Grade 4 Mathematicsarts, and mathematics. The sample items included in this resource provide...

Colorado Measures ofAcademic Success

Mathematics

Grade 4

Paper Practice Resource for Students

Paper Practice Resource for Students

The Colorado Measures of Academic Success (CMAS) is Colorado’s standards-based assessment program designed to measure the Colorado AcademicStandards (CAS) in the content areas of science, social studies, English languagearts, and mathematics. The sample items included in this resource providestudents with an opportunity to become familiar with the format of test itemsthat appear in the paper-based test books. The sample items are not intended tobe a complete test, nor are they intended to cover all assessed content or itemtypes.

While the use of the sample items is not required, it is strongly encouraged tohelp ensure students are familiar with the types of items they may encounterwhile taking the paper-based test.

Item Types:

Selected Response Items

Selected response items are multiple choice questions. To respond, the studentindicates their response in an answer grid or by filling in the circle(s) next totheir answer choice.

Constructed Response Items

Constructed response items are questions or prompts that require anindependent, written response. To respond, the student writes his or her answerin the response box in the test book.

A»CD

Correct Mark: Incorrect Marks:

ððððE

Converted Online Technology-Enhanced Item Types

Online technology-enhanced items converted to the paper testing format mayask students to:

• Circle the correct answer

• Complete a table with checkmarks, Xs, or letters from a list of answerchoices

• Fill in the blank

• Draw lines from boxes to correct answers

• Complete a bar graph or histogram

• Interact with a number line

• Graph points and lines on a coordinate grid

• Divide and shade shapes to indicate fractions

Directions for Completing the Answer Grids

1. Work the problem and find an answer.

2. Write your answer in the boxes at the top of the grid.

3. Print only one number or symbol in each box. Do not leave a blank box in themiddle of an answer.

4. Under each box, fill in the circle that matches the number or symbol youwrote above. Make a solid mark that completely fills the circle.

5. Do not fill in a circle under an unused box.

6. Fractions cannot be entered into an answer grid and will not be scored. Enterfractions as decimals.

7. See below for examples on how to correctly complete an answer grid.

EXAMPLES

To answer 632 in a question, fill inthe answer grid as shown below.

To answer .75 in a question, fill inthe answer grid as shown below.

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0!2»456789

0!»3456789

0!23456789

0!23456789

0!23456789

6 3 2\\\\\» . . . . .0!23456789

0!23456»89

0!234»6789

0!23456789

0!23456789

0!23456789

\\\\\\. . . . .»!23456789

0!23456789

0!23456»89

0!234»6789

0!23456789

0!23456789

. 7 5 0 . 7 5»

OR

ITEM SET 1

1. The area of the rectangular sandbox at Dave’s school is 108 square feet.

The sandbox has a width of 9 feet as shown in the diagram.

What is the length, in feet, of the sandbox?

Enter your answer in the box. Your answer must be a whole number or adecimal.

?

9 feet

feet

TURN THE PAGE ANDCONTINUE WORKING

Use the information provided to answer Part A and Part B for question 2.

The table shows the heights of three different plants.

2. Part A

Which statements about the heights of the plants are true?

Select the three correct statements.

Type ofPlant

PLANT HEIGHTS

tomato

pepper

bean

Height(feet)

13

36

512

A

B

C

D

E

The bean plant is the tallest plant.

The tomato plant is the shortest plant.

The pepper plant is taller than the bean plant.

The tomato plant is shorter than the bean plant.

The pepper plant is shorter than the tomato plant.

A

3. Select the three choices that are factor pairs for the number 28.

B

A

C

B

D

C

foot112

D

E

foot212

F

1 and 28

foot612

2 and 14

3 and 9

foot1012

4 and 7

6 and 5

Part B

How much taller is the tallest plant than the shortest plant?

8 and 3

Use the information provided to answer Part A, Part B and Part C for question 4.

Ms. Sloan asked 117 fourth-grade students the question, “How many pets doyou have?” She displayed the data she collected in the bar graph shown.

4. Part A

How many of the students that responded have 2 pets?

Enter your answer in the box.

Part B

How many more students have 1 pet than students who have 3 pets?Explain your answer.

Enter your answer and explanation in the space provided.

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0!23456789

0!23456789

0!23456789

0!23456789

0!23456789

Part C

Find the total number of pets the fourth-grade students have.

