MARS Tasks | Grade 2

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MARS Tasks - 2nd Grade. Page 1 .... a second grade group of children to answer questions. ... Demonstrate fluency in adding and subtracting whole numbers.
MARS Tasks | Grade 2 Page

Name of MARS Task

Year

Math Strand

Notes

* * * * *

Peanuts and Ducks Symmetry Drawings Chopsticks Raisin Boxes Marble Rows

2003 2003 2003 2003 2003

NP, NO GM NP, NO DA PFA, NP

Determine if enough peanuts for ducks Draw shapes with symmetry, mark line Find # of chopsticks needed, explain Line plot, predict, explain prediction Extend growing pattern, explain

* * * * *

Teeth Footsteps on the Rug Which Shape? Agree or Disagree Student Store

2004 2004 2004 2004 2004

DA, NO GM GM PFA NO

Bar graph, find teeth lost in all Find # of footsteps of diff size feet Identify shapes, 2 attributes of triangles Whether 2 quantities are equal, explain Find 2 items under $.70, calculate change

2 5 9 13 17

Pictures Pencils and Erasers Reading Books Growing Necklaces Half and Half

2005 2005 2005 2005 2005

GM NO, NP DA, NO PFA NP, GM

Visualize lines of symmetry Amount spent at store, combinations Frequency table, bar graph Find, describe growing pattern, explain Draw half of geom. shape, how you know

21 22 25 28 31 34

Overview of 2006 Tasks Our Class Graphs In One Minute Describing Shapes Pam’s Shopping Trip The Track Team

2006 2006 2006 2006 2006

DA NO GM NO GM

Prediction-2 graphs, defend choice Find values on chart, justify answer Identify attributes of shapes Calculate buying items, repeated + & Find # of jumps from start to finish line

36 37 39 42 45 48

Overview of 2007 Tasks Sheep and Ducks Backpack Colors Addition Shapes Making Designs Incredible Equations

2007 2007 2007 2007 2007

PFA DA NO GM NO

Calc. # of legs, poss. combos for 32 legs Complete bar graph & give 2 facts Use addends 3 and/or 5 to reach sum Name ident. shapes inside larger design Find missing parts of equations to 16

50 51 54 56 59 62

Overview of 2008 Tasks Pocket Money Our Pets Don’s Shapes Building Walls Carol’s Numbers

2008 2008 2008 2008 2008

NO DA GM PFA NO, NP

Use numbers in flexible ways, + Tally table, bar graph, explain reason Identify shapes in larger one, sort Identify extend growing pattern Arrange digits into largest/sm, n line

65 66 69 72 74 77

Overview of 2009 Tasks Same Shape/Number Apple Farm Field Trip Top Lunch Choices High Horse Auntie Em’s Cookies

2009 2009 2009 2009 2009

PFA NO DA GM NO, GM

Variables/unknowns in + - sentences 2-digit +- in story context, justify Pictograph, make math. statements Measure horse w/diff. hand sizes Halving shapes/numbers, symmetry

NP=Number Properties NO=Number Operations PFA=Patterns Functions Algebra GM=Geometry & Measurement DA=Data Analysis MARS Tasks – Grade 2

* Tasks from 2003 and 2004 are not included in this packet due to copyright restrictions. However, if you click on the name of the task, you can access it via the Noyce Foundation website. Tasks from 2005 to 2009 are available here with permission from the Mathematics Assessment Resource Service (MARS). www.scoe.org/mars

Page 1

2nd grade

Task 1

Pictures

Student Task

Visualize lines of symmetry in a completed picture as well as from a picture that has been folded in half.

Core Idea 4 Geometry and Measurement

Students will recognize and use characteristics properties, and relationships of two-and three-dimensional geometric shapes and apply appropriate techniques to determine measurements • Identify, visualize, construct and draw two-dimensional shapes according to their attributes and/or parts of their shapes • Show an understanding of line symmetry

MARS Tasks – Grade 2

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Page 2

Pictures 1. Jacob cut out a rhombus on a line of symmetry. Show what his picture would look like if he folded the paper on the line of symmetry.

2. Laura made a drawing using some shapes and a line of symmetry. She used the folded edge as the line of symmetry. Draw a picture of what the paper will look like when it is unfolded.

MARS Tasks – Grade 2

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Page 3

Pictures

Grade 2

Rubric

The core elements of the performance required by this task are: • Identify, visualize, construct and draw two-dimensional shapes according to their attributes and/or parts of their shapes. • Show an understanding of line symmetry. Based on these credit for specific aspects of performance should be assigned as follows

1.

Gives a drawing with: A vertical half of a rhombus on the folded sheet

points

section points

2 2

2.

Gives a drawing with A tree in center of the rectangular space 2 smaller squares above the tree 2 larger circles below the tree

1 1 1 Total Points

MARS Tasks – Grade 2

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3 5

Page 4

2nd grade

Task 2

Pencils and Erasers

Student Task

Find the amounts of money spent at the teacher’s store. Determine what items could have been purchased for $.60.

Core Idea 2 Number Operations

Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently • Demonstrate fluency in adding and subtracting whole numbers • Communicate reasoning using pictures, numbers and/or words. Understand numbers, ways of representing numbers, relationships among numbers, and number systems • Understand whole numbers and use them in flexible ways such as relating, composing, and decomposing numbers • Communicate reasoning using pictures, numbers and/or words.

Core Idea 1 Number Properties

MARS Tasks – Grade 2

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Page 5

Pencils and Erasers Leticia’s teacher sells erasers for 15¢ and pencils for 10¢. 1. On Monday, Leticia bought 1 eraser and 2 pencils. How much did she spend on the eraser? ______ How much did she spend for two pencils? ______ How much did she spend all together? _______

2. On Tuesday, Leticia bought 4 things from her teacher. What did she buy? 1. 2. 3. 4. How much did she spend to buy these four things? _____

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Remember: Leticia’s teacher sells erasers for 15¢ and pencils for 10¢. 3. On Wednesday, Leticia spent 60¢. What did she buy? Show how you figured out that she spent 60¢.

