quiz 1. Construct a hexagon with 3-inch sides inside a circle. 2. Construct a hexagon inside a circle with a 4-centimeter radius. © Harcourt

3. Construct a hexagon inside a circle with a 6-centimeter radius. 4. Construct a square inside a circle with a 2-inch radius. 5. Construct a square inside a circle with a 5-centimeter radius.

Grade 6

M09ATE6_C015DT.indd 7

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DT15.7

8/30/07 3:01:26 PM

15.7

Problem of the Day Van wants to add a rock garden to his front yard. He is considering several shapes. He decides to install a circular garden with a 8 ft regular hexagon inside it. What is the length of one side of the hexagon? 4 ft

Spiral Review 1. What is the radius of a circle with a diameter of 10 in.? 5 in. 3. What is the name of a line segment with endpoints on the circle? chord

2. What is the diameter of a circle with a radius of 7 mi? 14 mi 4. A circle has 4 central angles that measure 130°, 75°, 115°, and m. Find m. m 5 40˚

Lesson Quiz For 1–5, check students’ drawings. 1. Construct a hexagon with 3-inch sides inside a circle. 2. Construct a hexagon inside a circle with a 4-centimeter radius. © Harcourt

3. Construct a hexagon inside a circle with a 6-centimeter radius. 4. Construct a square inside a circle with a 2-inch radius. 5. Construct a square inside a circle with a 5-centimeter radius. Grade 6

Daily Transparency DT15.7

16.1

Problem of the Day Sam has a colored ink pad and some rubber stamps. He prints the two figures shown. Are the figures congruent? Explain.

Spiral Review Complete the given constructions. 1. Construct a hexagon with 4-cm sides inside a circle. 2. Construct a square inside a circle with a 3-cm radius.

Lesson Quiz Tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1.

4 ft

5 ft 3 ft

3.

8 ft

10 ft 6 ft

2. 2 cm

4.

5 cm

2 cm 2 cm 2 cm

3 cm 5 cm

8 cm © Harcourt

3 cm

8 cm

8 cm

10 cm

10 cm 10 cm

5. Pilar’s garden is a rectangle 10 feet long and 8 feet wide. Roy’s

garden is a rectangle 30 feet long and 24 feet wide. Are the two gardens similar, congruent, or neither? Explain.

Grade 6

M09ATE6_C016DT.indd 1

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DT16.1

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16.1

Problem of the Day Sam has a colored ink pad and some rubber stamps. He prints the two figures shown. Are the figures congruent? Explain. No, their shapes are the same, but their sizes are different. The figures are similar.

Spiral Review Complete the given constructions. 1. Construct a hexagon with 4-cm sides inside a circle. Check student’s work. 2. Construct a square inside a circle with a 3-cm radius. Check student’s work.

Lesson Quiz Tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1. 4 ft

5 ft

8 ft

10 ft

2. similar

3 ft 6 ft

3. © Harcourt

congruent

2 cm

4.

5 cm

2 cm 2 cm 2 cm

3 cm

neither

8 cm

8 cm

8 cm

10 cm

3 cm 5 cm 10 cm

similar 5. Pilar’s garden is a rectangle 10 feet long and 8 feet wide. Roy’s 10 cm

garden is a rectangle 30 feet long and 24 feet wide. Are the two gardens similar, congruent, or neither? Explain. The gardens are

similar because they have the same shape, but not the same size. The side lengths of Roy’s garden are three times as long as the side lengths of Pilar’s garden. Grade 6

Daily Transparency DT16.1

16.2

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he makes a print with the stamp below, the result is the image shown. Identify the transformation.

MAS SAM Spiral Review Use , or > to tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1.

cm

2 cm 2 cm cm

2 cm 2 cm

2. cm

cm

Lesson Quiz Identify the transformation. Write translation, rotation, or reflection. 2.

3.

4.

© Harcourt

1.

5. Carolyn is designing a mosaic wall mural made of identical tiles. She creates her design by using a transformation that changes the location, but not the orientation of each tile. What transformation does she use?

Grade 6

M09ATE6_C016DT.indd 2

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DT16.2

8/30/07 3:03:34 PM

16.2

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he makes a print with the stamp below, the result is the image shown. Identify the transformation. Reflection over a vertical line

MAS MAS SAM SAM Spiral Review

Use , or > to tell if the figures are similar or congruent. If the figures are not similar or congruent, write neither. 1.

2 cm cm

2 cm

2.

cm

2 cm

2 cm

cm cm

congruent

similar

Lesson Quiz Identify the transformation. Write translation, rotation, or reflection. 1.

2. rotation

© Harcourt

3.

translation

4. reflection

rotation or reflection

5. Carolyn is designing a mosaic wall mural made of identical tiles. She creates her design by using a transformation that changes the location, but not the orientation of each tile. What transformation does she use? translation

Grade 6

Daily Transparency DT16.2

16.3

Problem of the Day Sam has a colored ink pad and some rubber stamps. One of his stamps makes the print shown below. Make a model to describe the transformation he could use to make a hexagon.

Spiral Review Tell what transformations were made to transform each figure into its next position. 1.

3.

2.

4.

Lesson Quiz Make a model and tell which transformations you could perform to determine if the two figures are congruent. 1.

© Harcourt

2.

4.

5. Ned is using the pattern shown to draw the letter T. Describe how using the strategy make a model can help you determine if he will be able to fit more than one letter T on a rectangular piece of vinyl without wasting any of the material.

Grade 6

M09ATE6_C016DT.indd 3

3.

Daily Transparency

DT16.3

8/30/07 3:03:56 PM

16.3

Problem of the Day Sam has a colored ink pad and some rubber stamps. One of his stamps makes the print shown below. Make a model to describe the transformation he could use to make a hexagon. Possible answer: reflection over a horizontal line at the top of the figure.

Spiral Review Tell what transformations were made to transform each figure into its next position. translation to the right and down 1. 2.

3.

270˚ clockwise rotation or 90˚ counter clockwise rotation

4. reflection about a vertical line

rotation

Lesson Quiz Make a model and tell which transformations you could perform to determine if the two figures are congruent. 1.

3.

congruent; a reflection about a vertical line, or a translation

© Harcourt

2.

congruent; reflection about a vertical line or a translation 4.

congruent; reflection about a vertical line, followed by a 90˚ countercloskwise rotation 5. Ned is using the pattern shown to draw the letter T. Describe how using the strategy make a model can help you determine if he will be able to fit more than one letter T on a rectangular piece of vinyl without wasting any of the material. You could make a model by tracing and cutting out identical copies of the letter T. You could then try to make a rectangle by transforming and rearranging the letters of the model. not congruent

Grade 6

Daily Transparency DT16.3

16.4

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he prints a rectangular stamp on a coordinate plane, the coordinates of the vertices are (21,2), (21,5), (25,2), and (25,5). What are the coordinates of the same rectangular stamp if it is reflected over the x-axis?

Spiral Review Make a model to determine if the two figures are congruent.

Lesson Quiz Graph the transformation of the figure with the given vertices. 1. A(3,3), B(5,3), C(4,4) translation 1 unit down and 2 units right

9 8 7 6 5 4 3 2 1

y

C A

B y

x 1 2 3 4 5 6 7 8 9

2. E(26,24), F(26,0), G(21,24), H(21,0) reflection over the y-axis 3. R(25,4), S(24,1), T(22,3) 90° counterclockwise rotation about the origin

y T

R

F

H

E

G

x

S

© Harcourt

4. W(-5,-2), X(-5,0), Y(-7,-2), Z(-7,0) reflection over the y-axis, followed by a translation 5 units up and 3 units left 5. Hayley is using a coordinate plane to plan a design for a painting. Predict the results if she rotates pentagon ABCDE 90° clockwise about the origin, and then reflects it across the y-axis. Find the coordinates of the figure after the transformations.

y

Z X

y

ED

M09ATE6_C016DT.indd 4

x

YW

AB

Grade 6

x

x C

Daily Transparency

DT16.4

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16.4

Problem of the Day Sam has a colored ink pad and some rubber stamps. When he prints a rectangular stamp on a coordinate plane, the coordinates of the vertices are (21,2), (21,5), (25,2), and (25,5). What are the coordinates of the same rectangular stamp if it is reflected over the x-axis? (2 1,22), (2 1,25), (2 5,22), and (2 5,25)

Spiral Review Make a model to determine if the two figures are congruent. not congruent

congruent

congruent

congruent

Lesson Quiz Graph the transformation of the figure with the given vertices. 1. A(3,3), B(5,3), C(4,4) translation 1 unit down and 2 units right A’(5,2), B’(7,2), C’(6,3)

9 8 7 6 5 4 3 2 1

y

C A

A’

B’

y

x

y

3. R(25,4), S(24,1), T(22,3) 90° counterclockwise rotation about the origin R’(24,25), S’(21,24), T’(23,22)

© Harcourt

C’

1 2 3 4 5 6 7 8 9

2. E(26,24), F(26,0), G(21,24), H(21,0) reflection over the y-axis E’(6, 24), F’(6, 0), G’(1, 24), H’(1,0)

F

H F’

H’ x

E

G E’

G’

T

R S

4. W(-5,-2), X(-5,0), Y(-7,-2), Z(-7,0) reflection over the y-axis, followed by a translation 5 units up and 3 units left W’(2,3), X’(2,5), Y’(4,3), Z’(4,5) 5. Hayley is using a coordinate plane to plan a design for a painting. Predict the results if she rotates pentagon ABCDE 90° clockwise about the origin, and then reflects it across the y-axis. Find the coordinates of the figure after the transformations. After the rotation, the pentagon will be in Quadrant III. The reflection across the y-axis will bring it back to Quadrant IV, but with a different orientation. The coordinates of the figure after the transformations are A”(1,-1), B”(1,-2), C”(2,-3), D”(3,-2), E”(3,-1).

Grade 6

B

R’

x T’ S’

y Z’ X’ Y’ W’

Z X

x

YW

y

x

AB ED

C

E’ A’ B’ C’

D’

Daily Transparency DT16.4

16.5

Problem of the Day Sam has a color ink pad and some rubber stamps. He prints the letter H as shown. Does his letter H stamp have line symmetry? If so, draw the lines of symmetry.

Spiral Review Graph the transformation of the figure with the given vertices. 2. A(0,2), B(0,0), C(4,2), 1. X(2,1), Y(3,5), Z(4,1) D(4,0) reflection over translation 3 units down the x-axis and 3 units left 3. Q(22,24), R(22,22), 4. E(23,1), F(21,2), G(21,5) S(24,24), T(24, 22) 90° clockwise rotation reflection over the y-axis

Tell if the figure has line symmetry. If so, draw the lines of symmetry.

© Harcourt

1.

2.

Tell if the figure has rotational symmetry. If so, identify the symmetry as a fraction of a turn and in degrees. 3.

4.

5. Kathy drew a regular polygon with 45° rotational symmetry. What type of polygon did she draw? Grade 6

M09ATE6_C016DT.indd 5

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DT16.5

8/31/07 9:44:38 AM

16.5

Problem of the Day Sam has a color ink pad and some rubber stamps. He prints the letter H as shown. Does his letter H stamp have line symmetry? If so, draw the lines of symmetry. Sam’s letter H stamp has 2 lines of symmetry as shown.

Spiral Review Graph the transformation of the figure with the given vertices. Check students’ transformations. 2. A(0,2), B(0,0), C(4,2), 1. X(2,1), Y(3,5), Z(4,1) D(4,0) reflection over translation 3 units down the x-axis and 3 units left 2 2 2 2 3. Q( 2, 4), R( 2, 2), 4. E(23,1), F(21,2), G(21,5) S(24,24), T(24, 22) 90° clockwise rotation reflection over the y-axis

Lesson Quiz Tell if the figure has line symmetry. If so, draw the lines of symmetry.

© Harcourt

1.

Yes, the figure 2. has one line of symmetry.

Yes, the figure has two lines of symmetry.

Tell if the figure has rotational symmetry. If so, identify the symmetry as a fraction of a turn and in degrees. 3.

No, the figure does not have rotational symmetry.

4.

Yes, the figure has 1_6 turn, or 60°, rotational symmetry.

5. Kathy drew a regular polygon with 45° rotational symmetry. What type of polygon did she draw? an octagon Grade 6

Daily Transparency DT16.5

17.1

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Maggie has the figure shown at the right. Name the figure.

Spiral Review State how many lines of symmetry the figure has. Then identify the degree of rotational symmetry for the figures that have rotational symmetry. 1.

2.

3. square

4. regular octagon

Lesson Quiz Name the figure. Is it a polyhedron? 2.

3.

4.

© Harcourt

1.

5. Use the words base, lateral faces, and vertex to describe an octagonal pyramid.

Grade 6

M09ATE6_C017DT.indd 1

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17.1

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Maggie has the figure shown at the right. Name the figure. hexagonal pyramid

Spiral Review State how many lines of symmetry the figure has. Then identify the degree of rotational symmetry for the figures that have rotational symmetry. 1.

5; 72˚

3. square 4; 90˚

1; no rotational symmetry

2.