• Explain how you used the bar graph to solve the problem.

• Show your work using equations.

Enter your explanation, your work, and the total number of pets in thespace provided.

5. Which fractions complete the number sentences shown to make truecomparisons?

Complete each number sentence so that it is a true comparison.

Draw a line from one of the fractions shown to each correct box. Useeach fraction only once.

12

23

212

40100

=25

<35

20100

610


Jian’s family sells honey from beehives. They collected 3,311 ounces ofhoney from the beehives this season. They will use the honey to completelyfill 4-ounce jars or 6-ounce jars.

Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each.

Jian says if they use only 4-ounce jars, they could make $4,140 because3,311 ÷ 4 = 827 R 3. That rounds up to 828, and 828 multiplied by $5 is $4,140.

6. Part A

Explain the error that Jian made when finding the amount of money hisfamily could make if they use only 4-ounce jars.

Enter your explanation in the space provided.

Part B

Explain how to determine the money Jian’s family could make if they useonly 6-ounce jars. Include the total amount of money and the totalnumber of 6-ounce jars in your explanation.

Enter your answers and your explanation in the space provided.

7. Which numbers make the comparison true?

Select the two correct answers.

<27,768

A

B

C

D

E

27,759

28,744

26,773

27,568

27,836


Each student in a class chose one sport to play. This table shows the fractionsof all students who chose each sport.

8. Part A

Create an equation that can be used to find s, the fraction of all studentswho chose to play either soccer or basketball.

Draw a line from one of the fractions or operation symbols to each of theboxes to show the equation in the correct order. Use each fraction orsymbol only once.

Sport Fraction of All Students

soccer 310

football 210

hockey 110

basketball 410

+ – × ÷1/10 2/10 3/10 4/10

s=

Part B

Enter the fraction of all the students who chose to play either soccer orbasketball.

Enter your answer in the space provided. Enter only your answer.

This is the end of Item Set 1.

9. Enter your answer in the box. Your answer must be a whole number or adecimal.

, + =3 950 405

ITEM SET 2


=522 9÷

2. The value of the digit 4 in the number 42,780 is 10 times the value ofthe digit 4 in which number?

A

B

C

D

34,651

146,703

426,135

510,400

3. Part A

Shaun plotted a point on the number line by drawing 5 equally spaced

marks between 0 and 1 and placing a point on the third mark. He claims

that the point represents the fraction because each mark represents

, so the third mark represents .

• Explain why Shaun’s reasoning is incorrect.

• Explain how you can use the number line to determine the fractionthat Shaun’s point represents.

• Determine the fraction that Shaun’s point represents.

Enter your explanations and your answer in the space provided.

35

15

35

0 1

Part B

Shaun wants to write a fraction that is equivalent to the fraction .

Describe how Shaun can find a fraction that is equivalent to .

Enter your description in the space provided.

23

23


, × =3 649 6


7,564 + 8,239 =

6. Part A

The table shows the lengths of five different animals in a zoo. For each

animal, select a place in the table to show whether it is less than or

greater than meter in length.

Place only one check mark (✓) in each row.

510

Length(in meters)Animal

Cottontailrabbit

Blue jay

Raccoon

SnowyowlThreadsnake

410

Less than meter510 Greater than meter5

10

11100

25100

67100

810

Part B

Use the lengths in the table to compare the lengths of the animals.

Circle the correct answer option to complete each comparison.

blue jay _____ cottontail rabbit

<

=

>

<

=

>

<

=

>

thread snake _____ blue jay

raccoon _____ snowy owl

7. The rectangle is divided into eight equal sections.

Jodi colors 4 sections. Then she colors 3 more sections.

Which two of these represent the fraction of the rectangle that Jodicolors in all?


A

B

C

D

E

+48

38

+4 3

+84

83

+ 318

+ + + + + +18

18

18

18

18

18

18

8. Which statement about angles is true?

A

B

C

D

An angle is formed by two rays that do not have the same endpoint.

An angle that turns through of a circle has a measure of

360 degrees.

1360

An angle that turns through five 1-degree angles has a measure of5 degrees.

An angle measure is equal to the total length of the two rays thatform the angle.


The model shows a hallway in Clark’s house.

9. Part A

The perimeter of the hallway is meters.

What is the width, in meters, of the hallway?


