MARS Tasks | Grade 2piper3g.weebly.com/uploads/3/0/1/1/3011310/mars-grade2.pdf · 2020-03-19 ·...

MARS Tasks | Grade 2 Page Name of MARS Task Year Math Strand Notes

* Peanuts and Ducks 2003 NP, NO Determine if enough peanuts for ducks * Symmetry Drawings 2003 GM Draw shapes with symmetry, mark line * Chopsticks 2003 NP, NO Find # of chopsticks needed, explain * Raisin Boxes 2003 DA Line plot, predict, explain prediction * Marble Rows 2003 PFA, NP Extend growing pattern, explain

* Teeth 2004 DA, NO Bar graph, find teeth lost in all * Footsteps on the Rug 2004 GM Find # of footsteps of diff size feet * Which Shape? 2004 GM Identify shapes, 2 attributes of triangles * Agree or Disagree 2004 PFA Whether 2 quantities are equal, explain * Student Store 2004 NO Find 2 items under $.70, calculate change

2 Pictures 2005 GM Visualize lines of symmetry 5 Pencils and Erasers 2005 NO, NP Amount spent at store, combinations 9 Reading Books 2005 DA, NO Frequency table, bar graph

13 Growing Necklaces 2005 PFA Find, describe growing pattern, explain 17 Half and Half 2005 NP, GM Draw half of geom. shape, how you know

21 Overview of 2006 Tasks 22 Our Class Graphs 2006 DA Prediction-2 graphs, defend choice 25 In One Minute 2006 NO Find values on chart, justify answer 28 Describing Shapes 2006 GM Identify attributes of shapes 31 Pam’s Shopping Trip 2006 NO Calculate buying items, repeated + & - 34 The Track Team 2006 GM Find # of jumps from start to finish line

36 Overview of 2007 Tasks 37 Sheep and Ducks 2007 PFA Calc. # of legs, poss. combos for 32 legs 39 Backpack Colors 2007 DA Complete bar graph & give 2 facts 42 Addition Shapes 2007 NO Use addends 3 and/or 5 to reach sum 45 Making Designs 2007 GM Name ident. shapes inside larger design 48 Incredible Equations 2007 NO Find missing parts of equations to 16

50 Overview of 2008 Tasks 51 Pocket Money 2008 NO Use numbers in flexible ways, + - 54 Our Pets 2008 DA Tally table, bar graph, explain reason 56 Don’s Shapes 2008 GM Identify shapes in larger one, sort 59 Building Walls 2008 PFA Identify extend growing pattern 62 Carol’s Numbers 2008 NO, NP Arrange digits into largest/sm, n line

65 Overview of 2009 Tasks 66 Same Shape/Number 2009 PFA Variables/unknowns in + - sentences 69 Apple Farm Field Trip 2009 NO 2-digit +- in story context, justify 72 Top Lunch Choices 2009 DA Pictograph, make math. statements 74 High Horse 2009 GM Measure horse w/diff. hand sizes 77 Auntie Em’s Cookies 2009 NO, GM Halving shapes/numbers, symmetry

NP=Number Properties NO=Number Operations PFA=Patterns Functions Algebra GM=Geometry & Measurement DA=Data Analysis

* 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).

MARS Tasks – Grade 2 www.scoe.org/mars

http://noycefdn.org/documents/math/MARS/MARS2003/tft2003gr2.pdf#page=1





http://noycefdn.org/documents/math/MARS/MARS2004/tft2004gr2-teeth.pdf#page=2

http://noycefdn.org/documents/math/MARS/MARS2004/tft2004gr2-footsteps.pdf

http://noycefdn.org/documents/math/MARS/MARS2004/tft2004gr2-shape.pdf

http://noycefdn.org/documents/math/MARS/MARS2004/tft2004gr2-agree.pdf

http://noycefdn.org/documents/math/MARS/MARS2004/tft2004gr2-store.pdf

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


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.


