Extra Practice 1

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Name Master 1.21

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Extra Practice 1

Lesson 1: Input/Output Machines 1. Complete this table. The pattern rule that relates the input to the output is: Subtract 11 from the input.

Input 21 31 41 51 61

Output

Input 3 6 9 12 15 ?

Output 3 ? ? 6 ? 8

a) Write the pattern rule for the input.

b) Write the pattern rule for the output.

2. The pattern rule that relates the input to the output is: Divide the input by 3, then add 2. Find the missing numbers in the table.

How can you check your answers?

The right to reproduce or modify this page is restricted to purchasing schools. This page may have been modified from its original. Copyright © 2009 Pearson Education Canada

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Name Master 1.22

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Extra Practice 2

Lesson 2: Patterns from Tables 1. The table shows the input and output from a machine with one operation.

Input 81 72 63 54

Output 9 8 7 6

a) Identify the number and the operation in the machine.

b) Continue the pattern. Write the next 4 input and output numbers.

c) Write the pattern rule that relates the input to the output.

2. The table shows the input and output from a machine with two operations.

Input 5 10 15 20 25

Output 15 40 65 90 115

a) Identify the numbers and the operations in the machine.

b) Choose 4 different input numbers. Find the output for each input.

c) Write the pattern rule that relates the input to the output.

d) Predict the output when the input is 60. Check your prediction.


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Name Master 1.23

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Extra Practice 4

Lesson 4: Using Variables to Describe Patterns 1. Janine wants to have helium-filled balloons delivered to the home of a sick friend. Each balloon costs $4. Delivery costs $5. a) Make a table to show the cost of having 1, 2, 3, and 4 balloons delivered.

b) Write a pattern rule that relates the number of balloons to the total cost.

c) Write an expression with a variable to represent the pattern.

d) Find the cost of having 9 balloons delivered. How can you check your answer?

2. For each table of values, write an expression that relates the input to the output. a)

b) Input 24 22 20 18 16

Output 10 9 8 7 6

Input 1 2 3 4 5

Output 6 9 12 15 18


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Name Master 1.24

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Extra Practice 5

Lesson 5: Plotting Points on a Coordinate Grid 1. List the coordinates of each point on the grid.

A: _____________

B: _____________

D: _____________

E: _____________

C: _____________

2. Use grid paper. Draw and label a coordinate grid. Plot each ordered pair. Explain how you moved to do this. F(3, 5)

G(6, 7)

H(9, 2)

I(1, 10)

J(7, 0)

3. a) Point A has coordinates (0, 17). What do you know about Point A? b) Point B has coordinates (24, 0). What do you know about Point B? c) What is the location of a point with coordinates (0, 0)? How do you know?


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Extra Practice 6

Master 1.25

Lesson 6: Drawing the Graph of a Pattern 1. Use grid paper. a) Graph the data in the table. Input 1 2 3 4 5

Output 11 13 15 17 19

b) Describe the relationship shown on the graph.

c) Write an expression to represent the pattern.

d) Find the output when the input is 8. What strategy did you use? Could you use the same strategy to find the output when the input is 43? Explain.

2. Make an Input/Output table for this graph.


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Name Master 1.26

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Extra Practice 7

Lesson 7: Understanding Equality 1. Suppose you were using real balance scales. You place counters in the left pan to represent the first expression. You place counters in the right pan to represent the second expression. Would the scales balance each time? If not, tell what you could do to balance the scales. a) 17 – 6; 10 + 3

b) 5  8; 18 + 22

c) 9  5; 55 – 10

d) 25  4; 10  20

2. Which expressions can be rewritten using a commutative property? Justify your choices. a) 8 + 34

b) 18 – 5

c) 6  19

d) 45  9

e) 93 + 78

f) 0  3


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Name Master 1.27

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Extra Practice 8

Lesson 8: Keeping Equations Balanced 1. For each equation below: • • • •

Model the equation with counters. Use counters to model the preservation of equality for the operation shown. Draw a diagram to record your work. Use symbols to record your work.