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Pencils and Erasers

Grade 2

Rubric

The core elements of the performance required by this task are: • Demonstrate fluency in adding and subtracting whole numbers. • Understand whole numbers and use them in flexible ways such as relating, composing, and decomposing numbers. • Communicate reasoning using pictures, numbers and/or words. Based on these credit for specific aspects of performance should be assigned as follows

1

2

One eraser costs 15¢

1

Two pencils cost 20¢

1

She spent 35¢ altogether

1ft

Lists four permutations of pencils and/or erasers

1

3

1ft

2

cent sign is not required Shows work such as: Lists items totally 60¢ 4 erasers or 6 pencils or 3 pencils and 2 erasers

1

Shows work such as: 15¢+ 15¢+15¢+ 15¢ or 10¢+ 10¢+10¢+ +10¢+ 10¢+ 10¢ or 10¢+ 10¢+10¢+15¢+ 15¢ cent sign is not required

1 Total Points

MARS Tasks – Grade 2

section points

Gives these three answers:

Gives the correct total for the four items: 4 erasers 60¢ 3 erasers, 1 pencil 55¢ 2 erasers, 2 pencils 50¢ 1 eraser, 3 pencils 45¢ 4 pencils 40¢ 3

points

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2 7

Page 8

2nd grade

Task 3

Reading Books

Student Task

2nd graders are reading books. The information must be collected and organized to answer questions and explain the answers.

Core Idea 5 Data Analysis

Students collect, organize, display, and interpret data about themselves and their surroundings • Represent the same data in more than one way • Represent and interpret data using graphs or other representations • Describe and compare data using quantitative measures • Communicate reasoning using words, numbers, or pictures Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently • Demonstrate fluency in adding and subtracting whole numbers • Communicate reasoning using pictures, numbers and/or words.

Core Idea 2 Number Operations

MARS Tasks – Grade 2

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Page 9

Reading Books The students at Horace Mann Elementary School are reading books. This group of students recorded the number of books they read this week. Here are the results. Andrew 10 books

David 4 books

Rosie 7 books

Lionel 7 books

Maria 6 books

Ellen 3 books

1. Show all the results in this frequency chart. Student Andrew

Number of books read 10

David

4

Ellen Lionel Maria Rosie

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2. Now show the same results on this bar graph below. Books Read In A Week 10 9 8 7 6 5 4 3 2 1 Andrew

David

Ellen

Lionel

Maria

Rosie

Students 3. How many books were read by David, Ellen, and Maria? _____ Show how you figured it out.

4. How many more books did Rosie read than Ellen? Show how you figured it out.

________

5. How many books in all were read by the students? ________ Show how you figured it out.

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Page 11

Reading Books

Grade 2

Rubric

The core elements of the performance required by this task are: • Represents the same data in more than one way. • Represent and interpret data using graphs or other representation • Describe and compare data using qualitative and quantitative measures. • Communicate reasoning using words, numbers or pictures. Based on these credit for specific aspects of performance should be assigned as follows

1

Gives correct answer as Ellen – 3 Lionel -7 Maria – 6 Rosie – 7 Four or three correct answers

points

section points

1 1

2

Fills in the bars above David – 4 bars, Ellen – 3 bars, Maria – 6 bars.

1x3 3

3

4

Gives correct answer as: 13 Shows work such as: 4 + 3 + 6 = 13 Or explains what they counted or added to get the answer of 13 Gives correct answer as 4

5

Shows work such as: 7 – 3 = 4 Or explains what they counted, added or subtracted to get the answer of 4 Gives correct answer as: 37 Shows work such as: 10 +4+3+7+6+7 = 37 Or explains what they counted or added to get the answer of 37 Total Points

MARS Tasks – Grade 2

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1 ft 1 1 ft

2

1

2

1 ft 1 2 10

Page 12

2nd grade Student Task Core Idea 3 Patterns, Functions, and Algebra

MARS Tasks – Grade 2

Task 4

Growing Necklaces

Find and describe the pattern generated when “growing” a necklace of beads. Determine why a given number of beads would not fit with this necklace pattern. Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships. • Describe and extend growing patterns and translate from one representation to another • Communicate reasoning using numbers, pictures and/or words • Communicate mathematical thinking clearly and coherently

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Page 13

Growing Necklaces Every year Matthew makes a necklace for his sister, Janci. Here are drawings of the necklaces.

Year 1 Beads 3

beads

Year 2 5 beads

Year 3 7

Year 4

beads

1. Draw a picture of the necklace for Janci’s 4th year next to the 3rd necklace.

2. How many beads would Matthew need to make a necklace for Janci’s 6th year? ______beads in all Show how you figured it out.

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3. Would Matthew ever make a necklace like this for Janci with 12 beads? Yes or No ________________ Why or why not?

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Growing Necklaces

Grade 2

Rubric

The core elements of the performance required by this task are: • Describe and extend growing patterns and translate from one representation to another • Communicate reasoning using numbers, pictures and/or words Based on these credit for specific aspects of performance should be assigned as follows

points

1

Draws the 4th necklace with 9 beads

2

2

Gives correct answer as: 13

2

3

Explains thinking such as: 6 + 1 + 6 = 13, presents a series of numbers 3, 5, 7, 9, 11, 13 or explains their thinking in words Gives correct answer as: No

1 1

Explains how they got the answer of No such as: There are always an odd number of beads, Matt made one with 11 and 13 but not 12.

2

section points

2

Allow answer such as: it is not the same pattern

(1) Total Points

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3

3 8

Page 16

2nd grade

Task 5

Half and Half

Student Task

Draw and represent halves of geometric shapes. Describe how to know when a shape will show halves.