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

points

section points

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

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

3

Total Points 5


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.

Core Idea 1 Number Properties

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.


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? _____


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¢.


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.


points

section points

1 Gives these three answers: One eraser costs 15¢ Two pencils cost 20¢ She spent 35¢ altogether

1 1

1ft

3 2 Lists four permutations of pencils and/or erasers

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¢ cent sign is not required

1 1ft

2

3 Shows work such as: Lists items totally 60¢ 4 erasers or 6 pencils or 3 pencils and 2 erasers 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 1

2 Total Points 7


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

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.


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.

1. Show all the results in this frequency chart.

Student Number of books read

Andrew

10

David

4

Ellen

Lionel

Maria

Rosie

Andrew 10

books David

4 books Rosie

7 books

Lionel 7

books

Maria 6

books

Ellen 3

books


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.


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.


points

section points

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

1

1 2 Fills in the bars above

David – 4 bars, Ellen – 3 bars, Maria – 6 bars.

1 x 3

3

3 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

1 ft 1

2 4 Gives correct answer as 4

Shows work such as: 7 – 3 = 4 Or explains what they counted, added or subtracted to get the answer of 4

1 ft 1

2

5 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

1 ft 1

2 Total Points 10


2nd grade Task 4 Growing Necklaces Student Task

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.

Core Idea 3 Patterns, Functions, and Algebra

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


Growing Necklaces

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

Year 1 Year 2 Year 3 Year 4

Beads

3 beads

5 beads

7 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



3. Would Matthew ever make a necklace like this for Janci with 12

beads? Yes or No ________________ Why or why not?


Growing Necklaces Grade 2 Rubric


• 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

section points

1 Draws the 4th necklace with 9 beads

2 2

2 Gives correct answer as: 13 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

2 1

3 3 Gives correct answer as: No

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. Allow answer such as: it is not the same pattern

1 2

(1)

3 Total Points 8


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

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

• Represent commonly used fractions such as one-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

• Use number concepts in geometric contexts • Communicate reasoning using numbers, pictures and/or words • Communicate mathematical thinking clearly and coherently


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 No Yes No 2 + 2 =4 2+ 2 = 4 2 + 2 = 4 These shapes do not show halves. Yes No Yes No 3 + 2 = 5 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 No ___ +___= ___ ___ + ___= ___


3.)

Yes No ___ + ___= ___

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


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


points

section points

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

1 1 1

3 2 Gives correct answer as:

Drawing that shows inequality No Equation matches drawing Alternative solution: Divides the figure in half using fractions of a square Yes 4 ½ + 4 ½ =9

1 1 1

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.

1

1 Total Points 10


Grade Two – 2006 pg.(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:

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Second Grade Mars 2006 Task Descriptions

Overview of Exam

Core Idea Task

Data Analysis Our Class Graphs

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.


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Our Class Graphs

On Monday, the students in Mrs. Gong’s class answered twoquestions 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?

________________


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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, whichgraph might look different?

Circle one: What color is your hair?

How do you come to school?

Explain how you know your answer is correct.

__________________________________________________________

__________________________________________________________

__________________________________________________________

__________________________________________________________


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Mathematics Assessment CollaborativePerformance 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.

Based on these credit for specific aspects of performance

should be assigned as follows

1 5 1

1

2 Red, accept 2 1

1

3 5

shows work such as 7 - 2

1

1 2

4 Circles How do you come to school?

Explains answer such as: a person’s hair color won’t change

but they may come by a different way to school tomorrow

Alternative Solution:

Circles What color is your hair?

Explains answer such as: a student might have changed the

color of his/her hair

1

2

or

1

2 3

Total Points 7 7


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In One Minute

Lydia, Andres and Jim were playing “In One Minute”. First theyfound out how many numbers they could write in one minute.

Here’s what they could do.

Numbers

Lydia 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.