? meters

3 meters910

10 410

Part B

Clark’s family adds a closet that shortens the length of the hallway by

meter.

What is the new perimeter, in meters, of the hallway?


610


10. Ryan makes 6 backpacks. He uses yard of cloth to make each

backpack. What is the total amount of cloth, in yards, Ryan uses to

make all 6 backpacks?


34

ITEM SET 3

1. Circle the correct symbol to compare the measurements.

0.4 meter_____0.04 meter

<

=

>


<

=

>


<

=

>


Four teachers offer an after-school chess club. The table shows the number ofstudents who joined.

2. Part A

The teachers will divide the total group of students who joined intoteams of no more than 6 students.

What is the least number of teams that will include all of the students?


Grade Number of Students

third 12

fourth 36

fifth 9

teams

Part B

The chess club started with 18 chess sets. The teachers ordered 3 casesof 15 chess sets. They will divide the total number of chess sets so thateach teacher receives an equal number. Then they will give any extrasets to the school library.

What is the greatest number of chess sets each of the 4 teachersshould get?


chess sets

3. Henry cut a piece of yarn that was feet long into two pieces. List two

different pairs of fractions that could show the lengths, in feet, of the

two pieces. Explain how you found your pairs of fractions.

Enter your fraction pairs and your explanation in the space provided.

116

4. A basketball team scored a total of 747 points for the season. This was9 times the number of points scored in the first game. How many pointswere scored during the first game?

A

B

C

D

73

75

82

83


Two figures are shown. In Figure 1, the measure of angle MSG is 105°.

The measures of angle MSK, angle KSP, and angle PSG are shown in Figure 2.The measure of angle MSG is still 105°.

5. Part A

Write numbers or symbols in the boxes to complete an equation that canbe used to find the value of y. Each symbol may be used more than onceor not at all.

Write the numbers and symbols in the correct order.

105°

Figure 1

PG

K

S M

Figure 2

32°

44°

PG

K

S

y°

M

=105

y 105 32 44× ÷–+

6. Hayley has 272 beads. She buys 38 more beads. She will use 89 beadsto make bracelets and the rest to make necklaces. She will use 9 beadsfor each necklace.

What is the greatest number of necklaces Hayley can make?


necklaces

Part B

What is the value of y ?


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0!23456789

0!23456789

0!23456789

0!23456789

0!23456789

7. The length of a desktop is 4 feet. How many inches is the length ofthe desktop?


inches

8. Which two equations represent the statement “48 is 6 times as many as 8”?


A

B

C

D

E

= +48 6 8

= ×48 6 8

= ×48 6 6

= +48 8 6

= ×48 8 6


Martin cut a pan of corn bread into equal pieces as shown in the model.

9. Part A

Martin gave of the corn bread to his neighbor.

Explain how you can use the model to show . Then write a fraction

that is equivalent to .

Enter your explanation and your answer in the space provided.

13

13

13

Part B

Martin gave of the corn bread to his teacher.

Write a comparison using <, >, or = to compare the fractions

and . Explain how the model can be used to compare these fractions.

Enter your comparison and your explanation in the space provided.

612

13

612

10. For each figure pictured in the table, place a check mark (✓) to selectany statement that describes the figure. You may place more than onecheck mark (✓) in each row.

Appears to have at least2 parallel sides

Has at least2 perpendicular sides

11. The Amazon River is about 6,516 kilometers long.

The Mississippi River is about 3,775 kilometers long.

What is the difference, in kilometers, between these two lengths?


kilometers

12. A student has an unknown amount of water in Container 1. She poursthe amount into Container 2, which already has 450 milliliters of waterinside. After she combines the two amounts, there is a total of 1 liter ofwater in Container 2.

What was the original amount of water, in milliliters, in Container 1before the student combined the two amounts?

Draw a line and shade the container to the correct height.

1,000

900

800

700

600

500

400

300

200

100

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

mL

Container 1


13. What number on the number line represents the value of

Fill in the circle on the number line to plot the point.

×2 ?23

0 1 2 3 4 5 6

14. Create a fraction model with a denominator of 10 that is equivalent

to

Divide the figure into the correct number of equal parts. Then shade thecorrect number of parts.

.70100

1119834 ISD319351 2 3 4 5 A B C D E Printed in the USA

Grade 4 Mathematicsarts, and mathematics. The sample items included in this resource provide...

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