4. regular octagon 8; 45˚

Lesson Quiz Name the figure. Is it a polyhedron?

© Harcourt

1.

hexagonal pyramid; yes

2.

pentagonal prism; yes

3.

4.

triangular pyramid; yes

cone; no

5. Use the words base, lateral faces, and vertex to describe an octagonal pyramid. Possible answer: An octagonal pyramid has 1 base, which is an octagon. The lateral faces of an octagonal pyramid are triangles. They meet at 1 point, or vertex.

Grade 6

Daily Transparency DT17.1

17.2

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Lyle has drawn from the views shown at the right.

top

front

side

Spiral Review Draw the following figure. Is it a polyhedron? 1. square pramid

2. cylinder

Lesson Quiz Name the solid figure that has the given views. 1.

2. top

front

top

side

front

side

Draw a top view, a front view, and a side view for each solid. 4.

© Harcourt

3.

5. Name a solid figure whose top view is a triangle, front view is a rectangle, and side view is a rectangle.

Grade 6

M09ATE6_C017DT.indd 2

Daily Transparency

DT17.2

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17.2

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Lyle has drawn from the views shown at the right. pentagonal prism

top

front

side

Spiral Review Draw the following figure. Is it a polyhedron? Check students’ drawings. 1. square pramid yes 2. cylinder no

Lesson Quiz Name the solid figure that has the given views. 1.

2. top

front

top

side

triangular pyramid

front

cylinder

side

Draw a top view, a front view, and a side view for each solid. 4.

© Harcourt

3.

top

front and side

side

top

front

side

5. Name a solid figure whose top view is a triangle, front view is a rectangle, and side view is a rectangle. triangular prism

Grade 6

Daily Transparency DT17.2

17.3

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Vera can make from the net.

Spiral Review Name the solid figure that has the given views. top

front

top

front

top

front

side side side

Lesson Quiz

© Harcourt

Identify the figure from its net. 1.

2.

3.

4.

5. What shape should be added to the figure at the right so that the result is a net for a triangular prism?

Grade 6

M09ATE6_C017DT.indd 3

Daily Transparency

DT17.3

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17.3

Problem of the Day Mrs. Justice has the students in her class work with different types of solid figures. Name the figure that Vera can make from the net. square pyramid

Spiral Review Name the solid figure that has the given views. top

front

top

front

top

front

side side side

cone octagonal pyramid rectangular prism

Lesson Quiz Identify the figure from its net. 2.

1.

hexagonal pyramid

rectangular prism 4.

3.

© Harcourt

triangular pyramid pentagonal prism 5. What shape should be added to the figure at the right so that the result is a net for a triangular prism? rectangle

Grade 6

Daily Transparency DT17.3

17.4

Problem of the Day Mrs. Justice has the students in her class work with different types of prisms. Prism

Vertices (V)

Faces (F)

Octagonal

16

10

Pentagonal

10

V1F2? 5E

Edges (E) 24

Write a formula to find the number of edges of a prism, based on the number of vertices and faces. How many edges does a pentagonal prism have?

Spiral Review Identify the solid figure from its net.

1.

2.

Lesson Quiz 1. Julian draws the top views of three different pyramids and records the number of visible edges on each view. What type of pyramid has a top view with 18 visible edges? Top View

Triangular pyramid

© Harcourt

Number of visible edges

6

Rectangular pyramid

Pentagonal pyramid

8

10

2. Logan draws and cuts out nets for prisms. To make each net, he draws all the faces, then cuts each face out, and finally uses pieces of tape to make the solid figure.

If Logan makes a net for a hexagonal prism, how many pieces of tape must he use to form the prism?

Grade 6

M09ATE6_C017DT.indd 4

Daily Transparency

DT17.4

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17.4

Problem of the Day Mrs. Justice has the students in her class work with different types of prisms. Prism

Vertices (V)

Faces (F)

Octagonal

16

10

Pentagonal

10

V1F2? 5E

Edges (E) 24

Write a formula to find the number of edges of a prism, based on the number of vertices and faces. How many edges does a pentagonal prism have? Formula: V 1 F 2 2 5 E; a pentagonal prism has 15 edges.

Spiral Review Identify the solid figure from its net.

1.

2.

triangular pyramid

rectangular prism

Lesson Quiz 1. Julian draws the top views of three different pyramids and records the number of visible edges on each view. What type of pyramid has a top view with 18 visible edges? Top View

© Harcourt

Triangular pyramid

Rectangular pyramid

Pentagonal pyramid

Number of 6 8 10 visible edges a pyramid with a nonagon for a base 2. Logan draws and cuts out nets for prisms. To make each net, he draws all the faces, then cuts each face out, and finally uses pieces of tape to make the solid figure.

If Logan makes a net for a hexagonal prism, how many pieces of tape must he use to form the prism? 18

Grade 6

Daily Transparency DT17.4

© Harcourt

Unit 7 • Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They crossed the finish line at almost the same time. What units might be appropriate for measuring their times?

18

Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. Kirsty knows the sum of the lengths of two adjoining sides of her garden. How can she find the perimeter of the garden? Explain.

19

The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. What is the minimum area of a pool cover for this pool?

20

Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. If the top of the trailer is left open for dumping, what would the surface area of the model trailer be?

21

Grade 6

MXENl09ATE6_U07UDT.indd 1

Daily Transparency

DT • Unit 7

8/30/07 2:46:55 PM

© Harcourt

Unit 7 • Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They crossed the finish line at almost the same time. What units might be appropriate for measuring their times? Possible answer: hours, minutes, and seconds

18

Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. Kirsty knows the sum of the lengths of two adjoining sides of her garden. How can she find the perimeter of the garden? Explain. Possible explanation: Because the sum of the lengths of any two adjoining sides of a rectangle is equal to the sum of the lengths of the other two adjoining sides, Kirsty can multiply the original sum by 2 to find the perimeter.

19

The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. What is the minimum area of a pool cover for this pool? 2,250 ft2

20

Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. If the top of the trailer is left open for dumping, what would the surface area of the model trailer be? A 5 2 3 8 3 5 1 2 3 15 3 5 1 8 3 15 5 350 cm2.

21

Grade 6

Daily Transparency DT • Unit 7

18.1

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The race began at 9:25 A.M. Katie finished at 3:37 P.M. How long did it take Katie to complete the race?

Spiral Review 1. Subtract 4 1_7 from 7 _37

2. Subtract 3 1_3 from 7 _34

3. 5 2 3 2_5 5

4. 6 1_4 2 4 5_6 5

Lesson Quiz Find the elapsed time.

© Harcourt

1. start: 7:37 A.M. end : 11:06 A.M. Find the end time. 3. start: 1:47 P.M. work for 6 hr 21 min

Grade 6

M09ATE6_C018DT.indd 1

2. start: 10:37 A.M. end : 5:15 P.M.

4. start: 9:47 P.M. sleep for 7 hr 45 min

Daily Transparency

DT18.1

8/30/07 3:16:40 PM

18.1

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The race began at 9:25 A.M. Katie finished at 3:37 P.M. How long did it take Katie to complete the race? 6 hr 12 min

Spiral Review 5 __ 1. Subtract 4 1_7 from 7 37_ 3 2_7 2. Subtract 3 1_3 from 7 3_4 4 12

3. 5 2 3 2_5 5 1 3_5

5 4. 6 1_4 2 4 5_6 5 1 __ 12

Lesson Quiz

© Harcourt

Find the elapsed time. 1. start: 7:37 A.M. end : 11:06 A.M. 3 hr 29 min

2. start: 10:37 A.M. end : 5:15 P.M. 6 hr 38 min

Find the end time. 3. start: 1:47 P.M. work for 6 hr 21 min 8:08 P.M. Grade 6

4. start: 9:47 P.M. sleep for 7 hr 45 min 5:32 A.M. Daily Transparency DT18.1

18.2

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Katie got a flat tire only 15 yd from the starting line. How many feet from the starting line did she get a flat tire?

Spiral Review Find the elapsed time. Start time 5:32 A.M. Start time 6:47 A.M. End time 1:45 P.M. End time 3:25 P.M. Elapsed time ____ Elapsed time___

Lesson Quiz © Harcourt

Convert to the given unit. 1. 4 lb 2 oz 5 t oz

2. 45 in. 5 x ft y in.

3. 8 c 5 k qts Compare. Write , or = for each d . 4. 260 sec d 4 min 50 sec

Grade 6

M09ATE6_C018DT.indd 2

5. 13 sq yd d 117 sq ft

Daily Transparency

DT18.2

8/30/07 3:16:44 PM

18.2

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Katie got a flat tire only 15 yd from the starting line. How many feet from the starting line did she get a flat tire? 45 feet

Spiral Review Find the elapsed time. Start time 5:32 A.M. Start time 6:47 A.M. End time 1:45 P.M. End time 3:25 P.M. Elapsed time ____ Elapsed time___ 8 hr 13 min 8 hr 38 min

Lesson Quiz © Harcourt

Convert to the given unit. 1. 4 lb 2 oz 5 t oz 66 oz

2. 45 in. 5 x ft y in. 3 ft 9 in.

3. 8 c 5 k qts 2 Compare. Write , or = for each d . 4. 260 sec d 4 min 50 sec ,

Grade 6

5. 13 sq yd d 117 sq ft 5

Daily Transparency DT18.2

18.3

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They raced 13 km. One kilometer equals 1,000 m. How many meters did they race?

Spiral Review Convert to the given unit. 1. 120 ft 5 x in.

2. 150 oz 5 x lb y oz

3. 3 pt 3 c 5 n c

4. 511 ft 5 r yd s ft

Lesson Quiz © Harcourt

Convert to the given unit. 1. 325 mL 5 j L

2. 4.89 km 5 j m

3. 0.05 g 5 j kg Compare. Write , or 5 for each d. 4. 45,000 dL d 450 cL

Grade 6

M09ATE6_C018DT.indd 3

5. 90.2 g d 9,002 mg

Daily Transparency

DT18.3

8/30/07 3:16:46 PM

18.3

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. They raced 13 km. One kilometer equals 1,000 m. How many meters did they race? 13,000 m

Spiral Review Convert to the given unit. 1. 120 ft 5 x in. 1,440 in. 3. 3 pt 3 c 5 n c 9c

2. 150 oz 5 x lb y oz 9 lb 6 oz 4. 511 ft 5 r yd s ft 170 yd 1 ft

Lesson Quiz © Harcourt

Convert to the given unit. 1. 325 mL 5 j L 0.325 L

2. 4.89 km 5 j m 4,890 m

3. 0.05 g 5 j kg 0.00005 kg Compare. Write , or 5 for each d. 4. 45,000 dL d 450 cL .

Grade 6

5. 90.2 g d 9,002 mg .

Daily Transparency DT18.3

18.4

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Erin needed to drink 4 c of liquids per hour during the 3-hour race. She carried 3 pt of water and 2 qt of energy drink. Did Erin carry enough water and energy drink?

pt c

Water 1 2 2 4

Energy Drink qt 1 2 c 4 8

3 6

Spiral Review Convert to the given unit. 1. kg 5 n g 3. 0.41 L 5 y ml

2. 1.3 m 5 x hm 4. 8.7 cm 5 z mm

Lesson Quiz

© Harcourt

Make a model or make a table to solve. 1. Mrs. Cooper has 7 bird feeders to fill. Each bird feeder can hold 1 qt of birdseed. If Mrs. Cooper has a new bag of seed that contains 30 c of seed, will she have enough to fill all the bird feeders? 2. Ms. Smith is conducting an experimental study. The study involves making observations every 90 sec. If the study requires her to do this for 2 hr, about how many times does she make the observations?

Grade 6

M09ATE6_C018DT.indd 4

Daily Transparency

DT18.4

8/30/07 3:16:50 PM

18.4

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Erin needed to drink 4 c of liquids per hour during the 3-hour race. She carried 3 pt of water and 2 qt of energy drink. Did Erin carry enough water and energy drink? Yes, 6 c of water and 8 c of energy drink is more than the 12 c she wanted to drink during the race.

pt c

Water 1 2 2 4

3 6

Energy Drink qt 1 2 c 4 8

Spiral Review Convert to the given unit. 1. kg 5 n g 10,000 2. 1.3 m 5 x hm 0.013 3. 0.41 L 5 y ml 410 4. 8.7 cm 5 z mm 87

Lesson Quiz

© Harcourt

Make a model or make a table to solve. 1. Mrs. Cooper has 7 bird feeders to fill. Each bird feeder can hold 1 qt of birdseed. If Mrs. Cooper has a new bag of seed that contains 30 c of seed, will she have enough to fill all the bird feeders? Check students’ work; Yes, she needs 28 c and has 30c. 2. Ms. Smith is conducting an experimental study. The study involves making observations every 90 sec. If the study requires her to do this for 2 hr, about how many times does she make the observations? Check students’ work; 80 times Grade 6

Daily Transparency DT18.4

18.5

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Each cyclist’s bicycle was weighed before the race to make sure it met race regulations. Which is the more appropriate unit of measure for a bicycle’s mass— milligrams or kilograms?