Core Idea 1 Number Properties Core Idea 4 Geometry and Measurement

Understand numbers, ways of representing numbers, relationships among numbers, and number systems • Represent commonly used fractions such as one-half

MARS Tasks – Grade 2

Students will recognize and use characteristics properties, and relationships of two-and three-dimensional geometric shapes and apply appropriate techniques to determine measurements • Use number concepts in geometric contexts • Communicate reasoning using numbers, pictures and/or words • Communicate mathematical thinking clearly and coherently

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Half and Half These shapes show halves. One half of the shape is colored and one half of the shape is uncolored.

Yes

No

Yes

2 + 2 =4

No

Yes

2+ 2 = 4

No

2+2=4

These shapes do not show halves.

Yes

No

Yes

3+2=5

No

3+2=5

Look at the three shapes below and on the next page. Find out if you can color in one half of the shape. Circle “yes” or “no” below the shape. Then, write an addition sentence that describes how you colored in the shape. 1.)

2.)

Yes

No

Yes

___ +___= ___

MARS Tasks – Grade 2

No

___ + ___= ___

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3.)

Yes

No

___ + ___= ___

4. How can you tell by looking at a shape that it can be colored to show half? ______________________________________________________ ______________________________________________________ ______________________________________________________ _______________________________________________________

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Page 19

Half and Half

Grade 2

Rubric

The core elements of the performance required by this task are: • Uses number concepts in geometric contexts • Represents commonly used fractions such as ½ Based on these credit for specific aspects of performance should be assigned as follows

1

Gives correct answer as: Correct drawing that shows halves Yes 4+4=8

points

section points

1 1 1 3

2

Gives correct answer as: Drawing that shows inequality No Equation matches drawing

1 1 1

Alternative solution: Divides the figure in half using fractions of a square Yes 4 ½ + 4 ½ =9

or 1 1 1 3

3

Gives correct answer as: Correct drawing that shows halves Yes 6 + 6 = 12

1 1 1 3

4

Explains how they got the answer such as: The number sentence is always a double. There are even numbers of squares so you can find half and half. Each colored square has a partner that is uncolored. Total Points

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1 1 10

Page 20

Second Grade Core Idea

Mars 2006 Overview of Exam Task

Data Analysis

Our Class Graphs

Task Descriptions

The task asks students to read, interpret and answer a prediction question related to two graphs. Successful students can find numerical data and compare values. They can make a prediction as to which of two data sets might change if collected the following day and defend their choice.

Number Operations

In One Minute

The task asks students to find values on a chart and compare to find their differences. Successful students consider the relationships between the quantities and may use addition, subtraction, counting on or counting back to find the answers. They can use regrouping for addition or subtraction with accuracy. Answers are proven using words, numbers or pictures.

Geometry

Describing Shapes

The task asks students to identify the attributes of two-dimensional shapes. Students who are successful can identify the correct number of sides and corners of a given shape as well as compare the lengths of the sides on a shape. They can name common geometric shapes.

Number Operations

Pam’s Shopping Trip

The task asks students to calculate buying caps and balls for a baseball team. Successful students use repeated subtraction, equal sharing and forming equal groups to find the price for one unit. They can use repeated addition or counting by multiples to find the price for several items. Student use previously calculated information to find the total cost of equipment for four players.

Measurement

The Track Team

The task asks students to find the number of jumps two students will make from a start to a finish line. Successful students find the total number of jumps by iterating each jumping unit. Students compare units and predict whether the measures will be greater or smaller when a different unit is used. Successful students can identify the person to finish first and explain their thinking.

Grade Two – 2006

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Page 21

Our Class Graphs On Monday, the students in Mrs. Gong’s class answered two questions and displayed the information in these two graphs.

1. How many children have black hair? ____________ 2. Which color of hair do the fewest number of students have? ________________

Grade Two – 2006

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3. How many more students come by bus than by walking? _____. Show how you know your answer is correct.

On Tuesday, Mrs. Gong asked the same two questions. 4. If they made new graphs of the information on Tuesday, which graph might look different? Circle one:

What color is your hair? How do you come to school?

Explain how you know your answer is correct. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ Grade Two – 2006

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5

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Page 23

Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Our Class Graphs: Grade 2:

Points

Section Points

The core elements of the performance required by this task are: • Represent and interpret data using graphs or other representation • Describe and compare data using qualitative and quantitative measures. • Communicate reasoning using words, numbers or pictures.

1

Based on these credit for specific aspects of performance should be assigned as follows 5

1

2

Red, accept 2

1

3

5

1

4

shows work such as 7 - 2 Circles How do you come to school?

1 1

Explains answer such as: a person’s hair color won’t change but they may come by a different way to school tomorrow

2

Alternative Solution:

or

Circles What color is your hair?

1

Explains answer such as: a student might have changed the color of his/her hair Total Points

2 7

1

1

Grade Two – 2006

2

3 7

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6

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Page 24

In One Minute Lydia, Andres and Jim were playing “In One Minute”. First they found out how many numbers they could write in one minute. Here’s what they could do.

Lydia

Numbers 67

Andres

49

Jim

51

1. Who wrote the most numbers? _______________ 2. How many more numbers did Lydia write than Andres? _____ Show how you know your answer is correct.

Grade Two – 2006

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Next, they found out how many letters they could write in one minute. Here’s what Lydia and Andres could do.

Lydia Andres

Letters 46 84

Jim 3. Who wrote the most letters? _________________ 4.

Jim said to Andres, “I wrote 8 fewer letters than you did. How many letters did Jim write? __________

Show how you know your answer is correct.

