Release of Spring 2021

MCAS Test Items

from the

Grade 5 Mathematics
Paper-Based Test
June 2021
Massachusetts Department of
Elementary and Secondary Education
 This document was prepared by the
Massachusetts Department of Elementary and Secondary Education
Jeffrey C. Riley
Commissioner

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is committed to ensuring that all of its programs and facilities are accessible to all members of the public.
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© 2021 Massachusetts Department of Elementary and Secondary Education

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this document with the exception of English Language Arts passages that are not designated as in
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Please credit the “Massachusetts Department of Elementary and Secondary Education.”

Massachusetts Department of Elementary and Secondary Education

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Phone 781-338-3000 TTY: N.E.T. Relay 800-439-2370
www.doe.mass.edu
 Overview of Grade 5 Mathematics Test
The spring 2021 grade 5 Mathematics test was a next-generation assessment that was administered in two primary formats:
a computer-based version and a paper-based version. The vast majority of students took the computer-based test. The paper-
based test was offered as an accommodation for students with disabilities who are unable to use a computer, as well as for
English learners who are new to the country and are unfamiliar with technology.

Most of the operational items on the grade 5 Mathematics test were the same, regardless of whether a student took the computer-
based version or the paper-based version. In places where a technology-enhanced item was used on the computer-based test, an
adapted version of the item was created for use on the paper test. These adapted paper items were multiple-choice, multiple-select,
or short-answer items that tested the same Mathematics content and assessed the same standard as the technology-enhanced item.

This document displays released items from the paper-based test. Released items from the computer-based test are
available on the MCAS Resource Center website at mcas.pearsonsupport.com/released-items.

Test Sessions and Content Overview

The grade 5 Mathematics test was made up of two separate test sessions. Each session included selected-response, short-
answer, and constructed-response questions. On the paper-based test, the selected-response questions were multiple-choice
items and multiple-select items, in which students select the correct answer(s) from among several answer options.

In 2021, due to the COVID-19 pandemic, the Department reduced testing time for students in grades 3–8 through a session
sampling approach, in which each student took only a portion of each MCAS assessment. Instead of taking two sessions in
each subject, individual students took one session each.

Standards and Reporting Categories

The grade 5 Mathematics test was based on standards in the five major domains for grade 5 in the Massachusetts Curriculum
Framework for Mathematics (2017). The five major domains are listed below.

• Operations and Algebraic Thinking

• Number and Operations in Base Ten

• Number and Operations—Fractions

• Measurement and Data

• Geometry

The Massachusetts Curriculum Framework for Mathematics is available on the Department website at
www.doe.mass.edu/frameworks/current.html.

Mathematics test results are reported under five MCAS reporting categories, which are identical to the five framework domains
listed above.

The tables at the conclusion of this document provide the following information about each released and unreleased
operational item: reporting category, standard(s) covered, item type, and item description. The correct answers for released
selected-response and short-answer questions are also displayed in the released item table.

Reference Materials and Tools

Each student taking the paper-based version of the grade 5 Mathematics test was provided with a plastic ruler and a grade 5
Mathematics Reference Sheet. A copy of the reference sheet follows the final question in this document. An image of the
ruler is not reproduced in the document.

During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowed for current and former
English learner students only. No calculators, other reference tools, or materials were allowed.

1
 Grade 5 Mathematics
SESSION 1

This session contains 8 questions.

You may use your reference sheet during this session.

You may not use a calculator during this session.

Directions
Read each question carefully and then answer it as well as you can. You must record
all answers in this Test & Answer Booklet.

For some questions, you will mark your answers by filling in the circles in your
Test & Answer Booklet. Make sure you darken the circles completely. Do not make
any marks outside of the circles. If you need to change an answer, be sure to erase
your first answer completely.

For other questions, you will need to fill in an answer grid. Directions for completing
questions with answer grids are provided on the next page.

If a question asks you to show or explain your work, you must do so to receive full
credit. Write your response in the space provided. Only responses written within the
provided space will be scored.