Spiral Review Convert to the given unit. 1. 71 mg 5 v g

2. 5 lb 6 oz 5 t oz

3. 4.5 L 5 y mL

4. 72 in. 5 t yd

Lesson Quiz Tell which measurement is more precise.

© Harcourt

1. 19 ft or 6 yd

2. 1 km or 980 m

3. 8 hL or 873 L Choose the more appropriate unit of measure 4. the weight of a horse pounds or ounces

Grade 6

M09ATE6_C018DT.indd 5

5. length of a tennis court meters or hectometers

Daily Transparency

DT18.5

8/30/07 3:16:52 PM

18.5

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. Each cyclist’s bicycle was weighed before the race to make sure it met race regulations. Which is the more appropriate unit of measure for a bicycle’s mass— milligrams or kilograms? kilograms

Spiral Review Convert to the given unit. 1. 71 mg 5 v g 0.071 3. 4.5 L 5 y mL 4,500

2. 5 lb 6 oz 5 t oz 86 4. 72 in. 5 t yd 2

Lesson Quiz Tell which measurement is more precise.

© Harcourt

1. 19 ft or 6 yd 19 ft

2. 1 km or 980 m 980 m

3. 8 hL or 873 L 873 L Choose the more appropriate unit of measure 4. the weight of a horse pounds or ounces pounds Grade 6

5. length of a tennis court meters or hectometers meters Daily Transparency DT18.5

18.6

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The mass of each cyclist’s bike was measured before the race. Katie estimates that the mass of her bike is 6.5 kg. Its actual mass is 6,495 g to the nearest gram. Which mass is greater, the measurement or the estimate?

Spiral Review 1. Tell which measurement is more 2. Tell which measurement is more precise. 4 yd or 11 ft precise. 650 mL or 1 L 3. Choose the more appropriate 4. Choose the more appropriate unit. unit. Weight of a peanut butter Food for a baby bird: milliliter sandwich: ounces or pounds or liter

© Harcourt

Lesson Quiz 1. Estimate the length of 2 textbooks. 2. Find the actual lengths of 2 textbooks. 3. Compare the estimate and actual lengths of each textbook.

Grade 6

M09ATE6_C018DT.indd 6

Daily Transparency

DT18.6

8/30/07 3:16:55 PM

18.6

Problem of the Day Katie, Erin, and Shawnee competed in a cycling race. The mass of each cyclist’s bike was measured before the race. Katie estimates that the mass of her bike is 6.5 kg. Its actual mass is 6,495 g to the nearest gram. Which mass is greater, the measurement or the estimate? The estimate is greater.

Spiral Review 1. Tell which measurement is more 2. Tell which measurement is more precise. 4 yd or 11 ft 11 ft precise. 650 mL or 1 L 650 mL 3. Choose the more appropriate 4. Choose the more appropriate unit. unit. Weight of a peanut butter Food for a baby bird: milliliter sandwich: ounces or pounds or liter milliliter ounces

© Harcourt

Lesson Quiz 1. Estimate the length of 2 textbooks. Answers will vary. 2. Find the actual lengths of 2 textbooks. Answers will vary. 3. Compare the estimate and actual lengths of each textbook. Answers will vary.

Grade 6

Daily Transparency DT18.6

19.1

Problem of the Day Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. The length of the garden is 22 ft and the width is 14 ft. What is the perimeter of the garden? 22 ft 14 ft

Spiral Review 1. a. Estimate the lengths in mm of two small objects in your classroom. Record your estimates. b. Measure the lengths of the objects to the nearest millimeter. Record your measurements. c. Use ,, ., or 5 to compare your estimates to the actual measurements. Record your findings.

Lesson Quiz For 1–3, ﬁnd the perimeter. 1.

9 cm

4 cm

© Harcourt

11 cm

2.

3 21 m

3.

5 41 m

4.2 in. 3.8 in.

6.2 in. 6 in. 5.2 in.

4. Look at the ﬁgure below. 26 ft

28 ft

x 17 ft

If the perimeter is 81 ft, what is the length of the unknown side. 5. A rectangle has width w. Its length is 5 less than 3 times its width. Find the perimeter of the rectangle in terms of w.

Grade 6

M09ATE6_C019DT.indd 1

Daily Transparency

DT19.1

8/30/07 2:55:52 PM

19.1

Problem of the Day Kirsty has a circular flower bed in her backyard. The flower bed is in a rectangular garden. The length of the garden is 22 ft and the width is 14 ft. What is the perimeter of the garden? The perimeter of the garden is 72 ft. 22 ft 14 ft

Spiral Review 1. a. Estimate the lengths in mm of two small objects in your classroom. Record your estimates. b. Measure the lengths of the objects to the nearest millimeter. Record your measurements. c. Use ,, ., or 5 to compare your estimates to the actual measurements. Record your findings. Check students’ estimates and measurements.

Lesson Quiz For 1–3, find the perimeter. 1.

2.

9 cm

4 cm

24 cm

11 cm

3. 3 21 m 5 41 m

4.2 in.

© Harcourt

6 in.

3.8 in.

17 1_2 m

5.2 in.

25.4 in.

4. Look at the figure below. 26 ft

6.2 in.

28 ft

x 17 ft

If the perimeter is 81 ft, what is the length of the unknown side. 10 ft 5. A rectangle has width w. Its length is 5 less than 3 times its width. Find the perimeter of the rectangle in terms of w. 8w 2 10 5 P

Grade 6

Daily Transparency DT19.1

19.2

Problem of the Day Kirsty has a circular flower bed in her backyard. She wants to know its circumference. Kirsty knows that the diameter of the flower bed is 6 ft.

6 ft

How can Kirsty estimate the circumference of the flower bed?

Spiral Review 1. A rectangle has sides 2. A square has a perimeter 4 cm and 6 cm. What is of 40 in. What is its side its perimeter? length?

Lesson Quiz Use a compass and a ruler to draw each circle with the given radius. Estimate the circumference of each circle using a string and ruler. 1. radius 5 7 cm

2. radius 5 8.5 cm

© Harcourt

Estimate the circumference of each circle. 3.

5.

Grade 6

M09ATE6_C019DT.indd 2

321 m

4. ('dd

+]k

Daily Transparency

DT19.2

8/30/07 2:56:09 PM

19.2

Problem of the Day Kirsty has a circular flower bed in her backyard. She wants to know its circumference. Kirsty knows that the diameter of the flower bed is 6 ft.

6 ft

How can Kirsty estimate the circumference of the flower bed? multiply the diameter by 3

Spiral Review 1. A rectangle has sides 2. A square has a perimeter 4 cm and 6 cm. What is of 40 in. What is its side its perimeter? 20 cm length? 10 in.

Lesson Quiz Use a compass and a ruler to draw each circle with the given radius. Estimate the circumference of each circle using a string and ruler. 1. radius 5 7 cm 42 cm

2. radius 5 8.5 cm 51 cm

© Harcourt

Estimate the circumference of each circle. 3.

5.

Grade 6

321 m

+]k

10 1_ mi 2

4.

('dd

30 mm

24 ft

Daily Transparency DT19.2

19.3

Problem of the Day Kirsty has a circular flower bed in her backyard. The diameter of the flower bed is 6 ft. Kirsty wants to edge the flower bed with stones.

-]k

What is the circumference of the flower bed?

Spiral Review 1. A circle has a diameter of 6 in. Estimate its circumference.

2. A circle has a radius of 6 in. Estimate its circumference.

Lesson Quiz __ for pi. Find the circumference of each circle. Use 3.14 or 22 7

Round to the nearest whole number. 1.

),d

2.

-*(`e%

© Harcourt

__ for pi. Find the diameter of each circle. Use 3.14 or 22 7 Round to the nearest whole number.

3. circumference 5 15.6 ft 4. circumference 5 4 3_4 mi 5. A hamster’s exercise wheel has a radius of 4 inches. How far will the hamster have run after spinning the wheel 4 complete revolutions?

Grade 6

M09ATE6_C019DT.indd 3

Daily Transparency

DT19.3

8/30/07 2:56:52 PM

19.3

Problem of the Day Kirsty has a circular flower bed in her backyard. The diameter of the flower bed is 6 ft. Kirsty wants to edge the flower bed with stones.

-]k

What is the circumference of the flower bed? about 18.8 ft

Spiral Review 1. A circle has a diameter of 6 in. Estimate its circumference. 18 in.

2. A circle has a radius of 6 in. Estimate its circumference. 36 in.

Lesson Quiz __ for pi. Find the circumference of each circle. Use 3.14 or 22 7

Round to the nearest whole number. 1.

),d

about 79 m

2.

-*(`e%

about 40 in.

© Harcourt

__ for pi. Find the diameter of each circle. Use 3.14 or 22 7 Round to the nearest whole number.

3. circumference 5 15.6 ft d is about 5 ft 4. circumference 5 4 3_4 mi d is about 1 mi 5. A hamster’s exercise wheel has a radius of 4 inches. How far will the hamster have run after spinning the wheel 4 complete revolutions? 100.48 inches or about 100 inches

Grade 6

Daily Transparency DT19.3

19.4

Problem of the Day Kirsty has a circular flower bed in her backyard. The radius of the flower bed is 4 ft. Kirsty wants to edge the flower bed with bricks that cost $2 each. How many bricks will she need? Do you have too much or too little information to solve the problem? Explain.

Spiral Review 1. The diameter of a circle is 6 cm. Find the circumference. Use 3.14 for p. 3. The circumference of a circle is 21.98 m. Find the diameter of the circle. Use 3.14 for p.

2. The radius of a circle is 9 m. Find the circumference. Use 3.14 for p. 4. The circumference of a circle is 28.26 m. Find the radius of the circle. Use 3.14 for p.

Lesson Quiz

© Harcourt

Tell whether each problem has too much, too little, or the right amount of information. Then solve the problem if possible, or describe the information needed to solve it. 1. Peter jogs for 45 min three times a week on a circular track. The track has a diameter of 0.1 mi. How far does Peter jog each week? Use 3.14 for π.

2. Kari has a rectangular piece of poster board that is 18 in. by 24 in. She cuts a piece out of the corner that is 10 in. by 12 in. and uses it to mount a photograph. What is the perimeter of the remaining poster board?

Grade 6

M09ATE6_C019DT.indd 4

Daily Transparency

DT19.4

8/30/07 2:57:02 PM

19.4

Problem of the Day Kirsty has a circular flower bed in her backyard. The radius of the flower bed is 4 ft. Kirsty wants to edge the flower bed with bricks that cost $2 each. How many bricks will she need? Do you have too much or too little information to solve the problem? Explain. There is too little information to solve the problem. You need to know the size of the bricks to find out how many she will need. There is also irrelevant information: the price of the bricks.

Spiral Review 1. The diameter of a circle is 2. The radius of a circle is 9 m. 6 cm. Find the circumference. Find the circumference. Use Use 3.14 for p. about 18.84 cm 3.14 for p. about 56.52 m 3. The circumference of a circle 4. The circumference of a circle is 21.98 m. Find the diameter is 28.26 m. Find the radius of of the circle. Use 3.14 for p. the circle. Use 3.14 for p. about 7 m about 4.5 m

Lesson Quiz

© Harcourt

Tell whether each problem has too much, too little, or the right amount of information. Then solve the problem if possible, or describe the information needed to solve it. 1. Peter jogs for 45 min three times a week on a circular track. The track has a diameter of 0.1 mi. How far does Peter jog each week? Use 3.14 for π. Not enough information. You would need to know either the rate at which he is jogging or how many times he runs around the track in 45 minutes. 2. Kari has a rectangular piece of poster board that is 18 in. by 24 in. She cuts a piece out of the corner that is 10 in. by 12 in. and uses it to mount a photograph. What is the perimeter of the remaining poster board? The right amount; 84 in.

Grade 6

Daily Transparency DT19.4

20.1

Problem of the Day The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. A flat-roof tarp is suspended above the pool, extending beyond each edge by 1 ft. Estimate the area of the tarp. 75 ft 30 ft Pool Dimensions

Spiral Review 1. Find the perimeter of a rectangle with a length of 4 m and a width of 7 m. 3. Find the side length of a square with a perimeter of 18 in.

2. Find the circumference of a circle with a radius of 7 in. 4. Find the radius of a circle with a circumference of 314 cm.

Lesson Quiz

© Harcourt

For 1-4, estimate the area. 1.

2.

3.

4.

5. Use graph paper to draw a sandtrap on a golf course with an estimated area of 40 sq ft. Grade 6

M09ATE6_C020DT.indd 1

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20.1

Problem of the Day The high school is renovating its swimming pool. The new pool will be rectangular, with a length of 75 ft and a width of 30 ft. A flat-roof tarp is suspended above the pool, extending beyond each edge by 1 ft. Estimate the area of the tarp. about 2,400 ft2 75 ft 30 ft Pool Dimensions

Spiral Review 1. Find the perimeter of a rectangle with a length of 4 m and a width of 7 m. 22 m 3. Find the side length of a square with a perimeter of 18 in. 4.5 in.