5. How many more letters did Andres write than Lydia? ______ Show how you know your answer is correct.

Grade Two – 2006

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Page 26

Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Points

In One Minute: Grade 2:

Section Points

The core elements of the performance required by this task are: • Demonstrate fluency in adding and subtracting whole numbers. • Understand whole numbers and use them in flexible ways such as relating, composing, and decomposing numbers. • Understand the relative magnitude of whole numbers and the concepts of quantity and the relative position of numbers. • Demonstrate an understanding of the base-ten number system and place value concepts. • Communicate reasoning using pictures, numbers and/or words. Based on these credit for specific aspects of performance should be assigned as follows

1

Lydia

1

2

18

2

Shows work such as: 67 - 49

1

1

3 3

Andres

1 1

4

76

1

Shows work such as 84 – 8

1 2

5

38

2

Shows work such as 84 – 46 Total Points

1

Grade Two – 2006

3 10

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21

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Describing Shapes 1. Look at the shape on the geoboard below. Read the sentences and

circle whether they are true or false.

a. This shape is called a trapezoid.

true

false

b. This shape has 6 sides.

true

false

c. This shape has 4 corners.

true

false

d. Two sides of this shape are the same length.

true

false

2. Look at the shape on the geoboard below. Circle whether the

statements are true or false

a. This shape has 6 sides.

true

false

b. You could draw a line of symmetry.

true

false

c. All sides of this shape are the same length.

true

false

d. This shape is called a ____________ . Grade Two – 2006

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3. Look at the shape on the geoboard below. Write three true

sentences that describe this shape.

true

true

true

Grade Two – 2006

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Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Points

Describing Shapes: Grade 2:

Section Points

The core elements of the performance required by this task are: • Describe and classify two-dimensional shapes according to their attributes and/or parts of their shapes. • Develop an understanding of how shapes can be put together or taken apart to form other shapes • Communicate reasoning using pictures, numbers and/or words. Based on these credit for specific aspects of performance should be assigned as follows

1

2

3

a) true b) false c) true d) true all four correct 2 -3 correct a) true b) true c) false d) hexagon all four correct 2-3 correct Gives three correct statements such as: Four sides, four corners, can draw a line of symmetry, rectangle, two sides match in length

2 (1)

2

2 (1)

2

3x1 3 7

Total Points

Grade Two – 2006

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Pam’s Shopping Trip Pam’s baseball team needs some new equipment. At the store, the prices were shown like this:

$15.

Caps sell 3 for $15.00

$12.

Balls sell 4 for $12.00

1. Eight balls cost $_________ Show how you know your answer is correct.

2. One cap costs $ ________ Show how you know your answer is correct.

3. Two caps cost $_________ Show how you know your answer is correct.

Grade Two – 2006

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Pam has $25. If she only buys caps, 4. What is the greatest number of caps she can buy? ________ Show how you know your answer is correct.

Pam has 4 players on her team who need one new cap and one new ball. 5. How much will that cost all together? $_________ Show how you know your answer is correct.

Grade Two – 2006

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Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Points

Pam’s Shopping Trip: Grade 2:

Sectio n Points

The core elements of the performance required by this task are: • Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships. • Understand situations that entail multiplication and division such as equal groupings of objects and equal sharing. • Communicate reasoning using pictures, numbers and/or words. Based on these credit for specific aspects of performance should be assigned as follows

1

24

1

Shows work such as $12 + $12

1 2

2

$5

1

Shows work such as 5 + 5 + 5

1 2

3

$10

1f.t.

Shows work such as $5 + $5

1f.t.

4

5 caps

1f.t. 1f.t.

5

Shows work such as $15 + $5 = $20, $20 + $5 = $25 or 3+1+1 $32 Shows work such as 1 cap is $5, 1 ball is $3. 8 + 8 + 8 + 8 Or 5 + 5 + 5 + 5 + 3 + 3 + 3 + 3

1f.t.

2

Special case: 8 Shows work such as 3 + 5 = 8

2 1f.t.

1s.c.

2 10

Total Points

Grade Two – 2006

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The Track Team The track team was practicing jumping skills. Sarah and Brian are both jumping. After two jumps, their coach marked their spots on the jumping mat. Sarah

Brian

Start

Finish

Brian and Sarah always take the same sized jumps. 1. How many jumps will Sarah take to the finish line? _______ 2. How many jumps will Brian take to the finish line? ________ 3. Who will take more jumps to the finish line? _____________ 4. Who will get to the finish line first? ___________ 5. Explain how you know who finished first. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________

Grade Two – 2006

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Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Points

Track Team: Grade 2:

Section Points

The core elements of the performance required by this task are: • Understand how to measure using non-standard and standard units. • Select an appropriate unit and tool for the attribute being measured (length). • Communicate reasoning using pictures, numbers and/or words. Based on these credit for specific aspects of performance should be assigned as follows

1

6 (accept 4 more if matched with 10 in part 2)

1 1

2

12 (accept 10 more if matched with 4 in part 1)

1 1

3

Brian

1 1

4

Sarah

1 1

5

Explains answer such as Sarah is taking bigger jumps than Brian so she will win.

2 2 6

Total Points

Grade Two – 2006

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Second Grade

Mars 2007 Overview of Exam

Core Idea Algebra

Task Descriptions

Task Sheep and Ducks

This task asks students to find the number of legs for a given number of sheep, ducks and for sheep and ducks together. Successful students use mathematical models and/or symbols to represent these situations that involve repeated addition or multiplication of whole numbers. Students can find two combinations of sheep and ducks with 32 legs in all.

Data Analysis

Backpack Colors

The task asks students to read and interpret data from a class bar graph. Students who are successful are able to complete the graph with additional information find numerical and categorical information and compare values. Successful students will also provide two additional facts about the graph.

Number Operations

Addition Shapes

The task asks students to use the addends of 3 and/or 5 to reach given sums. Successful students demonstrate fluency in the addition of whole numbers to reach a sum. These students can think flexibly and design a similar problem. Students are able to use the conditions in the problem throughout the task.

Geometry

Making Designs

The task asks students to name and identify the attributes of two dimensional shapes and to find shapes within other shapes. Successful students are able to take apart and put together the same large shape in two different ways using triangles, trapezoids, and hexagons. They can identify the number and kinds of shapes inside the large designs.