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

Letters

Lydia 46

Andres 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? __________


5. How many more letters did Andres write than Lydia? ______



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Mathematics Assessment Collaborative

Performance Assessment Rubric Grade 2

In One Minute: Grade 2: Points Section

Points


• 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

1

2 18

Shows work such as: 67 - 49

2

1

3

3 Andres 1

1

4 76

Shows work such as 84 – 8

1

1

2

5 38

Shows work such as 84 – 46

2

1 3

Total Points 10


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Describing Shapes

1. Look at the shape on the geoboard below. Read the sentences andcircle 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 thestatements 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 ____________ .


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3. Look at the shape on the geoboard below. Write three truesentences that describe this shape.

true

true

true


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Describing Shapes: Grade 2: Points Section

Points


• 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



1 a) true

b) false

c) true

d) true

all four correct

2 -3 correct

2

(1) 2

2 a) true

b) true

c) false

d) hexagon

all four correct

2-3 correct

2

(1) 2

3 Gives three correct statements such as:

Four sides, four corners, can draw a line of symmetry, rectangle,

two sides match in length

3 x 1

3

Total Points 7


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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 $_________


2. One cap costs $ ________


3. Two caps cost $_________



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Pam has $25. If she only buys caps,4. What is the greatest number of caps she can buy? ________


Pam has 4 players on her team who need one new cap and onenew ball.

5. How much will that cost all together? $_________



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Pam’s Shopping Trip: Grade 2: Points Sectio

n

Points


• 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.



1 24

Shows work such as $12 + $12

1

1

2

2 $5

Shows work such as 5 + 5 + 5

1

1

2

3 $10

Shows work such as $5 + $5

1f.t.

1f.t.

2

4 5 caps

Shows work such as $15 + $5 = $20, $20 + $5 = $25 or

3 + 1 + 1

1f.t.

1f.t.

2

5 $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

Special case:

8

Shows work such as 3 + 5 = 8

1f.t.

1f.t.

1s.c.

2

Total Points 10


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The Track Team

The track team was practicing jumping skills. Sarah and Brian areboth jumping. After two jumps, their coach marked their spots on

the jumping mat.

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.

__________________________________________________________

__________________________________________________________

__________________________________________________________

__________________________________________

Sarah

Brian

Start Finish


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Track Team: Grade 2: Points Section

Points


• Understand how to measure using non-standard and

standard units.

• Select an appropriate unit and tool for the attribute being

measured (length).



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

Total Points 6


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

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Second Grade Mars 2007 Task Descriptions Overview of Exam

Core Idea Task Algebra

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.


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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? ________


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.


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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



• 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

1


1

4 Gives a correct answer as: 14

Shows work such as:

4 + 4 + 2 + 2 + 2

1

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

Shows a different correct answer from those listed above

1

2

3

Total Points 8


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

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Backpack Colors

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

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? ______


5. How many backpacks in all? ________________


Backpack Colors

Green

Red Blue Black Pink

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


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

___________________________________________________

___________________________________________________

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

______________________________________________________

______________________________________________________


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Backpack Colors


Task 2: Backpack Colors: Grade 2: Points Section

Points


• Interpret data using a bar graph

• Describe and compare data using qualitative and quantitative

measures


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 Gives correct answer: 6

Shows work such as:

9 – 3 = 6

Or shows comparison on the graph

1

1

2

5 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

1

1

2

6 &

7

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.

3

(1)

3

Total Points 10


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

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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.

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.

3

3 5

11

16

9

21


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Make a different addition shape around the 18 below. The number

put on each corner must be either 3 or 5.

18

18


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Addition Shapes


Task 3: Addition Shapes: Grade 2: Points Section

Points


• 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

1

3 Gives correct answer as: 3, 3, 5, 5, 5 1

1

4 Gives correct answer as: 3, 3, 3, 3, 3, 3 1

1

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

1

1

Total Points 5


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

70

Making Designs

Paul’s class is making designs with pattern blocks.

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.