2
Mathematics Session 1

Directions for Completing Questions with Answer Grids

1. Work the question and find an answer.
2. Enter your answer in the answer boxes at the top of the answer grid.
3. Print only one number or symbol in each box. Do not leave a blank box in
the middle of an answer.
4. Under each answer box, fill in the circle that matches the number or
symbol you wrote above. Make a solid mark that completely fills the
circle.
5. Do not fill in a circle under an unused answer box.
6. If you need to change an answer, be sure to erase your first answer
completely.
7. See below for examples of how to correctly complete an answer grid.

EXAMPLES

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3
Mathematics Session 1
MA273791 OP B

q The prices for renting a bicycle from Leo’s Bike Shop are shown in this box.

Bicycle Rental Prices

$6.50 for the first hour

$1.50 for each additional hour

What is the total price for renting a bicycle from Leo’s Bike Shop for 3 hours?

A $8.00

B $9.50

C $12.50

D $13.00

4
Mathematics Session 1
MA306456 OP

w A server at a restaurant puts the same number of cubes of butter on each

of 10 plates. One of the plates is shown.

All of the cubes of butter on the plate are visible. Each cube of butter has a
volume of 1 cubic inch.

What is the total volume, in cubic inches, of butter the server will need for
the 10 plates?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

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5
Mathematics Session 1
MA800652607_PA A,F

e In which of the following numbers does the 9 have a value that is 1 the
10
value of the 9 in the number 871.953?

Select the two correct answers.

A 146.792

B 219.73

C 394.821

D 429.13

E 593.427

F 652.49

6
Mathematics Session 1

This question has four parts. Be sure to label each part of your response.
MA704359650_PA

r A student created two number patterns, Pattern X and Pattern Y.

A. Pattern X starts with the number 2 and follows the rule “Add 3.”
Starting with 2, write the first four numbers of Pattern X.

B. Pattern Y starts with the number 13 and follows the rule “Subtract 3.”
Starting with 13, write the first four numbers of Pattern Y.

C. Write four coordinate pairs in the form (X, Y) for the first four
corresponding terms in Pattern X and Pattern Y.

D. On the coordinate plane provided in your answer space, plot your four
coordinate pairs from Part C.

Write your answers on the next page.

7
Mathematics Session 1

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

8
Mathematics Session 1
MA306435 OP C

t Charlotte added 550 milliliters of orange juice to 500 milliliters of

pineapple juice to make fruit punch.

What is the total amount of fruit punch, in liters, that Charlotte made?

A 1.0

B 1.5

C 1.05

D 1.005

9
Mathematics Session 1
MA802285965_PA OP B

y The numbers of hours that seven students spent reading are listed in this box.

5 1 5 1 5 2
1 , 11, 1 , 1 , 1 , 1 , 1
6 2 3 6 3 6 3

Which of the following line plots shows the number of hours each student
spent reading?

A Time Spent Reading B Time Spent Reading

X X
X X X X
X X X X X X X X

1 1
1 1– 2 1 1– 2
2 2
Hours Hours

C Time Spent Reading D Time Spent Reading

X X X
X X X X
X X X X X X X

1 1
1 1– 2 1 1– 2
2 2
Hours Hours

10
Mathematics Session 1
MA303315 OP D

u The length of a pencil is 13.8 centimeters. What is the length of the pencil
rounded to the ones place?

A 10 centimeters

B 12 centimeters

C 13 centimeters

D 14 centimeters

MA261200 OP C

i Which of the following statements about quadrilaterals is true?

A Every rhombus is also a square.

B Every trapezoid is also a square.

C Every rhombus is also a parallelogram.

D Every trapezoid is also a parallelogram.

11
 Grade 5 Mathematics
SESSION 2

This session contains 12 questions.

You may use your reference sheet during this session.

You may not use a calculator during this session.

Directions
Read each question carefully and then answer it as well as you can. You must record
all answers in this Test & Answer Booklet.

For some questions, you will mark your answers by filling in the circles in your Test
& Answer Booklet. Make sure you darken the circles completely. Do not make any
marks outside of the circles. If you need to change an answer, be sure to erase your
first answer completely.