2. Find the circumference of a circle with a radius of 7 in. about 44 in. 4. Find the radius of a circle with a circumference of 314 cm. about 50 cm

Lesson Quiz

© Harcourt

For 1-4, estimate the area. 1.

25 sq units

2.

3.

about 15 sq units 4.

58.5 sq units

about 54 sq units

5. Use graph paper to draw a sandtrap on a golf course with an estimated area of 40 sq ft. Check students’ drawings. Grade 6

Daily Transparency DT20.1

20.2

Problem of the Day The high school is renovating its swimming pool. Tiles will cover the bottom of the 75 ft by 30 ft pool. They will not cover the logo in the 10 ft by 8 ft center rectangle. Find the area of the pool floor that needs tiles.

Spiral Review Estimate the area of the figure. Each square represents 1 cm2. 1.

2.

Lesson Quiz Find the area for each. 9 ft

1.

2. 7 in.

3 ft

© Harcourt

4 in. 6m

3. 6m

4.

2m 5m

5. Paula is making a triangular ﬂag that will have base of 3_4 yd and a height of 1 yd. How many square yards of fabric does she need to make the ﬂag? Grade 6

M09ATE6_C020DT.indd 2

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8/30/07 3:12:05 PM

20.2

Problem of the Day The high school is renovating its swimming pool. Tiles will cover the bottom of the 75 ft by 30 ft pool. They will not cover the logo in the 10 ft by 8 ft center rectangle. Find the area of the pool floor that needs tiles. 2,250 ft2 2 80 ft2 2 2,170 ft2.

Spiral Review Estimate the area of the figure. Each square represents 1 cm2. 1.

2.

9 cm2

17 cm2

Lesson Quiz Find the area for each. 1.

2.

9 ft

7 in.

3 ft

© Harcourt

27 ft2

4 in.

6m

3.

4.

6m

36 m2

14 in.2

2m 5m

10 cm2

5. Paula is making a triangular flag that will have base of 3_4 yd and a height of 1 yd. How many square yards of fabric does she need to make the flag? 3_8 yd2 Grade 6

Daily Transparency DT20.2

20.3

Problem of the Day The high school is renovating its swimming pool. One of the banners from a swim competition is the shape of a trapezoid. Use graph paper and find the trapezoid’s area by counting the squares. ()Zd (*Zd

()Zd

(*Zd

))Zd

Spiral Review Triangle: b 5 18 cm, h 5 10 cm, A 5 ? Triangle: b 5 12.5 cm, h 5 ? cm, A 5 37.5 cm2

Lesson Quiz Find the area. )'`e%

1.

,d

2.

(,`e% ('`e%

0d

.d (-%*d

3.

4. )-%,]k

(/]

0%)Zd *Zd

© Harcourt

()]k

5. The city’s convention center has built a new auditorium for concerts. The stage is 52 feet from front to back. The front length of the stage measures 100 feet. The back length measures 76 feet. What is the area of the stage?

Grade 6

M09ATE6_C020DT.indd 3

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20.3

Problem of the Day The high school is renovating its swimming pool. One of the banners from a swim competition is the shape of a trapezoid. Use graph paper and find the trapezoid’s area by counting the squares. 209 cm2 ()Zd (*Zd

()Zd

(*Zd

))Zd

Spiral Review Triangle: b 5 18 cm, h 5 10 cm, A 5 ? 90 cm2 Triangle: b 5 12.5 cm, h 5 ? cm, A 5 37.5 cm2 6

Lesson Quiz Find the area. )'`e%

1.

(,`e% ('`e%

,d

2. 0d

200 in2

.d

74.55 m2

(-%*d

3.

4. )-%,]k

© Harcourt

()]k

(/]k267

ft2

0%)Zd *Zd

27.6 cm2

5. The city’s convention center has built a new auditorium for concerts. The stage is 52 feet from front to back. The front length of the stage measures 100 feet. The back length measures 76 feet. What is the area of the stage? 4,576 ft2

Grade 6

Daily Transparency DT20.3

20.4

Problem of the Day The high school is renovating its swimming pool. A rectangular whirlpool with a length of 6 ft and a width of 5 ft will be installed next to the pool. Describe a rectangle that has the same perimeter but a different area.

Spiral Review Find the areas of the figures below. 1.

2. 5m

4m

3 in.

6m

2 in. 2 in. 6 in.

3 in.

Lesson Quiz 1. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same area but a different perimeter.

2. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same perimeter but a different area. 9 cm

2 ft

4 cm

© Harcourt

6 ft

3. For each figure, find the perimeter and area. Double the dimensions and sketch a new figure, then find the new perimeter and area.

5 in.

7m 7m

Grade 6

M09ATE6_C020DT.indd 4

4. What’s the Error? Ben said doubling the side lengths and height of angle will double the perimeter and area.

4 in.

5 in.

6 in.

Daily Transparency

DT20.4

8/30/07 3:12:36 PM

20.4

Problem of the Day The high school is renovating its swimming pool. A rectangular whirlpool with a length of 6 ft and a width of 5 ft will be installed next to the pool. Describe a rectangle that has the same perimeter but a different area. Possible answer: The original whirlpool has a perimeter of 22 ft and an area of 30 ft2. A whirlpool with a length of 7 ft and a width of 4 ft also has a perimeter of 22 ft, but an area of 28 ft2.

Spiral Review Find the areas of the figures below. 1.

2. 5m

4m

3 in.

6m

2 in. 2 in. 6 in.

3 in.

24 m2

8 in.2

Lesson Quiz 1. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same area but a different perimeter. 16 ft; 12 ft2

9 cm

3 ft

2 ft 6 ft

© Harcourt

2. Find the perimeter and area of the following rectangle. Then draw another rectangle that has the same perimeter but a different area. 26 cm; 36 cm2 4 cm

4 ft

3. For each figure, find the perimeter and area. Double the dimensions and sketch a new figure, then find the new perimeter and area. 28 cm; 49 cm2 14 m

6 ft

4. What’s the Error? Ben said doubling the side lengths and height of angle will double the perimeter and area. 16 in.; 12 in.2 5 in.

7m

5 in. 4 in.

7m

7 ft

14 m

10 in.

10 in. 8 in.

6 in. 12 in.

Grade 6

Daily Transparency DT20.4

20.5

Problem of the Day The high school is renovating its swimming pool. The seat cushions on the chairs by the pool will be covered with material that has the school’s intials. To find the area of the material, the circumference 9 in. of the cushion is traced on graph paper. Estimate the area of the circle.

Spiral Review Find the perimeter and area of a rectangle that has a length of 4 cm and a width of 8 cm. Then describe another rectangle that has the same area but a different perimeter.

Lesson Quiz Find the area of a circle with the given radius. Use 3.14 for π. © Harcourt

1. r 5 3 ft

2. r 5 0.6 m

3. r 5 12 mm __ for π. Find the area of a circle with the given radius. Use 22 7

4. r 5 7_8 in. 5. r 5 14 cm

Grade 6

M09ATE6_C020DT.indd 5

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20.5

Problem of the Day The high school is renovating its swimming pool. The seat cushions on the chairs by the pool will be covered with material that has the school’s intials. To find the area of the material, the circumference 9 in. of the cushion is traced on graph paper. Estimate the area of the circle. about 250 in2

Spiral Review Find the perimeter and area of a rectangle that has a length of 4 cm and a width of 8 cm. Then describe another rectangle that has the same area but a different perimeter. P 5 24 cm, A 5 32 cm2; Possible answer: l 5 16 cm, w 5 2 cm.

Lesson Quiz Find the area of a circle with the given radius. Use 3.14 for π. © Harcourt

1. r 5 3 ft 28.26 ft2

2. r 5 0.6 m 1.1304 m2

3. r 5 12 mm 452.16 mm2 __ for π. Find the area of a circle with the given radius. Use 22 7 13 __ in.2 4. r 5 7_8 in. 2 32

5. r 5 14 cm 616 cm2

Grade 6

Daily Transparency DT20.5

20.6

Problem of the Day The high school is renovating its swimming pool. The pool will be lighted from within the pool with circular lights. A flat circular light has a diameter of 12 in. What is the area of the light’s surface?

Spiral Review 1. Radius of circle 5 10 cm. Diameter 5 _____? 2. Diameter of circle 5 6 in. Radius 5 _____?

Lesson Quiz Find the area of each circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

2.

-%,`e%

()bd

Find the area of each partial circle to the nearest __ for p. whole number. Use 3.14 or 22 7

© Harcourt

1 circle __ 3. 10

4. 54_ circle

((dd

5. Mr. Kim has a sprinkler system in his front yard. The sprinkler at the corner of the yard covers 1 _ of a circle with a radius of 14 feet. What is the 4 area watered by the sprinkler?

Grade 6

M09ATE6_C020DT.indd 6

()bd

Daily Transparency

DT20.6

8/30/07 3:13:02 PM

20.6

Problem of the Day The high school is renovating its swimming pool. The pool will be lighted from within the pool with circular lights. A flat circular light has a diameter of 12 in. What is the area of the light’s surface? 113 sq in.

Spiral Review cm 1. Radius of circle 5 10 cm. Diameter 5 20 _____? 3 cm 2. Diameter of circle 5 6 in. Radius 5 _____?

Lesson Quiz Find the area of each circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

-%,`e%

2.

133 in.2

113 km2

()bd

Find the area of each partial circle to the nearest __ for p. whole number. Use 3.14 or 22 7

© Harcourt

1 circle __ 3. 10

()bd

45 km2

4. 54_ circle

((dd

304 mm2

5. Mr. Kim has a sprinkler system in his front yard. The sprinkler at the corner of the yard covers 1 _ of a circle with a radius of 14 feet. What is the 4 area watered by the sprinkler? A 5 1_4 p 142 5 49p , 154 ft2 Grade 6

Daily Transparency DT20.6

20.7

Problem of the Day The high school 12 ft is renovating its swimming pool. A locker room will be built according to the 5 ft floor plan shown. All angles are right angles. 5 ft What is the area of the locker room?

5 ft

Spiral Review Find the area of the circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

2. 1 in.

14 cm

Lesson Quiz 1. Rashid is cleaning a ﬂoor with the dimensions as shown. How many square yards of ﬂoor must be cleaned? 10 yd

6 yd

© Harcourt

16 yd

4 yd

2. Liz is painting a wall with the door and window opening as shown. How many square feet of paint will she need to cover the surface of the wall? 22 ft 4 ft 6 ft

Grade 6

M09ATE6_C020DT.indd 7

4 ft 4 ft

10 ft

Daily Transparency

DT20.7

8/30/07 3:13:14 PM

20.7

Problem of the Day The high school 12 ft is renovating its 5 ft swimming pool. A locker room will be built according to the 5 ft floor plan shown. All angles are right angles. 5 ft What is the area of the locker room? 85 ft2

Spiral Review Find the area of the circle to the nearest whole __ for p. number. Use 3.14 or 22 7 1.

2. 1 in.

14 cm

about 3 in.2

about 154 cm2

Lesson Quiz 1. Rashid is cleaning a floor with the dimensions as shown. How many square yards of floor must be cleaned? 112 yd2 10 yd

6 yd

4 yd

© Harcourt

16 yd

2. Liz is painting a wall with the door and window opening as shown. How many square feet of paint will she need to cover the surface of the wall? 180ft2 22 ft 4 ft 6 ft

Grade 6

4 ft 4 ft

10 ft

Daily Transparency DT20.7

21.1

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the total area of the model’s surface.

,Zd /Zd (,Zd

Spiral Review 1. Parallelogram: base 5 18 in., height 5 9 in., A5? 2. Parallelogram: Area 5 72 in.2, base 5 12 in., height 5 ?

Lesson Quiz Find the surface area of each figure. Use 3.14 for p. 1.

2. -`e%

.%,Zd .%,Zd

© Harcourt

3.

5 cm 7 cm

()`e%

.%,Zd 13 cm

/`e%

,d

4. ()d

4 cm 15 cm

5. The length of a rectangular prism is three times the width. The height is half the width. The length is 12 meters. Find the dimensions and surface area of the prism.

Grade 6

M09ATE6_C021DT.indd 1

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DT21.1

8/30/07 3:10:12 PM

21.1

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the total area of the model’s surface. 470 cm2 ,Zd /Zd

(,Zd

Spiral Review 1. Parallelogram: base 5 18 in., height 5 9 in., A 5 ? 162 in.2 2. Parallelogram: Area 5 72 in.2, base 5 12 in., height 5 ? 6 in.

Lesson Quiz Find the surface area of each figure. Use 3.14 for p. 1.

337.5 cm2

© Harcourt

7 cm

()`e%

.%,Zd

.%,Zd 5 cm

432 in.2

-`e%

.%,Zd

3.

2.

,d

4.