Number Operations

Incredible Equations

The task asks students to find the missing parts of incomplete equations equal to 16. Students who are successful use strategies to estimate and to solve problems involving addition and subtraction. These students move flexibly between addition and subtraction and may know how these operations are related to one another. Successful students understand the equals sign as a balance point between the two sides of an equation.

1

Grade 2 – 2007 Copyright ©2007 by Noyce Foundation. All rights reserved.

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Sheep and Ducks The farmer raises sheep and ducks. 1. How many legs on one duck? _____________ 2. How many legs on 4 ducks? _____________ 3. How many legs on 5 sheep? _____________ 4. Next to the barn is a pen with 2 sheep and 3 ducks. How many legs altogether? ________ Show how you know your answer is correct.

5. One of the farmer’s pens has a high fence around it. He can see 32 legs under the fence. How many sheep and ducks are in this pen? Show one way to have sheep and ducks with 32 legs in all.

Show a different number of sheep and ducks with 32 legs in all.

4

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Sheep and Ducks Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Task 1: Sheep and Ducks: Grade 2:

Points

Section Points

The core elements of the performance required by this task are: • Demonstrate fluency in adding and subtracting whole numbers • Understand situations that entail multiplication such as equal groupings of objects • Describe and extend patterns of number and translate from one representation to another • Communicate reasoning using words, numbers or pictures

1

Gives correct answer as: 2

1 1

2

Gives correct answers as: 8

1

3

Gives correct answer as: 20

1

1 1 4

Gives a correct answer as: 14

1

Shows work such as: 4+4+2+2+2

1 2

5

Gives a correct answer from the following: 16 ducks 14 ducks, 1 sheep 12 ducks, 2 sheep 10 ducks, 3 sheep 8 ducks, 4 sheep 6 ducks, 5 sheep 4 ducks, 6 sheep 2 ducks, 7 sheep 8 sheep

1

Shows a different correct answer from those listed above

2 3 8

Total Points

5

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Backpack Colors Second graders recorded the color of their backpack on the graph.

Backpack Colors Green Red Blue Black Pink 0

1

2

3

4

5

6

7

8

9

10

11

1. The teacher has a green backpack. Add a green backpack to the graph. 2. How many backpacks are pink? ____________ 3. More of the backpacks are _________ than any other color. 4. How many more backpacks are pink than red? ______ Show how you know your answer is correct.

5. How many backpacks in all? ________________ Show how you know your answer is correct.

30

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6. Write one new fact about this Backpack Colors graph. ___________________________________________________ ___________________________________________________

7. Write another new fact about this Backpack Colors graph. ______________________________________________________ ______________________________________________________

31

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Backpack Colors Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Task 2: Backpack Colors: Grade 2:

Points

Section Points

The core elements of the performance required by this task are: • Interpret data using a bar graph • Describe and compare data using qualitative and quantitative measures • Communicate reasoning using words, numbers or pictures

1

Correctly adds the seventh square to “green” on the graph.

1 1

2

Gives correct answer: 9

1 1

3

Gives correct answer: blue

1 1

4

5

6& 7

Gives correct answer: 6

1

Shows work such as: 9–3=6 Or shows comparison on the graph Gives correct answer such as: 34, accept 33 (not counting the added square) Shows work such as: 11 + 9 = 20 7 + 3 = 10 20 + 10 + 4 = 34 Writes two facts about this graph such as: Red has the least number of backpacks. Red plus black equals green. Partial Credit: Writes one fact about the graph.

2 1 1 2

3 (1) 3 10

Total Points

32

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Addition Shapes Ted is making number shapes. The corners on each shape must add up to the number in the center of the shape. The number put on each corner must be either 3 or 5. For example, shape number 11 has corners of 3 and 3 and 5 because 11 = 3 + 3 + 5.

3

11 3

5

Put numbers on the corners of each shape to find the same total as the number in the center of the shape. The number put on each corner must be either 3 or 5.

16

9

21

52

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18

Make a different addition shape around the 18 below. The number put on each corner must be either 3 or 5.

18

53

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Addition Shapes Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Task 3: Addition Shapes: Grade 2:

Points

Section Points

The core elements of the performance required by this task are: • Understand whole numbers and use them in flexible ways • Demonstrate fluency in adding or subtracting whole numbers

1

Gives correct answer as: 3, 3, 5, 5

1 1

2

Gives correct answer as: 3, 3, 3

1

3

Gives correct answer as: 3, 3, 5, 5, 5

1

4

Gives correct answer as: 3, 3, 3, 3, 3, 3

1

5

Draws a quadrilateral with corners of: 3, 5, 5, 5

1

1 1 1 1 5

Total Points

54

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Making Designs Paul’s class is making designs with pattern blocks.

Rhombus

Trapezoid

1. Tanya found a shape that has 3 sides. What is the name of this shape?

________________

2. Paul picked out a hexagon. How many sides on a hexagon?

________________

3. Lucy found a trapezoid. How many corners on a trapezoid?

________________

These pattern block shapes were used to make two different designs.

70

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4. Lucy only used trapezoids to fill this shape. Draw the trapezoids inside the shape. How many did she use? _________ trapezoids

5. If Lucy filled the shape differently , what might it look like? Draw the shapes inside.

How many of each did she use? ________ hexagons ________trapezoids ________triangles

71

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Making Designs Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Task 4: Making Designs: Grade 2:

Points

Section Points

The core elements of the performance required by this task are: • Describe and classify two-dimensional shapes according to their attributes and/or parts of their shapes • Show an understanding of how shapes can be put together or taken apart to form other shapes • Communicate reasoning using words, numbers or pictures

1

Gives correct answer as: triangle

1

2

Gives correct answer as: 6

1

3

Gives correct answer as: 4

1

4

Gives correct answer as: 6

1

Shows design divided into 6 trapezoids

1

1 1 1

2 5

Shows work by dividing the design into a different combination of shapes to correctly fill Gives correct answer such as: 2 H, 2 Trap. or 1 H, 4 Trap. or 18 Triangles or 2 H, 6 triangles Etc.