For other questions, you will need to fill in an answer grid. Directions for completing
questions with answer grids are provided on the next page.

If a question asks you to show or explain your work, you must do so to receive full
credit. Write your response in the space provided. Only responses written within the
provided space will be scored.

12
Mathematics Session 2

Directions for Completing Questions with Answer Grids

1. Work the question and find an answer.
2. Enter your answer in the answer boxes at the top of the answer grid.
3. Print only one number or symbol in each box. Do not leave a blank box in
the middle of an answer.
4. Under each answer box, fill in the circle that matches the number or
symbol you wrote above. Make a solid mark that completely fills the
circle.
5. Do not fill in a circle under an unused answer box.
6. If you need to change an answer, be sure to erase your first answer
completely.
7. See below for examples of how to correctly complete an answer grid.

EXAMPLES

0 . 432 . 25 4 3 8 6 8 1 9
\»
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13
Mathematics Session 2
MA280476 OP D

o Olga ordered 144 packages of beads from a craft store. Each package
contains 25 beads.

What is the total number of beads Olga ordered?

A 1008

B 2500

C 3380

D 3600

MA803875524 OP C

a Which of the following expressions is equivalent to 1,000,000,000?

A 1011

B 1010

C 109

D 108

14
Mathematics Session 2
MA715102137 OP

s What is 375.933 rounded to the nearest tenth?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

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15
Mathematics Session 2

This question has four parts. Be sure to label each part of your response.
MA624376704 OP

d Two football games were played at a stadium on the same day.

A. At the start of the first game, 3 of the stadium’s seats were filled with
4
people. At the end of the game, 2 of those seats remained filled.
3
Write an equation that can be used to determine p, the fraction of the
stadium’s seats that remained filled with people at the end of the first
game.

B. What fraction of the stadium’s seats remained filled with people at the end
of the first game?
2
C. The stadium has 5,000 seats. At the end of the second game, of the
5
seats were filled with people.
What was the total number of seats that were filled with people at the
end of the second game? Show or explain how you got your answer.

D. Workers at the stadium gave posters to 1 of the people who were in their
4
seats when the second game ended.
What was the total number of people who received posters? Show or
explain how you got your answer.

Write your answers on the next page.

16
Mathematics Session 2

17
Mathematics Session 2
MA204869 OP B

f Which of the following boxes has the greatest volume?

A 2 in. B 4 in.
4 in. 6 in.

6 in.
10 in.

C 12 in. D 4 in.
2 in. 4 in.
2 in.

8 in.

18
Mathematics Session 2
MA802284503_PA OP A

g A baker weighed four batches of cookie dough. The weights of the batches
are shown.

• 2 pounds
• 46 ounces
• 3 pounds
• 26 ounces

Which of the these lists shows the weights in order from least to greatest
value?

A 26 ounces, 2 pounds, 46 ounces, 3 pounds

B 26 ounces, 46 ounces, 2 pounds, 3 pounds

C 2 pounds, 3 pounds, 26 ounces, 46 ounces

D 2 pounds, 26 ounces, 3 pounds, 46 ounces

MA801656092 OP B,E

h Which of the following expressions are equivalent to this decimal number?

2.097

Select the two correct answers.

1
A 2 × 1 + (97 × )
100

1
B 2 × 1 + (97 × )
1000

1 1
C 2 × 1 + (9 × 10) + (7 × 100)

1 1
D 2 × 1 + (9 × 10) + (7 × 1000)

1 1
E 2 × 1 + (9 × )
+ 7× ( )
100 1000

19
Mathematics Session 2

This question has two parts.

MA704359410_PA OP F,E,B; A

j Part A
2
Which of these expressions have a product greater than 3 ?

Select the three correct answers.

2 7
A 3
× 8

2 3
B 3
× 2

2 3
C 3
× 5

2 3
D 3
×
3
2
E 3
×3

2 1
F 3
× 18

Part B

Which of the following fractions can be multiplied by 5 to get a product

that is less than 5?

1
A 3

3
B 2

5
C 1

1
D 1

20
Mathematics Session 2
MA803876799 OP B

k The location of point B on a coordinate plane is represented by the

ordered pair (8, 4).