13 cm

/`e%

()d 4 cm 15 cm

291 cm

2

533.8 m2

5. The length of a rectangular prism is three times the width. The height is half the width. The length is 12 meters. Find the dimensions and surface area of the prism. l = 12 m, w = 4 m, h = 2 m; S = 160 m2

Grade 6

Daily Transparency DT21.1

21.2

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the quantity represented by multiplying the length 3 the width 3 the height. What does this quantity represent?

,Zd /Zd (,Zd

Spiral Review 1. The surface area of a cube is _____ times the area of one face. 2. Rectangular prism: / 5 12 in., w 5 10 in., h 5 8 in.; surface area 5 ?

Lesson Quiz Find the volume of each figure. 1.

2. .Zd

© Harcourt

(,Zd 6.9 ft

3.

7.4 ft

5.3 ft

.%)`e% 0%,`e%

/Zd

4.

.%)Zd

*%+`e%

('%+Zd

+%)Zd

5. Concrete is sold by the cubic yard. How many cubic yards of concrete would you need for a patio that is 9 yards by 5.3 yards by 0.16 yard?

Grade 6

M09ATE6_C021DT.indd 2

Daily Transparency

DT21.2

8/30/07 3:10:26 PM

21.2

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The toy trailer is 15 cm long by 8 cm wide by 5 cm high. Find the quantity represented by multiplying the length 3 the width 3 the height. What does this quantity represent? 600 cm3; this represents the volume of the model.

,Zd /Zd

(,Zd

Spiral Review 1. The surface area of a cube is _____ times the area of one face. 6 2. Rectangular prism: / 5 12 in., w 5 10 in., h 5 8 in.; surface area 5 ? 592 in.2

Lesson Quiz Find the volume of each figure. 1.

840 cm

3

.Zd

© Harcourt

(,Zd

3.

6.9 ft 7.4 ft

2.

.%)`e% 0%,`e%

/Zd

5.3 ft

135.309 ft3

232.56 in.3

4.

.%)Zd

+%)Zd

*%+`e%

('%+Zd

157.248 cm3

5. Concrete is sold by the cubic yard. How many cubic yards of concrete would you need for a patio that is 9 yards by 5.3 yards by 0.16 yard? 7.632 yd3

Grade 6

Daily Transparency DT21.2

21.3

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The model trailer is 15 cm long by 8 cm wide by 5 cm high and has a model of a cylinder-shaped water cooler attached to its rear door. If the radius of the model cooler is 0.5 cm and its height is 1 cm, how can you find the volume of the model cooler?

Spiral Review 1. Rectangular prism: / 5 10 in., w 5 10 in., h 5 8 in., Volume 5 ? 2. Rectangular prism: V 5 640 cm3, w 5 8 cm, / 5 8 cm, h 5 ?

Lesson Quiz For 1–2, use the rectangles to model a cylinder. Estimate the volume of each cylinder. 1.

-Zd

2.

,Zd

((Zd

(/Zd

.]k

,d

3.

4.

© Harcourt

))]k )*d /Zd

5. 0Zd

Grade 6

M09ATE6_C021DT.indd 3

Daily Transparency

DT21.3

8/30/07 3:10:39 PM

21.3

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The model trailer is 15 cm long by 8 cm wide by 5 cm high and has a model of a cylinder-shaped water cooler attached to its rear door. If the radius of the model cooler is 0.5 cm and its height is 1 cm, how can you find the volume of the model cooler? You can multiply 0.5 3 0.5 3 3.14 3 1.

Spiral Review 1. Rectangular prism: / 5 10 in., w 5 10 in., h 5 8 in., Volume 5 ? 800 in.3 2. Rectangular prism: V 5 640 cm3, w 5 8 cm, / 5 8 cm, h 5 ? 10 cm

Lesson Quiz For 1–2, use the rectangles to model a cylinder. Estimate the volume of each cylinder. Possible answers shown. 1.

2.

-Zd

(/Zd

about 58 cm3

((Zd .]k

3.

4.

© Harcourt

))]k

,Zd

about 3,385 ft3

/Zd

about 130 cm3

,d

)*d

about 1,805 m3

5. 0Zd

about 1,809 cm3

Grade 6

Daily Transparency DT21.3

21.4

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The container on the back of the transport truck is in the shape of a cylinder. The cylinder is 15 cm long, and the circular bases each have a radius of 8 cm. Find the area of one of the circular bases of the cylinder, and then multiply it by the length of the cylinder. What does this quantity represent?

Spiral Review Estimate the volume of a cylinder with a height of 10 cm and a radius of 5 cm.

Lesson Quiz Find the volume of each figure. Use 3.14 for pi. Round to the nearest unit3. .`e%

1.

2.

(+Zd

(*`e% *,Zd

3.

(.%,]k

4.

© Harcourt

*%,]k

)(%*Zd (/%0Zd

5. An outside cylinder has a radius of 5.7 m. The space between the inside and outside cylinders is 1.2 m. The height of both cylinders is 8.3 m. Calculate the volume of the inside cylinder.

Grade 6

M09ATE6_C021DT.indd 4

Daily Transparency

DT21.4

8/30/07 3:10:50 PM

21.4

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The container on the back of the transport truck is in the shape of a cylinder. The cylinder is 15 cm long, and the circular bases each have a radius of 8 cm. Find the area of one of the circular bases of the cylinder, and then multiply it by the length of the cylinder. What does this quantity represent? 200.96 cm2; 3,014.4 cm3; this represents the volume of the cylinder.

Spiral Review Estimate the volume of a cylinder with a height of 10 cm and a radius of 5 cm. V 5 about 3 3 5 3 5 3 10 5 about 750 cm3

Lesson Quiz Find the volume of each figure. Use 3.14 for pi. Round to the nearest unit3. .`e%

1.

2.

(+Zd

(*`e% *,Zd

2,000 in.3

© Harcourt

3.

(.%,]k

4.

*%,]k

841 ft

3

21,540 cm3

)(%*Zd (/%0Zd

6,731 cm3

5. An outside cylinder has a radius of 5.7 m. The space between the inside and outside cylinders is 1.2 m. The height of both cylinders is 8.3 m. Calculate the volume of the inside cylinder. 528 m3

Grade 6

Daily Transparency DT21.4

21.5

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. He needs to find out how much metal he needs to make the trailer. Which measure should he use to solve this problem?

Spiral Review 1. A cylinder has a radius of 7 in. and a height of 10 in. What is the volume?

2. A cylinder has a diameter of 6 m and a height of 6 m. What is its volume?

3. A cylinder has a radius of 12 ft and a volume of 45,216 ft3. What is the height?

4. A cylinder has a diameter of 20 cm and a volume of 12,560 cm3. What is the height?

Lesson Quiz

© Harcourt

Tell which measure, perimeter, area, surface area, or volume you will use to solve the problem. Then solve the problem. 1. Hallie was selling her homemade hand cream in cylindrical jars. If a jar is 4 in. high with a radius of 4 in., what is the maximum area of the label that can go around the jar?

2. Danielle is making and packaging potpourri to sell. If the box, that will hold the potpourri, is 10 cm by 8 cm by 6 cm, about how much potpourri can she place in the box?

Grade 6

M09ATE6_C021DT.indd 5

Daily Transparency

DT21.5

8/30/07 3:11:00 PM

21.5

Problem of the Day Navid is building a toy model of a transport truck that is similar to the one his father drives. The trailer is 15 cm long by 8 cm wide by 5 cm high. He needs to find out how much metal he needs to make the trailer. Which measure should he use to solve this problem? surface area

Spiral Review 1. A cylinder has a radius of 7 in. and a height of 10 in. What is the volume? about 1,539 in.3

2. A cylinder has a diameter of 6 m and a height of 6 m. What is its volume? about 169.56 m3

3. A cylinder has a radius of 12 ft and a volume of 45,216 ft3. What is the height? about 100 ft

4. A cylinder has a diameter of 20 cm and a volume of 12,560 cm3. What is the height? about 40 cm

Lesson Quiz

© Harcourt

Tell which measure, perimeter, area, surface area, or volume you will use to solve the problem. Then solve the problem. 1. Hallie was selling her homemade hand cream in cylindrical jars. If a jar is 4 in. high with a radius of 4 in., what is the maximum area of the label that can go around the jar? surface area; about 100.48 in.2 2. Danielle is making and packaging potpourri to sell. If the box, that will hold the potpourri, is 10 cm by 8 cm by 6 cm, about how much potpourri can she place in the box? volume; 480 cm3

Grade 6

Daily Transparency DT21.5

Unit 8 • Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles.

22

The family has traveled 325 mi in 5 hr. What is a ratio that can be used to describe how fast the Edwards family is driving?

The middle school Ski Club plans ski trips and participates in ski competitions.

23

© Harcourt

If 80% of the club members participated in the last competition, what fraction of the club participated?

Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equalsized marbles. The bag contains 3 blue marbles, 7 red marbles, and 2 green marbles. In simplest terms, what is the ratio of the green marbles to all marbles in the bag?

Grade 6

MXENl09ATE6_U08UDT.indd 1

Daily Transparency

24

DT • Unit 8

8/30/07 2:47:47 PM

Unit 8 • Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles.

22

The family has traveled 325 mi in 5 hr. What is a ratio that can be used to describe how fast the ___ , or 65 __ Edwards family is driving? 325 5 1

The middle school Ski Club plans ski trips and participates in ski competitions.

23

If 80% of the club members participated in the last competition, what fraction of the club participated? 80 5 4 ____ __ of the members participated

© Harcourt

100

5

Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equalsized marbles. The bag contains 3 blue marbles, 7 red marbles, and 2 green marbles. In simplest terms, what is the ratio of the green marbles to all marbles 2 1 _ in the bag? __ 12 5 6 , or 1:6, or 1 out of 6 marbles

Grade 6

24

Daily Transparency DT • Unit 8

22.1

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. They have traveled 325 mi in 5 hr. What is the average speed (unit rate) at which the Edwards family is driving?

Spiral Review Complete each number sentence. j 2 5 __ 1. __ 24 12

7 __ 5 __ 2. 14 j 26

5 __ 3. __ 5 15 j 45

10 j 5 __ 4. __ 6 48

Lesson Quiz Write three equivalent ratios.

© Harcourt

32 1. __ 24

6 2. __ 10

3. Write the following ratio in fraction form and then find the unit rate. 240 words in 3 minutes 4. Compare unit rates. Write . 250 mi in 5 hr j 80 mi in 2 hr 5. Gloria rode her bike 16 mi in 2 hr. At the same rate how long will it take her to ride 44 mi? Grade 6

M09ATE6_C022DT.indd 1

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DT22.1

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22.1

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. They have traveled 325 mi in 5 hr. What is the average speed (unit rate) at which the Edwards family is driving? 65 mi per hour

Spiral Review Complete each number sentence. j 2 5 __ 1. __ 24 4 12

7 __ 5 __ 2. 14 13 j 26

5 __ 15 3. __ 5 15 j 45

__ j 5 10 4. __ 6 80 48

Lesson Quiz Write three equivalent ratios. Possible answers given.

© Harcourt

32 1. __ 24

16 _ __ , 8 , 4_ 2 6 3

6 __ 2. 10

18 3 24 , __ __ ,_ 40 30 5

3. Write the following ratio in fraction form and then find the unit rate. 240 words in 3 minutes 240 ___ ; 80 words per min. 3 4. Compare unit rates. Write . 250 mi in 5 hr j 80 mi in 2 hr . 5. Gloria rode her bike 16 mi in 2 hr. At the same rate how long will it take her to ride 44 mi? 5.5 hr Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. On the first 5 day Ben drove __ of the distance to 15 Raleigh and on the second day Laura __ of the distance. Determine drove 15 30 whether Ben and Laura drove the same distance.

Spiral Review Write two equivalent ratios. 14 1. __ 28

20 2. __ 25

Determine whether the ratios are equivalent. in. in. ____ 3. 6____ and 18 9 in. 27 in.

mi mi and 25 ____ ____ 4. 24 50 hr 48 hr

Lesson Quiz

© Harcourt

Use cross products or common denominators to determine whether the ratios form a proportion. 1. 2_6 5

3 _ 9

40 3. 8_5 5 __ 50

18 6 5 __ 2. __ 30 10 49 4. 7_5 5 __ 35

6 5. 1_5 5 __ 10

Grade 6

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22.2

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 515 miles. On the first 5 __ day Ben drove 15 of the distance to Raleigh and on the second day Laura __ of the distance. Determine drove 15 30 whether Ben and Laura drove the same distance. No; 1_3 ? 1_2 .

Spiral Review Write two equivalent ratios. __ Shown. 1. 14 28

7 ___ 14

and

2 __ 4

20 __ 4_ and 2. 25 5

8 ___ 10

Determine whether the ratios are equivalent. in. in. ____ 3. 6____ and 18 Yes 9 in. 27 in.

mi Yes mi and 25 ____ ____ 4. 24 50 hr 48 hr

Lesson Quiz

© Harcourt

Use cross products or common denominators to determine whether the ratios form a proportion. 1. 2_6 5

3 _ 9

yes

__ no 3. 8_5 5 40 50

6 5 18 __ yes 2. __ 30 10

__ yes 4. 57_ 5 49 35

6 no 5. 1_5 5 __ 10

Grade 6

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22.3

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. If the car used 3 gallons of gasoline to go 105 mi, how many gallons of gasoline would be used after the family has driven 270 miles?