1

1 2 7

Total Points

72

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Incredible Equations On March 16th, some of the students in Mrs. Daniels’ class wrote equations equal to 16. During recess, Mrs. Daniels erased parts of each equation. Find the missing parts.

16 7 + _____ = 16

___ + 8 + ___= 16

16 = 3 + _____

27 - _____ = 16

100 - ____ = 16

16 = _____ + 10

_____ - 4 = 16 Mrs. Daniels added this equation. Can you find the number that fits in the blank?

11 + 5 = ____ + 8

Show how you know your answer is correct.

83

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Incredible Equations Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Task 5: Incredible Equations: Grade 2:

Points

Section Points

The core elements of the performance required by this task are: • Demonstrate fluency in adding and subtracting whole numbers • Use strategies to estimate and solve problems involving addition and subtraction • Communicate reasoning using words, numbers or pictures

1

Gives correct answers, starting from top left to right:

2

9 Any two addends equal to 8 13 11 84 6 20 Gives correct answer as: 8

7x1

7 1

Explains answer such as: 11 + 5 = 16 and 8 + 8 = 16

2 3 10

Total Points

84

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Balanced Assessment Test – Second Grade 2008 Core Idea

Task

Score

SC This task asks students to demonstrate an understanding of whole numbers and how to represent and use them in flexible ways, including relating, composing, and decomposing numbers. Successful students demonstrate fluency in adding and subtracting whole numbers in context, and they are able to communicate reasoning using words, numbers, or pictures. SC Data Analysis Pets This task asks students to represent the same data in more than one way. Students who are successful are able to compare and combine values on the graph, and use words, numbers, or pictures to explain their reasoning. Students should demonstrate that they understand that the data represented in the tally table and in the bar graph is the same information, and should be consistent. Successful students will also provide a statement that shows they can differentiate between the types of information provided about the data set based on the type of graph used to represent the data. SC Geometry Don’s Shapes This task asks students to describe and classify two-dimensional shapes. Successful students are able to identify the two shapes that make up a larger shape, using triangles, rectangles, and squares. They can sort a set of two-dimensional shapes based on the attribute of having straight sides or not. Successful students demonstrate that they can identify and compare shapes based on geometric attributes such as number of sides and angles, rather than size, appearance, or orientation. SC Algebra Building Walls This task asks students to identify and extend a growing pattern of blocks in a wall, using drawings and numbers to describe the growth. Successful students identify and use the growth element to determine the number of blocks used to create walls at various stages of the pattern. They can also communicate reasoning using words, numbers, or pictures to translate between representations of shape and number in the pattern. SC Number Operations Carol’s Numbers This task asks students to use their knowledge of place value to arrange three digits to make the largest and smallest combination. Students are also asked to place numbers on a number line. Successful students were able to think about scale and order is arranging the numbers on the number line.

Number Operations Pocket Money

2nd Grade – 2008

1

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Pocket Money

50¢

25¢

10¢





Margie says, “I have 10¢ in my pocket but I do not have a dime.” 1. What coins could Margie have in her pocket?

Jeff says, “I can make 17¢ with the coins in my pocket.” 2. Show two different ways to make 17¢ with coins. First way

Second way

2nd Grade – 2008

4

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50¢

25¢

10¢





Tim says, “I have one half-dollar, one quarter, one dime, one nickel, and one penny in my pocket.” 3. If Tim pulls three coins from his pocket, what is the most money he would have in his hand? ______ ¢ Show how you know your answer is correct.

Anna bought some gum for 18¢. She gave 50¢ to pay for the gum. 4. How much change did Anna get? ______¢

What coins did Anna get back?

8

2nd Grade – 2008

5

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Pocket Money Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Pocket Money: Grade 2

Points

Section Points

The core elements of the performance required by this task are: • Understand whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers • Demonstrate fluency in adding and subtracting whole numbers • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: Gives correct answer such as: 1

2

2 nickels or 1 nickel 5 pennies or 10 pennies Shows one correct way to have 17¢ Shows a second correct way to have 17¢

1

Partial credit: Shows 2 ways to get to a number other than 17¢

1 1

(1) 2

3

Gives correct answer: 85 ¢

1

Shows work such as: 50 + 25 + 10 = 85 ¢

1

Gives correct answer: 32 ¢

2

2 4

Shows coins such as: 3 dimes, 2 pennies Or 1 quarter, 1 nickel, 2 pennies

1 ft. 3

Total 8

2nd Grade – 2008

6

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OUR PETS Sam asked his classmates: “What kind of pets do you have?” He made a tally table to show the answers.

OUR PETS BIRDS CATS DOGS FISH NO PETS 1. Use the information in the tally table to fill in the bar graph below.

OUR PETS

14

N u m b e r s o f P e t s

13 12 11 10 9 8 7 6 5 4 3 2 1 0

BIRDS

CATS

DOGS

FISH

NO PETS

Kinds of Pets

2. Which kind of pet do the fewest children have? ___________ 2nd Grade – 2008

23

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3. How many dogs and cats do these children have in all?______ Show how you know that your answer is correct.

4. How many more children have dogs than fish? __________ Show how you know that your answer is correct.

5. Using the same data, Sam found out how many of the children in his class have pets. He wasn’t able to finish the table. Finish it for him. Have pets Do not have a pet 6. What is one thing you can learn from the bar graph that you can’t learn from the table above? ________________________________________________________

________________________________________________________ 10

2nd Grade – 2008

24

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Don’s Shapes These are Don’s favorite shapes.

Name this shape from Don’s favorites. 1.

_______________

Don made these figures from 2 of the shapes. Name the two shapes Don used.

