Mathematics Grade 5 - Colorado

Colorado Measures ofAcademic Success

Mathematics

Grade 5

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.

\\\\\\. . . . . .0!2345»789

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. Which statement about the corresponding terms in both Pattern A andPattern B is always true?

Pattern A: 0, 5, 10, 15, 20, 25, 30

Pattern B: 0, 10, 20, 30, 40, 50, 60

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

. .+ =5 63 14 37

A

B

C

D

Each term in Pattern A is 2 times the corresponding term inPattern B.

Each term in Pattern A is times the corresponding term in

Pattern B.

12

Each term in Pattern A is 5 less than the corresponding term inPattern B.

Each term in Pattern A is 10 less than the corresponding term inPattern B.

TURN THE PAGE ANDCONTINUE WORKING

Use the information provided to answer Part A and Part B for question 3.

This table shows the three different ways that toy animals are packaged at afactory.

3. Part A

What is the total number of toy animals in one crate?

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

Package Type Amount in the Package

Bag 36 toy animals

Box 48 bags

Crate 18 boxes

Bag36 toy animals

not to scale

Crate18 boxes

Box48 bags

toy animals

Part B

One bag of toy animals weighs 12 ounces. What is the total weight, inounces, of the bags of toy animals in one crate?


ounces

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

Shannon is building a rectangular garden that is 18 feet wide and 27 feet long.

4. Part A

Write an equation that represents the area of Shannon’s garden. In yourequation, let g represent the area of Shannon’s garden. Then solve yourequation.

Enter your equation and your solution in the space provided.

Part B

Shannon is putting a fence around the garden, except where there is agate that is 3 feet wide.

One foot of the fence costs $43. The cost of the gate is $128.

Write an expression that represents the total cost of the fence and thegate.

Explain how you determined your expression.

Enter your expression and your explanation in the space provided.

Part C

Use your expression from Part B to find the total cost, in dollars, of thefence and the gate.

Enter your answer in the space provided.

5. The right rectangular prism shown is made from cubes. Each cube is1 cubic unit.

What is the volume, in cubic units, of the right rectangular prism?

Enter your answer in the box. Your answer must be a whole number ora decimal.

cubic units

6. On Saturday, Craig rode his bike of a mile. On Sunday, he rode his

bike of a mile. Craig added and to find the total distance, in

miles, he rode his bike on the two days. Craig said and

plotted on this number line.

• Explain why Craig’s answer is not reasonable.

• Find the total distance, in miles, Craig rode on his bike onSaturday and Sunday.

• Explain how to use the number line to show your answer iscorrect.

Enter your answer and explanations in the space provided.

58

12

58

12

58

12

610+ =

610

0 1610

7. Circle the answer option that correctly completes each of the sentences.

The product of and 4 is _____________ 4.35

less than

equal to

greater than

The product of and 2 is _____________ 2.

less than

equal to

greater than

112

The product of and is _____________ .

less than

equal to

greater than

52

134

134


Trevor is making a flower box in the shape shown in the diagram.

Trevor will fill the flower box completely with soil.

8. Part A

What volume of soil, in cubic feet, does Trevor need?

Enter your answer in the box.

6 ft

3 ft

2 ft

3 ft

2 ft2 ft

\\\\\\. . . . . .0!23456789

0!23456789

0!23456789

0!23456789

0!23456789

0!23456789

Part B

Trevor only has enough soil to fill the flower box 1 foot from the top.How much soil, in cubic feet, does he have?

Enter your answer in the box.

\\\\\\. . . . . .0!23456789

0!23456789

0!23456789

0!23456789

0!23456789

0!23456789

This is the end of Item Set 1.

9. Matt went running on four days. The table shows the distance he ran oneach day.

On which two days did Matt run an estimated total distance that wasclosest to 3 miles?

Day Distance (miles)

Sunday 2 12

Monday 156

Tuesday 58

Wednesday 123

A

B

C

D

Sunday and Tuesday

Monday and Tuesday

Monday and Wednesday

Sunday and Wednesday

ITEM SET 2


5 1. .× =0 3 5

2. Jim uses ribbon to make bookmarks. Jim has 9 feet of ribbon. He uses

foot of ribbon to make each bookmark.

What is the total number of bookmarks Jim makes with all 9 feet ofribbon?


13

bookmarks


For a family gathering, Brittany made 5 meat loaves using 9 pounds ofground beef. She also made 14 hamburgers using 4 pounds of ground beef.

3. Part A

Each meat loaf was made with the same amount of ground beef.

Which of these is closest to the amount of ground beef in each meatloaf?

Part B

Each hamburger was made with the same amount of ground beef.

Which of these is closest to the amount of ground beef in eachhamburger?

A

B

C

D

pound12

1 pound

pounds112

2 pounds

A

B

C

D

pound12

pound14

pound34

1 pound

4. A teacher drew an area model to find the value of

• Determine the number that each letter in the model representsand explain each of your answers.

• Write the quotient and remainder for

• Explain how to use multiplication to check that the quotient iscorrect. You may show your work in your explanation.

Enter your answers and your explanations in the space provided.

6,986 8÷ .

Teacher’s Model for 6,986 ÷ 8

8

not to scale

M 560

800 N P R

Q

6,986 8÷ .

5. Which expression represents the statement “12 divided by 3, then add 5”?

6. Graph points A, B, and C on the coordinate plane. Point A should belocated at point B should be located at and point C shouldbe located at Plot point A and label it “Point A.” Plot point B andlabel it “Point B.” Plot point C and label it “Point C.” Be sure to graph allthree points.