Spiral Review Determine whether the ratios form a proportion. 6 4 and __ 1. __ 15 10

4 and _ 2 2. __ 12 3

Lesson Quiz 28 1. Solve the proportion. 7_3 5 __ n

2. Use a common denominator to form equivalent x fractions. 3_4 5 ___ 200 3. Use proportions to convert to the given unit. 40 oz = x lb © Harcourt

4. Which two of the given ratios can be used to write a 9 6 ,_ proportion? 3_5 , __ 15 9 5. A brownie recipe calls for 1 1_2 c of powdered chocolate and 3 c of flour. Ann made a mistake and used 5 c of flour. How many cups of powdered chocolate should she use to keep the proportion correct?

Grade 6

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22.3

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. If the car used 3 gallons of gasoline to go 105 mi, how many gallons of gasoline would be used after the family has driven 270 miles? 7 5_7 gal

Spiral Review Determine whether the ratios form a proportion. 6 4 and __ __ 1. 10 Yes 15

4 and 2 _ Yes 2. __ 12 3

Lesson Quiz 28 n 5 12 1. Solve the proportion. 7_3 5 __ n

2. Use a common denominator to form equivalent x fractions. 3_4 5 ___ 200 x 5 150 3. Use proportions to convert to the given unit. 40 oz = x lb x 5 2.5 © Harcourt

4. Which two of the given ratios can be used to write a 9 9 6 , _ 3_ 5 __ proportion? 3_5 , __ 15 15 9 5 5. A brownie recipe calls for 1 1_2 c of powdered chocolate and 3 c of flour. Ann made a mistake and used 5 c of flour. How many cups of powdered chocolate should she use to keep the proportion correct? 2.5 c

Grade 6

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22.4

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 520 miles. If Mr. Edwards drives at an average speed of 65 miles per hour, about how long does the trip take?

Spiral Review 1. Write as a ratio in

lowest terms: 8 pies to 12 cakes.

2. There are 5 girls

and 8 boys on a team. What is the ratio of boys to girls on the team?

Lesson Quiz © Harcourt

Find the missing term in each proportion. 14 1. _n2 5 __ 28

18 __ 5 __ 2. 12 n 4

5 3. n_2 5 __ 20

5 n 4. __ 5 __ 15 12

5. A car travels 85 kilometers in 1 1_6 hours. How far will it travel in 4 1_5 hours?

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of 520 miles. If Mr. Edwards drives at an average speed of 65 miles per hour, about how long does the trip take? about 8 hours

Spiral Review 1. Write as a ratio in

lowest terms: 8 pies to 12 cakes. 8 __ 12

5 2_3 2:3

2. There are 5 girls

and 8 boys on a team. What is the ratio of boys to girls on the team? 8 _ or 8:5 5

Lesson Quiz © Harcourt

Find the missing term in each proportion. __ n 5 4 1. _n2 5 14 28

__ 5 18 __ n 5 6 2. 12 n 4

5 1 _ 3. n_2 5 __ 20 n 5 2 or 0.5

5 n n5 4 4. __ 5 __ 15 12

5. A car travels 85 kilometers in 1 1_6 hours. How far will it travel in 4 1_5 hours? 306 kilometers Grade 6

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Problem of the Day The Edwards family is driving their car from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Along the way, the Edwards children watch the car DVD player, which has a width and height one-fifth as large as their television screen at home. If the screen at home is 40 in. wide and 22.5 in. high, what are the width and height of the car DVD player?

Spiral Review 1. d 5 ?

2. d 5 150 mi

r 5 60 cm per min t 5 10 min

r 5 60 mi per hr t5?

3. d 5 3 km

4. d 5 0.01 m

r5? t 5 12 min

r5? t 5 0.5 hr

Lesson Quiz Tell whether the pair of figures is similar. Explain why or why not. B

Y

1. 21 m

24 m

28 m

2.

32 m

4 in.

E 2 in.

Z

18 m

A

© Harcourt

3. B

398

V

F

938 20 in.

32 in.

Q

T

Q

C 24 in.

G

F

24 m

S

6 in.

3 in.

D X

R

F

488

6 in.

D

E

398

938 8 in.

5 in. 488

G

12 m

U

4.

R

6m

Q

10 m

W

X

4m

S

P

5. Mark makes a triangular flag with sides measuring 4 inches, 7 inches, and 7 inches. Katya makes a triangular flag with sides measuring 6 inches, 8 inches, and 8 inches. Are the triangles similar? Explain.

Grade 6

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22.5

Problem of the Day The Edwards family is driving their car from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Along the way, the Edwards children watch the car DVD player, which has a width and height one-fifth as large as their television screen at home. If the screen at home is 40 in. wide and 22.5 in. high, what are the width and height of the car DVD player? width 5 8 in., height 5 4.5 in.

Spiral Review 1. d 5 ? 600 cm

2. d 5 150 mi

r 5 60 cm per min t 5 10 min

r 5 60 mi per hr t 5 ? 2.5 hr

3. d 5 3 km r 5 ? 1_4 km per min

4. d 5 0.01 m

t 5 12 min

Y

r 5 ? 2.0.02 m per hr t 5 0.5 hr B B

Y 21 m

Lesson Quiz 21 m

X

B

Y

28 m

24 m 24 m 18 m

32 m

28 m

Z

32 m

A

F

24 m

24 m A or F S 6 in. not. R why Tell whether the pair of figures is similar. Explain why F

X

21Ym

1.

X

21 m

18 m 24 m

E 18 m

X

28Bm

24 m

4 in. Z

32 m

2.

Z 28 m A F

32 m 24 m

R A

F

F

© Harcourt

C

3.

24 in.

398 B24 in.

3 in.

20Qin. C 938 488 D 32 in. 20 in.

6 in.

E 6 in.

398 F 938

T 938 8 in. 5 in.

5 in. 488

Z

R 3 in.

F

4 in.

D

24 in.

S

6 in.

G 3 in.

C

Q

CG 938

T TF 938

Q 20 in.

5 in. F Yes, the 938ratios of the6 in.lengths of the 24 in. 20 in. 488 488 398 6 in. 398 938 5 in. 8 in. E G B D 32 in. corresponding sides are equal. 398 488

B

F

938 G

2 in.

S

6 in. 24 m

E2 in.

D

2 in. 3 in. Yes, the ratios ofR the lengths of 6 in. S F E D4 in. G the2 in.corresponding Qsides are Tequal.

D

18 m 4 in. E

4.

398

V 32 in. 12 m 12 m

V

488

U

10 m

E

R R

10 m X

W

G

UD

G Q

8 in. 6m

6m

Q

4m

4 mP

S

12 m V U No, the ratios of the corresponding sides Yes, of 398 Rlengths 488 488 of the 398 the ratios 6m Q 8 in. E G B D 32 in. are not equal. the corresponding 10 m sides are equal. 4m 12 m V U 6 m R Q 5. MarkW makes aX triangular flPag with sides measuring 4 inches, 7 inches, and 7 inches. S 10 m Katya makes a triangular4 mflag with sides measuring 6 inches, 8 inches, and X P 8 Winches. Are theS triangles similar? Explain. No, the ratios of the lengths of the corresponding sides are not equal.

Grade 6

W

X

S

P

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. They use 25.75 gal of gas on the trip. Write and solve an equation to find how many miles they traveled per gallon of gas.

Spiral Review Rectangle ABCD has length 4 cm and width 16 cm. Rectangle EFGH has length 6 cm and width 18 cm. Are the rectangles similar? Explain.

© Harcourt

Lesson Quiz 1. A 4-lb bag of peanuts costs $16. If the price per pound remains the same, write and solve an equation to find the cost of a 3-lb bag of peanuts. 2. Randall has 240 stamps in his collection. He organizes them in an album with 8 stamps on each page. Write and solve an equation to find how many pages are in Randall’s stamp collecting album.

Grade 6

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22.6

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. They use 25.75 gal of gas on the trip. Write and solve an equation to find how many miles they traveled per gallon of gas. 25.75 3 m 5 515; 20 mi/gal

Spiral Review Rectangle ABCD has length 4 cm and width 16 cm. Rectangle EFGH has length 6 cm and width 18 cm. Are the rectangles similar? Explain. No; the ratios of the corresponding sides, 1 _ and 1_ , are not the same. 4 3

© Harcourt

Lesson Quiz 1. A 4-lb bag of peanuts costs $16. If the price per pound remains the same, write and solve an equation to find 4 5 3 _ c 5 12; the cost of a 3-lb bag of peanuts. __ c 16 a 3-lb bag of peanuts costs $12. 2. Randall has 240 stamps in his collection. He organizes them in an album with 8 stamps on each page. Write and solve an equation to find how many pages are in Randall’s stamp collecting album. 8p 5 240, p 5 30; there are 30 pages in Randall’s stamp collecting album.

Grade 6

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22.7

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. The road map that the family is using has a scale of 1 in. 5 75 mi. About how many inches represent the distance they are driving?

Spiral Review 1. If the ratios of sides of similar figures are 8 to 5 and 4 to d, d 5 ? 2. If the ratios of sides of similar figures are 4 to 6 and d to 3, d 5 ?

Lesson Quiz

© Harcourt

Find the unknown dimension. 1. scale: 1 in. = 9 in. drawing length: 12 in. actual length:

3. scale: 2 cm = 5 m drawing length: 6 cm actual length:

2. scale: 4 ft = 8 in. drawing length: actual length: 24 in.

4. scale: 1 in. = 35 mi drawing length: actual length: 105 mi

5. A jeweler is making a scale drawing of a small engraving that is 9 mm wide. The scale is 4 cm = 1 mm. How wide will the engraving be in the drawing?

Grade 6

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22.7

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. The road map that the family is using has a scale of 1 in. 5 75 mi. About how many inches represent the distance they are driving? Possible answer: about 7 in.

Spiral Review 1. If the ratios of sides of similar figures are 8 to 5 and 4 to d, d 5 ? 2.5 2. If the ratios of sides of similar figures are 4 to 6 and d to 3, d 5 ? 2

Lesson Quiz

© Harcourt

Find the unknown dimension. 1. scale: 1 in. = 9 in. drawing length: 12 in. actual length: 108 in.

3. scale: 2 cm = 5 m drawing length: 6 cm actual length: 15 m

2. scale: 4 ft = 8 in. drawing length: 12 ft actual length: 24 in.

4. scale: 1 in. = 35 mi drawing length: 3 in. actual length: 105 mi

5. A jeweler is making a scale drawing of a small engraving that is 9 mm wide. The scale is 4 cm = 1 mm. How wide will the engraving be in the drawing? 36 cm

Grade 6

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Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Mrs. Edwards estimates that the total cost of all driving expenses averages $2 for every 5 mi traveled. What is her estimate of the total cost of the driving expenses?

Spiral Review 1. scale: 3 cm 5 18 m drawing length: 12 cm actual length: ? 3. scale: 4 cm 5 3 mm drawing length: ? actual length: 6.9 mm

2. map scale: 1 in. 5 4 mi. measured distance: ? actual distance: 48 mi 4. map scale: 1 in. 5 25 mi measured distance: 23 in. actual distance: ?

Lesson Quiz Use proportional reasoning to find the unknown amount. 1. Martin types 60 words in 2 min. How long does it take him to type 90 words? 2. Grace walks 5 mi in 2 hr. How many miles does she walk in 5 hr? 3. Two packages of spaghetti make 8 servings. How many packages make 20 servings? © Harcourt

4. You can buy 24 tulip bulbs for $6.48. How much would 15 bulbs cost? 5. Sharon takes 15 hr to make 6 quilt squares. She expects to complete a quilt with 100 squares within 200 hrs. Is her expectation reasonable? Explain.

Grade 6

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22.8

Problem of the Day The Edwards family is driving from New York City, NY, to Raleigh, NC, a distance of about 515 mi. Mrs. Edwards estimates that the total cost of all driving expenses averages $2 for every 5 mi traveled. What is her estimate of the total cost of the driving expenses? $206

Spiral Review 1. scale: 3 cm 5 18 m drawing length: 12 cm actual length: ? 72 m 3. scale: 4 cm 5 3 mm drawing length: ? 9.25 cm actual length: 6.9 mm

2. map scale: 1 in. 5 4 mi. measured distance: ? 12 in. actual distance: 48 mi 4. map scale: 1 in. 5 25 mi measured distance: 23 in. actual distance: ? 575 mi

Lesson Quiz Use proportional reasoning to find the unknown amount. 1. Martin types 60 words in 2 min. How long does it take him to type 90 words? 3 min 2. Grace walks 5 mi in 2 hr. How many miles does she walk in 5 hr? 12.5 mi 3. Two packages of spaghetti make 8 servings. How many packages make 20 servings? 5 © Harcourt

4. You can buy 24 tulip bulbs for $6.48. How much would 15 bulbs cost? $4.05 5. Sharon takes 15 hr to make 6 quilt squares. She expects to complete a quilt with 100 squares within 200 hrs. Is her expectation reasonable? Explain. No. Think: If it takes her 15 hr to make 6 squares, it takes her 5 hr to make 2 squares. Since 100 squares is 50 3 2 squares, it should also take 50 3 5 hr, or 250 hr to make the quilt.