a) 7 + 8 = 15 (addition)

b) 3  6 = 18 (subtraction)

c) 25 – 18 = 21  3 (multiplication) d) 3  4 = 7 + 5 (division)

2. For each equation below: • • • a)

Apply the preservation of equality. Write an equivalent form of the equation. Use paper strips to check that equality has been preserved. 2n = 16 b) 5b = 25

c) 42 = 6s

d) 49 = 7t


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Name Master 1.28

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Extra Practice Answers

Extra Practice 1 – Master 1.21 Lesson 1 1. Input Output 21 10 31 20 41 30 51 40 61 50 a) Start at 21. Add 10 each time. b) Start at 10. Add 10 each time.

d) $41; I can check by substituting b = 9 into the expression. 2. a) n  2 – 2 b) 3n + 3

Extra Practice 5 – Master 1.24 Lesson 5 1. A(0, 9), B(5, 8), C(8, 5), D(6, 2), E(1, 12) 2.

2. Input Output 3 3 6 4 9 5 12 6 15 7 18 8 When the input was given, I used the pattern rule to find the output. When the output was given, I worked backward and used the inverse operations: I subtracted 2, then multiplied by 3.

Extra Practice 2 – Master 1.22 Lesson 2 1. a) b) c) 2. a) b) c) d)

9 45, 5; 36, 4; 27, 3; 18, 2 Divide the input by 9 to get the output.  5, – 10 30, 140; 35, 165; 40, 190; 45, 215 Multiply the input by 5, then subtract 10. 290; 60  5 = 300 and 300 – 10 = 290

Extra Practice 4 – Master 1.23 Lesson 4

To plot point F, I moved 3 squares right and 5 squares up. To plot point G, I moved 6 squares right and 7 squares up. To plot point H, I moved 9 squares right and 2 squares up. To plot point I, I moved 1 square right and 10 squares up. To plot point J, I moved 7 squares right and 0 squares up. 3. a) The point is on the vertical axis. b) The point is on the horizontal axis. c) The point is at the origin. To plot a point, I always start at the origin. Since I move 0 squares right and 0 squares up, I am still at the origin.

Extra Practice 6 – Master 1.25 Lesson 6 1. a)

1. a) Number of Cost ($) Balloons 1 9 2 13 3 17 4 21 b) Multiply the number of balloons by 4, then add 5. c) Let b represent the number of balloons. Then an expression that represents the pattern is: 4b + 5


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Name b) The graph shows that as the input increases by 1, the output increases by 2. c) Let n represent the input. An expression that represents the pattern is: 2n + 9 d) 25; I extended the table to the 8th term. No, it would take a long time to extend the table to the 43rd term. It would be more efficient to substitute n = 43 into the expression: 2  43 + 9 = 95; the output is 95.

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c)

For clarity, only one group of 7 is shown on the right side. 72=72

2. Input 1 2 3 4 5

Output 9 16 23 30 37

Extra Practice 7 – Master 1.26 Lesson 7 1. a) No, I could take away 2 counters from the right pan. b) Yes c) Yes d) No, I could multiply the number of counters in the left pan by 2. 2. a) Yes, 34 + 8, addition is commutative. b) No, subtraction is not commutative. c) Yes, 19  6; multiplication is commutative. d) No, division is not commutative. e) Yes, 78 + 93; addition is commutative. f) Yes, 0  3; multiplication is commutative.

d)

For clarity, only one group of 6 is shown on each side. 12  2 = 12  2 2. a) 2n  2 = 16  2 b) 5b  5 = 25  5 c) 42  2 = 6s  2 d) 49 + 5 = 7t + 5 Students’ answers should include drawings of paper strips.

Extra Practice 8 – Master 1.27 Lesson 8 1. a)

15 + 2 = 15 + 2 b)

18 – 6 = 18 – 6