Rhombus Trapezoid


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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


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Making Designs


Task 4: Making Designs: Grade 2: Points Section

Points


• 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


1 Gives correct answer as: triangle 1

1


1


1

4 Gives correct answer as: 6

Shows design divided into 6 trapezoids

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

Total Points 7


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83

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

Mrs. Daniels added this equation. Can you find the number that fits

in the blank?

11 + 5 = ____ + 8


27 - _____ = 16

7 + _____ = 16 ___ + 8 + ___= 16

100 - ____ = 16

16 = 3 + _____

16 = _____ + 10

_____ - 4 = 16


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84

Incredible Equations


Task 5: Incredible Equations: Grade 2: Points Section

Points



• Use strategies to estimate and solve problems involving addition

and subtraction


1 Gives correct answers, starting from top left to right:

9

Any two addends equal to 8

13

11

84

6

20

7 x 1

7

2 Gives correct answer as: 8

Explains answer such as:

11 + 5 = 16 and 8 + 8 = 16

1

2

3

Total Points 10


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2nd Grade – 2008 1 Copyright ©2008 by Noyce Foundation All rights reserved.

Balanced Assessment Test – Second Grade 2008

Core Idea Task Score Number Operations Pocket Money 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. Data Analysis Pets SC 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. Geometry Don’s Shapes SC 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. Algebra Building Walls SC 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. Number Operations Carol’s Numbers SC 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.


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2nd

Grade – 2008 4 Copyright ©2008 by Noyce Foundation

All rights reserved.

Pocket Money

50¢ 25¢ 10¢ 5¢ 1¢

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


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50¢ 25¢ 10¢ 5¢ 1¢

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


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Pocket Money


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

Based on these credit for specific aspects of

performance should be assigned as follow:

1 Gives correct answer such as:

2 nickels or

1 nickel 5 pennies or

10 pennies

1

1

2 Shows one correct way to have 17¢

Shows a second correct way to have 17¢

Partial credit:

Shows 2 ways to get to a number other than 17¢

1

1

(1)

2

3 Gives correct answer: 85 ¢

Shows work such as:

50 + 25 + 10 = 85 ¢

1

1

2

4 Gives correct answer: 32 ¢

Shows coins such as:

3 dimes, 2 pennies

Or

1 quarter, 1 nickel, 2 pennies

2

1 ft.

3

Total

8


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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

BIRDS CATS DOGS FISH NO PETS

2. Which kind of pet do the fewest children have? ___________

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

N

u

m

b

e

r

s

o

f

P

e

t

s

Kinds of Pets


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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


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2nd

Grade – 2008 42 Copyright © by Noyce Foundation


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. _________________ and ________________

3. _________________ and _________________


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Here are Don’s favorite shapes again.

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

A B C D E F G


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Don’s Shapes


Don’s Shapes: Grade 2 Points Section

Points


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


numbers or pictures



1

Rectangle

1

1

2 Square and triangle

Accept rectangle and triangle.

1

1

3 Triangle and triangle

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


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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.

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________


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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


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Building Walls


Building Walls: Grade 2 Points Section

Points


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


numbers or pictures



1 Correctly draw the 4th

shape

1

1

2 10 blocks

1

1

3 Correctly describes how to build the 5th shape such

as:

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

1

1

4 16 blocks

Shows work such as:

7th

wall of blocks or extends the numerical pattern

1

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


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Grade – 2008 75 Copyright ©2008 Noyce Foundation


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.


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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


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Carol’s Numbers


Carol’s Numbers: Grade 2 Points Section

Points


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


numbers or pictures



1 Gives correct answer of : 742

1

1

2 Gives correct answer of: 247

Gives correct explanation such as:

Put the smallest number on the left, then the next

smallest number and the largest number last

1

1

2

3 Places 85 approximately twice the length of 42

1

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 placement-

Gives 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

1

1

2

Total 8


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2nd Grade – 2009 Copyright ©2009 by Noyce Foundation All rights reserved. pg. 1

Second Grade Mars 2009 Overview of Exam

Task Descriptions

Core Idea Task Algebra, Patterns, and

Functions Same Number, Same Shape

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 two-digit 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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2nd Grade – 2009 Copyright ©2009 by Noyce Foundation


pg. 4

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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pg. 5

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.