Grade 6

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23.1

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty out of every 100 students at the middle school belong to the ski club. Write 20 out of 100 as a percent.

Spiral Review Express as a decimal number. 1. _38

2. _45

3. 1 5_8

4. _34

Lesson Quiz

© Harcourt

Compare. Write , .. or 5 for each n. 2. 0.35% n 30%

3. 3_4 % n 0.75%

4. 110% n 210%

5. Kim, Jerry, and Emmett each had $50 to spend at the mall. Kim spent 60% of $50, Jerry spent 65% of $50, and Emmett spent 62% of $50. Write the percents in order from least to greatest.

Grade 6

M09ATE6_C023DT.indd 1

1. 15% n 12%

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23.1

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty out of every 100 students at the middle school belong to the ski club. Write 20 out of 100 as a percent. 20%

Spiral Review Express as a decimal number. 1. 3_8 0.375

2. 4_5 0.8

3. 1 5_8 1.625

4. 3_4 0.75

Lesson Quiz

© Harcourt

Compare. Write , .. or 5 for each n. 1. 15% n 12% .

2. 0.35% n 30% ,

3. 3_4 % n 0.75% 5

4. 110% n 210% ,

5. Kim, Jerry, and Emmett each had $50 to spend at the mall. Kim spent 60% of $50, Jerry spent 65% of $50, and Emmett spent 62% of $50. Write the percents in order from least to greatest. 60%, 62%, 65% Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty students belong to the ski club. Out of those 20 students, 7 also 7 as a enjoy snowboarding. Write __ 20 percent.

Spiral Review Write ,, ., or 5 to make the statement true. 1. 34%

40%

2. 55%

55.05%

3. 40%

40.0%

4. 100%

10%

Lesson Quiz Write each number as a percent. 1. 0.08

4 __ 2. 25

3. Write 135% as a decimal and as a fraction in simplest form. © Harcourt

4. Which number is greater, 53_ or 65%? 5. At a middle school, 43_ of sixth graders, 72% of seventh graders, and 0.7 of eighth graders attended a pep rally. Write each number as a percent. Then order the percents from greatest to least.

Grade 6

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23.2

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Twenty students belong to the ski club. Out of those 20 students, 7 also 7 as a __ enjoy snowboarding. Write 20 35 7 5 ___ percent. __ 35% 20 100

Spiral Review Write ,, ., or 5 to make the statement true. 1. 34%

40% ,

2. 55%

3. 40%

40.0% 5 4. 100%

55.05% , 10% .

Lesson Quiz Write each number as a percent. 1. 0.08 8%

4 __ 2. 25 16%

3. Write 135% as a decimal and as a fraction in 7 simplest form. 1.35, 1 __ 20

© Harcourt

4. Which number is greater, 53_ or 65%? 65% 5. At a middle school, 43_ of sixth graders, 72% of seventh graders, and 0.7 of eighth graders attended a pep rally. Write each number as a percent. Then order the percents from greatest to least. 75%, 72%, 70% Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. There are 20 students in the Ski Club. If 25% can go on the next trip, how many members can go?

Spiral Review 1. Write 0.004 as a percent.

2. Write 5.0 as a percent.

3. Write 27% as a decimal.

4. Write 35% as a fraction in simplest form. 6. Write 0.6% as a fraction in simplest form.

5. Write 3.8% as a decimal.

Lesson Quiz 1. Find 150% of 64. © Harcourt

2. Find 0.5% of 400. 3. Estimate a 20% tip for $5.75. 4. Estimate a 15% tip for $7.20. 5. There are 80 students in sixth grade. If 15 percent of them can play the piano, and 20 percent can play the guitar, how many students can play a musical instrument?

Grade 6

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23.3

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. There are 20 students in the Ski Club. If 25% can go on the next trip, how many members can go? 20 3 0.25 5 5 members

Spiral Review 1. Write 0.004 as a percent. 0.4%

2. Write 5.0 as a percent. 500%

3. Write 27% as a decimal. 0.27

4. Write 35% as a fraction in 7 simplest form. __ 20 6. Write 0.6% as a fraction 3 ___ in simplest form. 500

5. Write 3.8% as a decimal. 0.038

Lesson Quiz 1. Find 150% of 64. 96 © Harcourt

2. Find 0.5% of 400. 2 3. Estimate a 20% tip for $5.75. Possible answer: about $1.20 4. Estimate a 15% tip for $7.20. Possible answer: about $1.05 5. There are 80 students in sixth grade. If 15 percent of them can play the piano, and 20 percent can play the guitar, how many students can play a musical instrument? 28

Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. Each of 18 club members will compete in the first race, 6 members will compete in the second, and 9 members in the third. Construct a circle graph using this information.

Spiral Review 1. Find 2% of 25.

2. Find 150% of 36.

3. Use mental math to find 15% of 80.

4. Write an equation to find 20% of 6.30.

© Harcourt

Lesson Quiz Convert the following to degrees. 1. 35%

2. 85%

90 3. ___ 200

80 4. ___ 200

21 ___ 5. 150

Grade 6

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23.4

Problem of the Day The middle school Ski Club Members Competing Ski Club plans Race 1 16.7% ski trips and Race 3 participates in Race 2 50% 33.3% ski competitions. Each of 18 club members will compete in the first race, 6 members will compete in the second, and 9 members in the third. Construct a circle graph using this information.

Spiral Review 1. Find 2% of 25. 0.5

2. Find 150% of 36. 0.54

3. Use mental math to find 15% of 80. 12

4. Write an equation to find 20% of 6.30. 0.2 3 6.30 5 1.26

© Harcourt

Lesson Quiz Convert the following to degrees. 1. 35% 126˚

2. 85% 306˚

90 3. ___ 200 45% 5 162˚

80 4. ___ 200 40% 5 144˚

21 5. ___ 150 14% 5 50.4˚

Grade 6

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23.5

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The graph below shows the number of races won by club members in each of the last six weeks. How many races were won during week 5?

Number of Races

Races Won by Members 14 12 10 8 6 4 2 0

1

2

3

4

6

5

Week

Spiral Review Convert each percent to degrees in a circle graph. 1. 25%

2. 30%

3. 55%

4. 80%

5. _34

9 6. __ 10

A student is doing a science experiment on plant growth. One plant is fed water and fertilizer and the other just water. The results are shown in the graph.

Plant Growth

10 Growth in Inches

© Harcourt

Lesson Quiz

1. How much did the plant fed with fertilizer grow between weeks 1 and 3?

8

with fertilizer without fertilizer

6 4 2 0

1

2 3 4 5 Number of Weeks

6

2. How many inches per week did each plant grow?

Grade 6

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23.5

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The graph below shows the number of races won by club members in each of the last six weeks. How many races were won during week 5? 7

Number of Races

Races Won by Members 14 12 10 8 6 4 2 0

1

2

3

4

6

5

Week

Spiral Review Convert each percent to degrees in a circle graph. 1. 25% 90°

2. 30% 108°

3. 55% 198°

4. 80% 288°

5. _34 270°

9 324° 6. __ 10

A student is doing a science experiment on plant growth. One plant is fed water and fertilizer and the other just water. The results are shown in the graph.

10 Growth in Inches

© Harcourt

Lesson Quiz Plant Growth

8

with fertilizer without fertilizer

6 4 2

1. How much did the plant fed with 1 2 3 4 5 Number of Weeks fertilizer grow between weeks 1 and 3? 3 inches 2. How many inches per week did each plant grow? The plant with fertilizer grew 1.3 inches per week. The plant without fertilizer grew 1 inch per week. 0

Grade 6

6

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23.6

Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The regular price of a one-day lift ticket at a local ski resort is $32. Members of the club receive a 5% discount. What will be the total cost for 12 of the members to ride the ski lift for one day?

Spiral Review 1. Find 20% of 35.

2. Find 18% of 224.

3. Find 80% of 350.

4. Find 105% of $5.75.

5. Find 95% of 25.

6. Find 108% of $23.75.

Lesson Quiz Find the discount. 1. 45% of $24.00

2. 15% of $70.00

© Harcourt

Find the discounted price. 3. 25% off $60.00

4. 30% off $85.00

5. The price to go to an amusement park is $35.00. If you have a coupon for 15% off, how much will you pay if a 5% sales tax is applied to the discounted price?

Grade 6

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Problem of the Day The middle school Ski Club plans ski trips and participates in ski competitions. The regular price of a one-day lift ticket at a local ski resort is $32. Members of the club receive a 5% discount. What will be the total cost for 12 of the members to ride the ski lift for one day? $364.80

Spiral Review 1. Find 20% of 35. 7 3. Find 80% of 350. 280 5. Find 95% of 25. 23.75

2. Find 18% of 224. 40.32 4. Find 105% of $5.75. $6.04 6. Find 108% of $23.75. $25.65

Lesson Quiz Find the discount. 1. 45% of $24.00 $10.80

2. 15% of $70.00 $10.50

© Harcourt

Find the discounted price. 3. 25% off $60.00 $45.00

4. 30% off $85.00 $59.50

5. The price to go to an amusement park is $35.00. If you have a coupon for 15% off, how much will you pay if a 5% sales tax is applied to the discounted price? $31.24

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. What is the probability that Mikayla will roll 4 or 5 on the number cube?

Spiral Review 1. Hardcover books are on sale at a 15% discount. The regular price of a book is $35. What is the sale price? 2. A helmet is priced at $19.95. Quinn buys the helmet and pays 7.25% sales tax. What is his total purchase cost? 3. Find the discount rate used when the regular price is $72 and the sale price is $39.60.

Lesson Quiz

© Harcourt

Walter has a bag that contains 3 New Jersey quarters, 5 Massachusetts quarters, 3 Ohio quarters, and 4 Pennsylvania quarters. Find each probability. 1. P(Massachusetts)

2. P(Massachusetts or Ohio)

3. P(not New Jersey)

4. P(New Jersey or Pennsylvania)

5. Do the statements P(New Jersey or Massachusetts) and P(Ohio or Pennsylvania) represent complementary events? Why or why not?

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. What is the probability that Mikayla will roll 4 or 5 on the number cube? 1_3

Spiral Review 1. Hardcover books are on sale at a 15% discount. The regular price of a book is $35. What is the sale price? $29.75 2. A helmet is priced at $19.95. Quinn buys the helmet and pays 7.25% sales tax. What is his total purchase cost? $21.40 3. Find the discount rate used when the regular price is $72 and the sale price is $39.60. 45%

Lesson Quiz

© Harcourt

Walter has a bag that contains 3 New Jersey quarters, 5 Massachusetts quarters, 3 Ohio quarters, and 4 Pennsylvania quarters. Find each probability. 1. P(Massachusetts) _13

8 2. P(Massachusetts or Ohio) __ 15

3. P(not New Jersey) 4_5

7 4. P(New Jersey or Pennsylvania) __ 15

5. Do the statements P(New Jersey or Massachusetts) and P(Ohio or Pennsylvania) represent complementary events? Why or why not? yes; Sample answer: Complementary events are events whose probabilities add up to 1. Since P(New Jersey or Massachusetts) 1 8 7 5 1, the statements 1 __ P(Ohio or Pennsylvania) 5 __ 15 15 represent complementary events.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She records that she tossed heads 15 times and tails 10 times. What is the experimental probability of tossing heads?

Spiral Review A bag contains equally-sized cards numbered 1 to 15. One card is drawn randomly. Find each probability. 1. P(2)

4. P(5 or 10)

2. P(not 7)

5. P(greater than 8)

3. P(odd)

6. P(less than or equal to 12)

Lesson Quiz A vending machine in a restaurant randomly dispenses four types of prizes. The restaurant owner, Glen, records the first 40 prizes in a table. Find each experimental probability. ring 12 1. P(ring)

ball 8

bracelet 9 2. P(ball)

eraser 11 3. P(eraser)

© Harcourt

4. How many times can Glen expect the machine to dispense a ring in the next 30 wins? 5. If there were equal amounts of each prize, what would the theoretical probability be of winning a bracelet? 6. Compare the experimental and theoretical probability of winning a bracelet.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She records that she tossed heads 15 times and tails 10 times. What is the experimental probability of tossing heads? 3_5

Spiral Review A bag contains equally-sized cards numbered 1 to 15. One card is drawn randomly. Find each probability. 1 2 1. P(2) __ 4. P(5 or 10) __ 15

15

7 5. P(greater than 8) __ 15

__ 2. P(not 7) 14 15 8 3. P(odd) __

6. P(less than or equal to 12) 4_

15

5

Lesson Quiz A vending machine in a restaurant randomly dispenses four types of prizes. The restaurant owner, Glen, records the first 40 prizes in a table. Find each experimental probability. ring 12

ball 8

3 1. P(ring) __ 10

bracelet 9

eraser 11

2. P(ball) 1_ 5

__ 3. P(eraser) 11

40

© Harcourt

4. How many times can Glen expect the machine to dispense a ring in the next 30 wins? 9 times 5. If there were equal amounts of each prize, what would the theoretical probability be of winning a bracelet? 1_ 4

6. Compare the experimental and theoretical probability of winning 9 , 1 _ : The experimental probability is less than the a bracelet. __ 4 40 theoretical probability.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. Mikayla knows there are 10 marbles in her bag and that 3 of them are red. Can she predict the number of red marbles in a bag of 50 marbles? Why or why not?