2.

3.

_________________ and ________________

_________________ and _________________

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Here are Don’s favorite shapes again. A

B

C

D

E

F

G

4. Which of Don’s shapes have straight sides? Write the shape’s letter in the box it belongs. Have straight sides Don’t have straight sides

Look at these three shapes.

5. How is the 1st shape different from the other two? ______________________________________________________________ ______________________________________________________________ ________________________________________________________ 7

2nd Grade – 2008

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Don’s Shapes Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Don’s Shapes: Grade 2

Points

Section Points

The core elements of the performance required by this task are: • Describe and classify two-dimensional shapes according to their attributes and /or parts of their shape • Develop an understanding of how shapes can be put together or taken apart to form other shapes • Communicate reasoning using words, numbers or pictures Based on these credit for specific aspects of performance should be assigned as follow: 1

2 3

1

Rectangle

1

Square and triangle Accept rectangle and triangle. Triangle and triangle

1 1 1 1

4

Gives correct answers to include all: Straight sides: B,C,D,F,G Not straight sides: A,E

2 2

5

Gives correct explanation such as: The first shapes has three sides but the others have 4 Gives an attribute of only one set such as: It is a triangle.

2 (1) 2

Total 7

2nd Grade – 2008

44

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Building Walls Maya is using blocks to make a wall grow.

1st wall

2nd wall

3rd wall

1. Draw the 4th wall below:

2. How many blocks are needed to make the 4th wall? ________ blocks

3. Tom wants to build the 5th wall. Tell Tom how to build the 5th wall. _____________________________________________________________ _____________________________________________________________ _____________________________________________________________

2nd Grade – 2008

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4. How many blocks would it take to build the 7th wall? _______ blocks Show how you know that your answer is correct.

5. Tom and Maya’s teacher gave them 21 blocks and asked them to build a wall with all the blocks. Can they build a wall with exactly 21 blocks? Yes or No ___________ Why or Why not? _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________

7

2nd Grade – 2008

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Building Walls Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Building Walls: Grade 2

Points

Section Points

The core elements of the performance required by this task are: • Describe, extend, and create patterns of shape and number and translate from one representation to another • Describe. extend and create growing patterns • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: Correctly draw the 4th shape

1

2

10 blocks

1

3

Correctly describes how to build the 5th shape such as:

1

5 blocks on the top and 7 blocks on the bottom.

1

1 1

4

16 blocks

1

Shows work such as: 7th wall of blocks or extends the numerical pattern

1 2

5

No and An correct reasoning such as: The blocks are always an even number. Or It needs to 22 not 21.

2 2

Total 7

2nd Grade – 2008

59

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Carol’s Numbers Carol has three number cards.

4 7 2 1. What is the largest three-digit number Carol can make with her cards?

2. What is the smallest three-digit number Carol can make with her cards?

Explain to Carol how she can make the smallest possible number using her three cards. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _______________________________________________________________

Carol’s teacher drew a number line on the board. 2nd Grade – 2008

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0

42

3. About where would 85 be? Place 85 on the number line where it belongs. 4. About where would 21 be? Place 21 on the number line where it belongs. 5. About where would 31 be? Place 31 on the number line where it belongs.

Tell Carol how you knew where to place 31 and why. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

8

2nd Grade – 2008

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Carol’s Numbers Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Carol’s Numbers: Grade 2

Points

Section Points

The core elements of the performance required by this task are: • Understand the relative magnitude of whole numbers and the concepts of sequences, quantity, and the relative position of numbers • Use strategies to estimate and judge the reasonableness of results • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: Gives correct answer of : 742

1

2

Gives correct answer of: 247

1

3

Gives correct explanation such as: Put the smallest number on the left, then the next smallest number and the largest number last Places 85 approximately twice the length of 42

1 1

1

2 1

4

Places 21 approximately one half the length of 42 (use a range from approximately 15 -25)

2 2

5

Places 31 approximately on half the length between 21 and 42 Dependent upon the correct placementGives correct explanation such as: 31 is almost in the middle of 21 and 42. Or Because 31 is 10 more than 21 or Because 31 is 11 less than 42

Total

2nd Grade – 2008

1 1

2 8

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Second Grade

Mars 2009 Overview of Exam

Core Idea

Task Descriptions

Task

Algebra, Patterns, and Same Number, Same Shape Functions The task asks students to think about variables and unknowns in number sentences that use addition and subtraction. Successful students understand that the same shape represents the same quantity, and can follow this constraint when composing and decomposing numbers to 20. They can also successfully add and subtract in a variety of circumstances, including mixed operations in a single number sentence and performing missing addend calculations. Number Operations Apple Farm Field Trip The task asks students to interpret story situations in order to set up and perform twodigit addition and subtraction calculations. Students who are successful can accurately determine if a situation in context is combining, separating, or comparing quantities, and can choose an appropriate operation and number sentence to solve the problem. They can use a variety of strategies for performing addition or subtraction with accuracy and flexibility. They can prove their answer using words, numbers or pictures. Data Top Lunch Choices The task asks students to read and interpret a pictograph. Students who are successful can use the relevant features of the graph and the data represented on the graph to make mathematical statements about quantity and comparison. Measurement High Horse The task asks students to find the number of hands a mom and child will need to measure the height of a horse. Successful students find the total number of hands by iterating each hand unit. They can compare units and predict whether the measures will be greater or smaller when a different unit is used. Successful students can identify the person to use the fewest and greatest number of hands, and explain their thinking. Number Operations Auntie Em’s Cookies The task asks students to make sense of halving shapes and numbers. Successful students can identify a line of symmetry for a variety of regular and irregular shapes. They can also work backwards to complete a shape from half to whole. They are also asked to think about halving different quantities, even when the results are not a whole number.

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Same Shape, Same Number Fill in the shapes with numbers. Same shapes have same numbers. Different shapes have different numbers. 1. Write the numbers in the shapes to make the number sentences true.