3. Tell how you figured out the number for the

________________________________________________________________

_________________________________________________________________

_________________________________________________________________

7 = + 5

= 16 +

= 10 +

= 6

+

+ -


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pg. 6

Same Shape, Same Number Mathematics Assessment Collaborative

Performance Assessment Rubric Grade 2: 2009

Same Shape, Same Number: Grade 2: 2009 Points Section

Points


this task are:

• Use concrete, pictorial and verbal

representations to develop an understanding

of symbolic notations


subtracting whole numbers.


numbers or pictures



1 3 + 3 = 6

8 = 4 + 4

3 + 4 + 1 = 8

4 + 4 – 3 = 5

1 point per correct number sentence

1 x 4

4

2 2 + 5 = 7

16 = 8 + 8

2 + 8 + 0 = 10

8 + 2 – 4 = 6

1 x 4

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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pg. 23

1. 63 second graders are going on the field trip. 19 parents will also go. How many people are going on the field trip?


__________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?


Apple Farm Field Trip


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pg. 24

________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?


________ ¢

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?


_______ students


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pg. 25


Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2: 2009

Apple Farm Field Trip: Grade 2: 2009 Points Section

Points


this task are:







numbers or pictures



1 82

Shows work such as:

63 + 19 = 82 or

63 + 20 = 83, 83 – 1 = 82

1

1

2

2 34

Shows work such as:

58 + ? = 92

or

92 – 58 = 34

1

1

2

3 17

Shows work such as:

48 + 2 = 50. 50 + 15 = 65. 15 + 2 = 17

or

Uses pictures to show total

1

2

3

4 27

Shows work such as:

63 – 36 = 27

or

Draws a picture to show total

1

2

3

10


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pg. 48

Top Lunch Choices

1. What is the least favorite lunch choice? _________________

2. How many more students like chicken nuggets than pasta?


_________ more

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

b.____________________________________________________

Key: 1 equals 1 child

Hamburgers

Chicken Nuggets

Super Nachos

Pasta

Pizza

Top Lunch Choices


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pg. 49

Top Lunch Choices


Top Lunch Choices: Grade 2: 2009 Points Section

Points


this task are:

• Interpret data from a pictograph

• Describe and compare data using qualitative

and quantitative measures


numbers or picture



1 Pasta (accept 2)

1

1

2 3

Shows work such as:

5 – 2 = 3 or

2 + 3 = 5

1

1

2

3 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.

1 x 2

2

5


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64

2. If Mom measures the whole horse, how many hand spans will she use?


_________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?


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65

High Horse


High Horse: Grade 2: 2009 Points Section

Points


this task are:

• Understand how to measure using non-

standard units

• Correctly iterates the unit of measure


numbers or pictures



1 Mom

1

1

2 8 hand spans

Show work such as:

Drawing hand spans on the horse measure

1

2

3

3 12 hand spans

Show work such as:

Drawing hand spans on the horse measure

1

2

3

4 Jean

1

1

8


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pg. 90

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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pg. 91

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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pg. 92



Apple Farm Field Trip: Grade 2: 2009 Points Section

Points


this task are:







numbers or pictures



1 82

Shows work such as:

63 + 19 = 82 or

63 + 20 = 83, 83 – 1 = 82

1

1

2

2 34

Shows work such as:

58 + ? = 92

or

92 – 58 = 34

1

1

2

3 17

Shows work such as:

48 + 2 = 50. 50 + 15 = 65. 15 + 2 = 17

or

Uses pictures to show total

1

2

3

4 27

Shows work such as:

63 – 36 = 27

or

Draws a picture to show total

1

2

3

10


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