4,6( ), 6,4( ),3,0( ).

8

7

6

5

4

3

2

1

20 4 6 81 3 5 7

A

B

C

D

12 (3 5)÷ +

3 12 5÷ +

12 3 5÷ +

3 12 5+ ÷

7. Part A


6 3 0 1. .× =


625 847× =

Part B


6 3 0 1. .÷ =

9. Students in Mrs. Johnson’s class drew several different two-dimensionalfigures.

Select the four two-dimensional figures that are rectangles.

A

B

C

D

E

F


10. What fraction completes the equation using a like denominator when

adding

Write each correct number in the appropriate box. Each number may beused only once.

?13

36+

36++ =1

336

1 2 4 6 12 18

ITEM SET 3


1 534 26, ÷ =

2. For each sentence, circle the answer option that correctly compares thevalues.

The value of the 6 in 26.495 is ___________ the value of the 6 in 17.64.

The value of the 3 in 0.931 is ___________ the value of the 3 in 0.384.

1/10

10 times

1/100

100 times

1/10

10 times

1/100

100 times

TURN THE PAGE ANDCONTINUE WORKING


Mia is playing several rounds of a word game. Each coordinate pair shows thenumber of the round and Mia’s score for that round. She is keeping track ofthese coordinate pairs on a coordinate plane.

• Round 1: (1, 3)

• Round 2: (2, 6)

• Round 3: (3, 3)

3. Part A

Graph Mia’s scores for the first three rounds of play. Plot round 1 andlabel it “Point A.” Plot round 2 and label it “Point B.” Plot round 3 andlabel it “Point C.” Be sure to plot all three points.

x

y

8

7

6

5

4

3

2

1

20 4 6 81 3 5 7

A

B

C

D

(4, 5)

(9, 4)

(5, 4)

(4, 9)

Part B

In round 4, Mia scores the same number of points as in rounds 2 and 3combined.

What is the coordinate pair that represents Mia’s score for round 4?


Nick measured two crickets in science class. The lengths of the two cricketsare shown.

• Cricket A: inch

• Cricket B: inch

The science teacher asked Nick to compare the length of each cricket to

inch.

4. Part A

Nick claims that the length of each cricket is greater than because the

numerator of each cricket length is greater than the numerator in .

Compare inch to the length of each cricket using the or

symbol. Then explain whether Nick’s reasoning is correct.

Enter your comparisons and your explanation in the space provided.

3858

12

12

12

12 , ,> < =

Part B

Nick recorded the distance each cricket jumped.

• Distance for cricket A: feet

• Distance for cricket B: feet

Nick claims that cricket B jumped feet farther than cricket A because

the difference between the whole numbers is 2 and the difference

between the numerators is 1.

• Explain why Nick’s reasoning is incorrect.

• What is the correct difference, in feet, between the distancecricket A jumped and the distance cricket B jumped?

Enter your explanation and your answer in the space provided.

1 34

3 24

2 14

5. Which of these are equal to 83.041?

Select the two correct answers.

6. Emma has a board that is 5 feet long. She cuts the board into 6 equal pieces.

Which equation shows how to find the length, in feet, of each piece ofthe board?

A

A

B

B

C

C

D

D

E

5 6 30× =

eighty-three and forty-one tenths

8 10 3 1 4 1110

1100× + × + × + ×

6 5 1− =

eighty-three and forty-one hundredths

6 5 115÷ =

8 10 3 1 4 11100

11,000× + × + × + ×

5 6 56÷ =

eighty-three and forty-one thousandths

7. An egg farm packages 264 total cartons of eggs each month. The farmhas 3 different sizes of cartons.

• The small carton holds 8 eggs, and of the total cartons aresmall.

• The medium carton holds 12 eggs, and of the total cartons aremedium.

• The large carton holds 18 eggs, and the rest of the total cartonsare large.

Determine how many of each size of carton is needed each month. Thendetermine how many eggs are needed to fill the 264 cartons. Show yourwork or explain your answers.

Enter your answers and your work or explanations in the space provided.

16

23

8. A cereal box has a height of 32 centimeters. It has a base with an areaof 160 square centimeters.

What is the volume, in cubic centimeters, of the cereal box?


cubic centimeters

9. Kurt drew a rectangular maze with a length of foot and a width of

foot.

What is the area, in square feet, of Kurt’s maze?

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

____________________

34

512


Tom has a water tank that holds 5 gallons of water.

10. Part A

Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces

and a pitcher that holds gallon.

How many ounces of water are left in the water tank?


12

ounces

Part B

Tom drinks 4 pints of water a day.

How many full tanks of water will he drink in 30 days?


full tanks of water

11. Circle the two values that are less than seven hundred three and forty-seven thousandths.

× + × + × + × + × + ×7 100 0 10 3 1 0 1 81

101

1001

1000

7 100 2 10 1 1 0 2110

1100× + × + × + × + ×

seven hundred three and one-hundredth

seven hundred three and nine-tenths

703.46

703.1


12. A piece of yarn is foot long. The piece of yarn is divided equally into

2 smaller pieces.

What is the length, in feet, of each smaller piece of yarn?

Beginning at 0, shade part of the bar to show the correct length.

12

0 1 2 3 4feet

13. Create a fraction model to show the answer to

Divide the figure into the correct number of equal parts and then shadethe correct number of parts.

.12

34×

1119835 ISD319351 2 3 4 5 A B C D E Printed in the USA

Mathematics Grade 5 - Colorado

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