+

= 6 +

8= +

+

=8

+

-

=

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Fill in the shapes with numbers. Same shapes have same numbers. Different shapes have different numbers. 2. Write the numbers in the shapes to make the number sentences true.

+5 = 7 16 = + +

+ + -

= 10 = 6

3. Tell how you figured out the number for the ________________________________________________________________ _________________________________________________________________ _________________________________________________________________

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Same Shape, Same Number Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2: 2009 Same Shape, Same Number: Grade 2: 2009

Points

Section Points

The core elements of the performance required by this task are: • Use concrete, pictorial and verbal representations to develop an understanding of symbolic notations • Demonstrate fluency in adding and subtracting whole numbers. • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: 3+3=6 8=4+4 3+4+1=8 4+4–3=5 1 point per correct number sentence

1x4 4

2

2+5=7 16 = 8 + 8 2 + 8 + 0 = 10 8+2–4=6 1x4 4

3

Gives an explanation such as: The two sides must be equal because 6 = 10 – 4. Well, you had 8 and you add 2 and you have to take away 4 to make 6.

1 f.t. 1

9

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Apple Farm Field Trip 1. 63 second graders are going on the field trip. 19 parents will also go. How many people are going on the field trip? Show how you know your answer is correct.

__________people

2. The Apple Farm is 92 miles from the school. They have traveled 58 miles so far. How many more miles do they have to go? Show how you know your answer is correct.

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________miles 3. Molly wants to buy an apple pen. She sees a red apple pen that cost 48¢. She sees a sparkle apple pen for 65¢. How much more does the sparkle apple pen cost? Show how you know your answer is correct.

________

¢

4. Time to leave! 36 students got on the bus. They waited until all 63 students were there. How many students were late to the bus? Show how you know your answer is correct.

_______ students 2nd Grade – 2009 Copyright ©2009 by Noyce Foundation All rights reserved.

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Apple Farm Field Trip Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2: 2009 Apple Farm Field Trip: Grade 2: 2009

Points

Section Points

The core elements of the performance required by this task are: • Understand whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers • Demonstrate fluency in adding and subtracting whole numbers • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: 82

1

Shows work such as: 63 + 19 = 82 or 63 + 20 = 83, 83 – 1 = 82

1 2

2

34

1

Shows work such as: 1

3

58 + ? = 92 or 92 – 58 = 34 17

4

Shows work such as: 48 + 2 = 50. 50 + 15 = 65. 15 + 2 = 17 or Uses pictures to show total 27

2 1

Shows work such as: 63 – 36 = 27 or Draws a picture to show total

2

2 1

3

3 10

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Top Lunch Choices Top Lunch Choices Hamburgers Chicken Nuggets Super Nachos Pasta Pizza Key: 1

equals 1 child

1. What is the least favorite lunch choice? _________________ 2. How many more students like chicken nuggets than pasta? Show how you figured it out.

_________ more 3. What are 2 other things this graph tells you? a.____________________________________________________ b.____________________________________________________

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Top Lunch Choices Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2: 2009 Top Lunch Choices: Grade 2: 2009

1

The core elements of the performance required by this task are: • Interpret data from a pictograph • Describe and compare data using qualitative and quantitative measures • Communicate reasoning using words, numbers or picture Based on these credit for specific aspects of performance should be assigned as follow: Pasta (accept 2)

Points

Section Points

1 1

2

3

3

1

Shows work such as: 5 – 2 = 3 or 2+3=5

1 2

Gives 2 additional items of information about the top lunch choices such as: Pizza is four more than pasta. Pizza and Super Nachos are the same. Chicken Nuggets is one more than Hamburgers. Pizza has 6 people who like it. Questions rather than statements are allowed.

1x2 2 5

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2. If Mom measures the whole horse, how many hand spans will she use? Show how you figured it out.

_________hand spans 3. If Jean measures the whole horse, how many hand spans will she use? Show how you figured it out.

_________hand spans 4. Who will use more hand spans to measure the whole horse?

64

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High Horse Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2: 2009 High Horse: Grade 2: 2009

Points

Section Points

The core elements of the performance required by this task are: • Understand how to measure using nonstandard units • Correctly iterates the unit of measure • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: Mom

1 1

2

8 hand spans

1

Show work such as: Drawing hand spans on the horse measure

2 3

3

12 hand spans

1

Show work such as: Drawing hand spans on the horse measure

2 3

4

Jean

1 1 8

65

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Auntie Em’s Cookies Auntie Em is making interesting cookies for Holly and David. She wants to cut the cookies so each child gets half a cookie. 1. Use a dotted line to show Auntie Em how to cut each cookie below.

2. Auntie Em cut a cookie in half. Here is David’s half. Draw the whole cookie.

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3. There are 12 cookies on a tray. David gets home first and eats half of them. How many cookies are left? _______cookies

4. When Holly gets home, she eats half of the cookies that were left. How many cookies does Holly eat? _______cookies

5. Auntie Em eats half of the cookies that are still on the tray. How many cookies does Auntie Em eat? ________cookies

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Apple Farm Field Trip Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2: 2009 Apple Farm Field Trip: Grade 2: 2009

Points

Section Points

The core elements of the performance required by this task are: • Understand whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers • Demonstrate fluency in adding and subtracting whole numbers • Communicate reasoning using words, numbers or pictures

1

Based on these credit for specific aspects of performance should be assigned as follow: 82

1

Shows work such as: 63 + 19 = 82 or 63 + 20 = 83, 83 – 1 = 82

1

34

1

2 2

Shows work such as: 1

3

58 + ? = 92 or 92 – 58 = 34 17

4

Shows work such as: 48 + 2 = 50. 50 + 15 = 65. 15 + 2 = 17 or Uses pictures to show total 27

2 1

Shows work such as: 63 – 36 = 27 or Draws a picture to show total

2

2 1

3

3 10

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