Spiral Review When tossing a fair 6-sided number cube, P(NOT 4) 5 ? Explain.

Lesson Quiz Cross multiply to solve for x. 1. 3_8 5 _9x

1 x 2. ___ 5 __ 100 50

Latoya buys a small box of 20 cookies. In the box, there are 10 chocolate chip, 5 almond, and 5 peanut butter cookies. 3. What is the P(almond cookie)?

© Harcourt

5 x 5 __ 4. Predict how many almond cookies are in a box of 60. __ 20 60

5. Can Latoya predict how many cookies are not peanut butter in a box of 60 cookies? Explain.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. Mikayla knows there are 10 marbles in her bag and that 3 of them are red. Can she predict the number of red marbles in a bag of 50 marbles? Why or why not? Possible answer: Probably not. She would need to know that the bag of 50 marbles has the same proportion of red marbles as the bag of 10. Otherwise, she cannot make a valid prediction.

Spiral Review When tossing a fair 6-sided number cube, P(NOT 4) 5 ? Explain. Five possible favorable events (1, 2, 3, 5, 6) out of 6 possible outcomes, (1, 2, 3, 4, 5, 6), so P(NOT 4) 5 5_6

Lesson Quiz Cross multiply to solve for x. 1. 3_8 5 9_x 24

1 x 1 _ 2. ___ 5 __ 100 50 2

Latoya buys a small box of 20 cookies. In the box, there are 10 chocolate chip, 5 almond, and 5 peanut butter cookies. 5 5 _14 3. What is the P(almond cookie)? __ 20

© Harcourt

5 x 5 __ 4. Predict how many almond cookies are in a box of 60. __ 20 60 x 5 15 almond cookies 5. Can Latoya predict how many cookies are not peanut butter in a box of 60 cookies? Explain. Yes; possible answer: since there are equal amounts of almond and peanut butter cookies, we can use the results for almond cookies. 60 total cookies 2 15 peanut butter cookies 5 45 cookies that are not peanut x butter cookies, or P(not peanut butter) 5 1 2 1_4 5 3_4 . So, 3_4 5 __ . 60 x 5 45. 45 cookies are not peanut butter cookies.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has a red box, a green box, and a blue box. In each box she wants to place 2 marbles, each a different color. There are 4 different colors of marbles for her to choose from. How many combinations of marbles and boxes are there?

Spiral Review A spinner has 8 equal sections that are either blue, green, or yellow. Sam spins the pointer of the spinner 30 times and records 9 blue spins, 15 green spins, and 6 yellow spins. Find each experimental probability. 1. P(blue) 2. P(green) 3. P(yellow)

Lesson Quiz An ice cream parlor offers chocolate, strawberry, or vanilla ice cream. You can buy it in a cup or a cone. The available toppings are nuts, sprinkles, and hot fudge. 1. How many possible choices are there? © Harcourt

2. How many choices do you have if you leave the topping off? 3. June definitely wants a cup. How many choices does she have? 4. Izzy does not like strawberry. How many choices does she have? 5. Suppose the parlor adds mint chip as an additional flavor and stops serving nuts. How many possible ice cream choices are there now?

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has a red box, a green box, and a blue box. In each box she wants to place 2 marbles, each a different color. There are 4 different colors of marbles for her to choose from. How many combinations of marbles and boxes are there? There are 18 different combinations

Spiral Review A spinner has 8 equal sections that are either blue, green, or yellow. Sam spins the pointer of the spinner 30 times and records 9 blue spins, 15 green spins, and 6 yellow spins. Find each experimental probability. 3 1. P(blue) __ 2. P(green) 1_ 3. P(yellow) 1_ 2 10

5

Lesson Quiz An ice cream parlor offers chocolate, strawberry, or vanilla ice cream. You can buy it in a cup or a cone. The available toppings are nuts, sprinkles, and hot fudge. 1. How many possible choices are there? 18 © Harcourt

2. How many choices do you have if you leave the topping off? 6 3. June definitely wants a cup. How many choices does she have? 9 4. Izzy does not like strawberry. How many choices does she have? 12 5. Suppose the parlor adds mint chip as an additional flavor and stops serving nuts. How many possible ice cream choices are there now? 16

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. How many outcomes are possible for the compound events of flipping the coin and rolling the number cube?

Spiral Review 1. How many different outfits can be made from 3 pairs of pants, 3 shirts, and 2 jackets? 2. How many different outfits can be made from 3 pairs of pants, 2 shirts, and 2 jackets?

Lesson Quiz Use the Fundamental Counting Principle to find the number of possible outcomes for each event. 1. Rolling a 6-sided number cube and flipping two coins 2. Visiting one of 3 friends on a day during the week 3. Spinning the points of 3 spinners, each with 3 sections

© Harcourt

4. Choosing a number from 0 to 9 and flipping a coin 5. Andrew is ordering shirts for the soccer team. He has 4 sizes to choose from (small, medium, large, and extra large), 3 colors (white, blue, and black) and 2 styles (short sleeve and long sleeve). Make a list of all possible outcomes. How many different shirts does Andrew have to choose from?

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. How many outcomes are possible for the compound events of flipping the coin and rolling the number cube? 12

Spiral Review 1. How many different outfits can be made from 3 pairs of pants, 3 shirts, and 2 jackets? 3 3 3 3 2 5 18 2. How many different outfits can be made from 3 pairs of pants, 2 shirts, and 2 jackets? 3 3 2 3 2 5 12

Lesson Quiz Use the Fundamental Counting Principle to find the number of possible outcomes for each event. 1. Rolling a 6-sided number cube and flipping two coins 24 2. Visiting one of 3 friends on a day during the week 21 3. Spinning the points of 3 spinners, each with 3 sections 27

© Harcourt

4. Choosing a number from 0 to 9 and flipping a coin 20 5. Andrew is ordering shirts for the soccer team. He has 4 sizes to choose from (small, medium, large, and extra large), 3 colors (white, blue, and black) and 2 styles (short sleeve and long sleeve). Make a list of all possible outcomes. How many different shirts does Andrew have to choose from? Check students’ work; 24

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. There are 10 red and 10 blue marbles in the bag. Mikayla selects a marble, does not replace it, and selects another marble. Find P(red, not red).

Spiral Review Determine the number of outcomes for each compound event. 1. spinning a 3-section spinner and rolling a 6-sided number cube 2. flipping a coin and selecting a token from a bag of 15 different-color tokens 3. rolling a 6-sided number cube and choosing a month of the year 4. spinning an 8-section spinner and a 6-section spinner

Lesson Quiz For problems 1-4 below, write independent or dependent to describe the events. 1. Spin the pointer twice on a spinner divided equally into 9 sections.

© Harcourt

2. Select a marble from 20 colored marbles in a bag, do not replace it, and select a second marble. 3. Draw a card from a box of cards labeled 20 to 40, replace it, and draw a second card. 4. Roll two six-sided number cubes. For problem 5, find the probability. 5. Suppose the bag in Question 2 has 8 blue marbles, 6 pink marbles, and 6 green marbles. Find P(pink, pink).

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. There are 10 red and 10 blue marbles in the bag. Mikayla selects a marble, does not replace it, and selects another marble. Find P(red, 5 not red). __ 19

Spiral Review Determine the number of outcomes for each compound event. 1. spinning a 3-section spinner and rolling a 6-sided number cube 18 2. flipping a coin and selecting a token from a bag of 15 different-color tokens 30 3. rolling a 6-sided number cube and choosing a month of the year 72 4. spinning an 8-section spinner and a 6-section spinner 48

Lesson Quiz For problems 1-4 below, write independent or dependent to describe the events.

© Harcourt

1. Spin the pointer twice on a spinner divided equally into 9 sections. independent 2. Select a marble from 20 colored marbles in a bag, do not replace it, and select a second marble. dependent 3. Draw a card from a box of cards labeled 20 to 40, replace it, and draw a second card. independent 4. Roll two six-sided number cubes. independent For problem 5, find the probability. 5. Suppose the bag in Question 2 has 8 blue marbles, 6 pink marbles, and 6 3 green marbles. Find P(pink, pink). __ 38

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She plans to use one of these items to conduct a simulation. Each time she buys a pack of trading cards, she collects 1 of 8 bonus cards. She wants to know how many packs she can expect to buy to collect all 8 cards. How can Mikayla simulate this situation?

Spiral Review Hugh has a quarter and a number cube labeled 1–6. Find each probability. 1. P(heads, 3)

2. P(tails, odd)

3. P(tails, 1 or 6)

4. P(heads, greater than 2)

Lesson Quiz Describe a simulation that you could use to model the situation. 1. Collecting 7 randomly generated letters

© Harcourt

2. Finding 5 students who each received 5 different club assignments 3. Collecting 6 randomly generated number cards 4. Finding 14 randomly generated puzzle pieces 5. Name three simulations that can be used to find the experimental probability of randomly generating an 8?

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She plans to use one of these items to conduct a simulation. Each time she buys a pack of trading cards, she collects 1 of 8 bonus cards. She wants to know how many packs she can expect to buy to collect all 8 cards. How can Mikayla simulate this situation? Possible answer: Place 8 marbles of different colors in the bag. Select a marble, tally its color, and replace it. Repeat until each color has been selected once.

Spiral Review Hugh has a quarter and a number cube labeled 1–6. Find each probability. 1 1. P(heads, 3) __

2. P(tails, odd) 1_ 4

12

3. P(tails, 1 or 6) 1_ 6

4. P(heads, greater than 2) 1_ 3

Lesson Quiz Describe a simulation that you could use to model the situation. Possible answers are given. 1. Collecting 7 randomly generated letters spinner with 7 sections

© Harcourt

2. Finding 5 students who each received 5 different club assignments spinner with 5 sections 3. Collecting 6 randomly generated number cards number cube 4. Finding 14 randomly generated puzzle pieces bag of 14 tokens 5. Name three simulations that can be used to find the experimental probability of randomly generating an 8? Possible answers: spinner with 8 sections, spinner with 9 sections, and the bag of 14 tokens Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has 6 marbles in the bag, and she needs to take 4 of them out for her next experiment. Find the number of combinations of 4 marbles that she could remove.

Spiral Review Describe how you can simulate the situation.

1. collecting each letter of the word SIMULATION 2. collecting 30 trading cards 3. finding 3 students who each selected one of the 3 available lunch choices 4. finding 45 people who each opened cookies and received one of 45 different fortunes

Lesson Quiz Find the number of permutations for each situation. 1. There are 16 girls at cheerleading auditions. The director chooses the first 3 to audition. 2. Kirk bought 9 souvenirs on his vacation. He plays to display 4 of them from left to right on a shelf. Find the number of combinations for the situation.

© Harcourt

3. Mr. Martin writes out 5 monthly bills. He selects 3 to put stamps on. 4. Mrs. Amos has 6 paintings to show to her art class. She picks 4 to show today. 5. A cafeteria dietician offers 7 proposed meals for the upcoming school week. The cafeteria manager will select 5 meals and assign one to each day of the week. Is this a permutation or a combination? Find the number of ways the manager can select and assign the meals.

Grade 6

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Problem of the Day Mikayla is performing experiments using a fair coin, a 6-sided fair number cube, and a bag of equally-sized marbles. She has 6 marbles in the bag, and she needs to take 4 of them out for her next experiment. Find the number of combinations of 4 marbles that she could remove. 15

Spiral Review Describe how you can simulate the situation. Answers will vary. Students should describe simulations that take into account the number of items in each situation. 1. collecting each letter of the word SIMULATION 2. collecting 30 trading cards 3. finding 3 students who each selected one of the 3 available lunch choices 4. finding 45 people who each opened cookies and received one of 45 different fortunes

Lesson Quiz Find the number of permutations for each situation. 1. There are 16 girls at cheerleading auditions. The director chooses the first 3 to audition. 3,360 2. Kirk bought 9 souvenirs on his vacation. He plays to display 4 of them from left to right on a shelf. Find the number of combinations for the situation. 3,024

© Harcourt

3. Mr. Martin writes out 5 monthly bills. He selects 3 to put stamps on. 10 4. Mrs. Amos has 6 paintings to show to her art class. She picks 4 to show today. 15 5. A cafeteria dietician offers 7 proposed meals for the upcoming school week. The cafeteria manager will select 5 meals and assign one to each day of the week. Is this a permutation or a combination? Find the number of ways the manager can select and assign the meals. permutation; 2,520

Grade 6

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