Grade 6 MathematicsPage 22 This is the end of Item Set 1 Section 2. 17. In a store, 1 can of soup...

Colorado Measures ofAcademic Success

Mathematics

Grade 6

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 –3 in a question, fill inthe answer grid as shown below.

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

OR

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ITEM SET 1 -SECTION 1

(Non-Calculator)Directions:

This Item Set has two sections: a non-calculator section and a calculator section.

You will now take the non-calculator section. You may not use a calculator.

1. This table shows the numbers of books, by type, checked out from theschool library on Monday.

Circle the correct answer options to complete the statement.

Book Checkout

Book Type Number of Books

mystery

nonfiction

adventure

humor

24

18

12

16

For every ____ mystery books checked out,

____ nonfiction books were checked out.

2

3

4

6

2

3

4

6

2. The area of a rectangular patio is square yards, and its length is

yards. What is the patio’s width, in yards?

5 58

112

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

34 992 81, ÷ =

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

÷ =32.533.8

A

B

C

D

3 34

4 18

7 18

8 716

5. What is the greatest common factor of 16 and 48?

Enter your answer in the box.

6. Show the location of

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

−1 .23

0

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7. Water freezes at 0° Celsius. The table shows five different temperaturesin degrees Celsius. Indicate whether each temperature is above or belowfreezing.

Place one check mark (✔) in each row.

Above Freezing Below FreezingTemperature

.2 25−

13−

8. Point P is located at A second point on the coordinate grid islocated 4 units from point P and has an x-coordinate of What is onelocation of the second point?

Plot the second point on the coordinate grid.

− −( 2, 3)..−2

-1-2-3-4-5 0 1 2 3 4 5x

y

P

-1-2-3-4-5

5

4

3

2

1

9. Cirrus clouds form more than 6,000 meters above Earth. Write aninequality to represent , the height, in meters, of cirrus clouds.

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

h

10. Sally rents a life jacket for a one-time fee of $5. She then rents a canoefor $15 per hour. Which expression represents the total cost, in dollars,to rent the life jacket and the canoe for h hours?

A

B

C

D

+ h5 15

h10

+ h15 5

h20

11. Small cubes with edge lengths of inch will be packed into the right

rectangular prism shown.

How many small cubes are needed to completely fill the rightrectangular prism?

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

14

14

in.

in.334

412

in.

5 in.

cubes

12. Which questions are statistical questions?

Select each correct answer.

A

B

C

D

E

How old is Mr. Patterson?

How many states has Juanita visited?

How many students are in Mrs. Lee’s class today?

How many students eat lunch in the cafeteria each day?

How many pets does each student at your school have at home?

13. This table shows the ages of 20 visitors at a library.

Create a histogram that represents the data by graphing each bar to thecorrect height.

15 27 53 9 48

3 56 12 10 15

18 15 2 31 20

21 33 6 52 56

8

6

4

2

0

Num

ber

of V

isitor

s

Age

Library Visitors

0–9 10–19 20–29 30–39 40–49 50–59

This is the end of Item Set 1 Section 1.

14. Thomas buys a case of bottled water. A case contains 36 bottles of waterand costs $4.69. Thomas will sell each bottle of water for $0.75 at aschool event.

How much profit, in dollars, will Thomas earn if he sells all the bottlesof water?


$

15. Graph the inequality that shows all the possible values of

Select the correct ray and then graph the ray beginning at the correctplace on the number line.

x1 .− >

0 1 2 5435− 4− 3− 2− 1−

ITEM SET 1 -SECTION 2(Calculator)

You may use a calculator for Item Set 1 - Section 2.

16.

The diagram represents the unit rate of making copies on a copymachine.

0 1Seconds

0 4Copies

A

B

C

D

Time (in seconds) Number of Copies

40 10

60 15

100 25

400 100


10 40

15 60

25 100

100 400


13 10

18 15

28 25

103 100


10 13

15 18

25 28

100 103

Which table represents the rate of making copies on this copy machine?

This is the end of Item Set 1 Section 2.

17. In a store, 1 can of soup costs $1.80. The store also sells a pack of 6 cans of the soup. A customer who buys 1 pack saves 15% comparedto buying 6 cans separately. How much money does a customer save bybuying 1 pack instead of buying 6 cans separately?


$

18. Which expressions represent “the sum of and ”?

Select all that apply.

3 n

A

B

C

D

E

n3

+n 3

+ n3

+ +n n n

n3

ITEM SET 2(Calculator)

You may use a calculator for Item Set 2.

Use the information provided to answer Part A and Part B for question 1.

The number of blueberry muffins that a baker makes each day is 40% of thetotal number of muffins she makes.

1. Part A

On Monday, the baker makes 36 blueberry muffins.

What is the total number of muffins that the baker makes on Monday?


muffins

Part B

On Tuesday, the baker makes a total of 60 muffins.

How many blueberry muffins does the baker make on Tuesday?


blueberry muffins

2. Sam’s two new aquariums each hold exactly 200 gallons of water. Oneaquarium will hold small fish and the other will hold large fish. Now heneeds new fish for his aquariums.

• He will buy 5 small fish for every 10 gallons of water in theaquarium.

• He will buy 8 large fish for every 40 gallons of water in theaquarium.

What is the total number of fish Sam will have? What will be the ratio ofSam’s small fish to large fish? Show or explain the steps you used tosolve this problem.

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


Joanna earns $12 per hour at her job. Last week, Joanna earned $432.

3. Part A

Create an equation that can be used to determine the number of hours,h, Joanna worked last week.

Write the correct number or operation into each box.

Part B

What is the number of hours Joanna worked last week?


h=

43212 + − • ÷

hours

TURN THE PAGE ANDCONTINUE WORKING

Use the information provided to answer Part A through Part D for question 4.

Amy can ride her bike 4 miles in 30 minutes. Sebastian can ride his bike 3 miles in 24 minutes.

4. Part A

At her current rate, what is the distance, in miles, Amy can ride her bikein 12 minutes?

Part B

At his current rate, what is the distance, in miles, Sebastian can ride hisbike in 1 hour?

A

B

C

D

1.6

2.5

3.0

9.0

A

B

C

D

0.125

3.0

7.5

8.0

A

B

C

D

Amy will have to wait 0.5 minute for Sebastian.

Amy will have to wait 1.5 minutes for Sebastian.

Sebastian will have to wait 3 minutes for Amy.

Sebastian will have to wait 6 minutes for Amy.

A

B

C

D

0.5

1.1

3.6

6.0

Part C

Sebastian and Amy both ride from their homes to the park.

If they both start riding at the same time and ride at their current rates,how long will one have to wait for the other to arrive?

Amy’shome

Sebastian’shome

3 miles 3 miles

Park

Part D

Amy and Sebastian leave the park at the same time and ride their bikesat their current rates back toward their homes.

How far apart are they, to the nearest tenth of a mile, after 14 minutes?

Amy’shome

Sebastian’shome

3 miles 3 miles

Park

5. The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P.

Point Q is graphed at The distance from point P to point Q isequal to the distance from point P to point R.

What is the distance from point P to point Q? What is the value of n?Explain how you determined the distance from point P to point Q, andthe value of n.

Enter your answers and your explanations in the space provided.

P (n, 3)R

x

y

¯n( , 2).

This is the end of Item Set 2.

6. What is the value of , when , and


+ ÷ −a b c d3 22 = = =a b c3, 8, 2=d 5?

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ITEM SET 3(Calculator)

You may use a calculator for Item Set 3.


This right rectangular prism is built with small cubes.

1. Part A

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

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

inch34

inch12

1 inch

Part B

What is the volume, in cubic inches, of 1 of the small cubes?

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

2. Brianna’s teacher asks her which of these three expressions areequivalent to each other.

Brianna says that all three expressions are equivalent because the valueof each one is when

Brianna’s thinking is incorrect.

• Identify the error in Brianna’s thinking.

• Determine which of the three expressions are equivalent.

• Explain or show your process in determining which expressions areequivalent.

Enter your answers and your explanation or process in the spaceprovided.

x xx

x x

Expression A: 9 3 4Expression B: 12 4Expression C: 5 4

− −−

+ −

−4 =x 0.

TURN THE PAGE ANDCONTINUE WORKING

3. Part A

A group of hikers buys 8 bags of mixed nuts. Each bag contains cups

of mixed nuts. The mixed nuts are shared evenly among 12 hikers. How

many cups of mixed nuts will each hiker receive? Show your work or

explain your answer.

Enter your answer and your work or explanation in the space provided.

312

Part B

The hikers plan to visit a scenic lookout. They will rest after they hike

2 miles. Then they will hike the remaining miles to the lookout. The

trail the hikers will use to return from the lookout is mile shorter than

the trail they will use to go to the lookout. Each hiker will bring gallon

of water for each mile to and from the lookout.

• Determine the total distance, in miles, each hiker will hike. Showyour work or explain your answer.

• Determine the total number of gallons of water each hiker willbring. Show your work or explain your answer.

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

1 34

12

14


This frequency table shows the number of hours each student in Ms. Claiborne’s class spent volunteering in one week.

4. Part A

What is the total number of hours that the students volunteered thatweek?


Number of Hours Students

1

2

3

4

5

6

Volunteering

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Part B

What is the mean number of hours volunteered by a student that week?


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A student filled a right rectangular prism-shaped box with one inch cubes tofind the volume, in cubic inches. The student’s work is shown.

Top layer(63 cubes)

Box Filled with Cubes

Student’s WorkI packed my box full of cubes. Each cubehas a volume of 1 cubic inch.I counted 63 cubes in the top layer.Since there are 9 layers of cubes below thetop layer, I solved 63 × 9 = 567. So thereare 567 cubes.The volume of my box is 567 cubic inches.

•

••

•

5. Part A

Explain why the student’s reasoning is incorrect. Provide the correctvolume, in cubic inches, of the box.

Enter your explanation and the correct volume in the space provided.

Part B

A second box also has a base area of 63 square inches, but it has avolume of 756 cubic inches.

What is the height, in inches, of the second box? Explain or show howyou determined the height.

Enter the height and your explanation or work in the space provided.

This is the end of Item Set 3.

6. Which of the given values will make the inequality true?

Select all that apply.

− >n 93 175

A

B

C

D

E

=n 82

=n 105

=n 268

=n 300

=n 312

1119836 ISD319351 2 3 4 5 A B C D E Printed in the USA

Grade 6 MathematicsPage 22 This is the end of Item Set 1 Section 2. 17. In a store, 1 can of soup...

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Transcript of Grade 6 MathematicsPage 22 This is the end of Item Set 1 Section 2. 17. In a store, 1 can of soup...