Which of the following statements describes the location of point B on the

coordinate plane?

A Point B is 4 units to the right of the origin and 8 units up from the origin.

B Point B is 8 units to the right of the origin and 4 units up from the origin.

C Point B is 4 units to the left of the origin and 8 units down from the origin.

D Point B is 8 units to the left of the origin and 4 units down from the origin.

MA221208_PA OP C

l Compute:

3
4
×6

18
A 24

3
B 6
18
C 4

9
D 4

21
Mathematics Session 2
MA301167 OP D

; What is the value of this expression?

6 × 4 − (5 + 3) ÷ 2

A 0

B 8

C 11

D 20

22
Mathematics Session 2
MA804579588 OP

2) A right rectangular prism is made of cubes, with no gaps or overlaps.

Each cube has a side length of 1 centimeter, as shown.

1 cm

What is the volume, in cubic centimeters, of the prism?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

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23
 Massachusetts Comprehensive Assessment System
Grade 5 Mathematics Reference Sheet

CONVERSIONS

1 cup = 8 fluid ounces 1 mile = 5280 feet 1 pound = 16 ounces

1 pint = 2 cups 1 mile = 1760 yards 1 ton = 2000 pounds
1 quart = 2 pints
1 gallon = 4 quarts

AREA (A) FORMULAS VOLUME (V) FORMULAS

square . . . . . . . A = s × s right rectangular prism . . . . V = l × w × h

(s = length of a side) (l = length; w = width; h = height)
OR
rectangle . . . . . A = b × h
V = B × h
(b = length of base; h = height)
OR (B = area of base; h = height)

A = l × w
(l = length; w = width)

24
 Grade 5 Mathematics
Spring 2021 Released Operational Items

PBT
Page Reporting Item Correct
Item Standard Item Description
No. Category Type* Answer**
No.
Number and Operations Solve a real-world problem involving addition and
1 4 5.NBT.B.7 SR B
in Base Ten multiplication of money.
Solve a real-world volume problem by counting unit
2 5 Measurement and Data 5.MD.C.4 SA 30
cubes.
Demonstrate understanding of place value by
Number and Operations selecting multi-digit decimal numbers that have a
3 6 5.NBT.A.1 SR A,F
in Base Ten digit that is one-tenth the value of the same digit in a
given number.
Given the rules for two patterns, determine the first
Operations and Algebraic several terms of each pattern and create and graph
4 7 5.OA.B.3 CR
Thinking ordered pairs using corresponding terms of the two
patterns.
Solve a real-world word problem by converting
5 9 Measurement and Data 5.MD.A.1 SR C
milliliters to liters.
Identify which line plot displays a set of data
6 10 Measurement and Data 5.MD.B.2 SR measurements given as mixed numbers with unlike B
denominators.
Number and Operations Round a decimal number to the nearest whole
7 11 5.NBT.A.4 SR D
in Base Ten number.
Identify which statement is true about the properties
8 11 Geometry 5.G.B.4 SR C
of special quadrilaterals.
Number and Operations Multiply a three-digit whole number by a two-digit
9 14 5.NBT.B.5 SR D
in Base Ten whole number.
Number and Operations Identify which power of ten is equivalent to a given
10 14 5.NBT.A.2 SR C
in Base Ten whole number.
Number and Operations
11 15 5.NBT.A.4 SA Round a decimal to the nearest tenth. 375.9
in Base Ten
Write an equation to represent a given problem and
Number and Operations-
12 16 5.NF.B.6 CR multiply fractions and whole numbers to solve real-
Fractions
world problems.
Determine which right rectangular prism, shown
13 18 Measurement and Data 5.MD.C.5 SR B
with side lengths, has the greatest volume.
Select the list that orders measures of weight
14 19 Measurement and Data 5.MD.A.1 SR expressed in different units from least to greatest A
value.
Number and Operations Select which expressions correctly show a decimal
15 19 5.NBT.A.3 SR B,E
in Base Ten to the thousandths in expanded form.
Identify expressions with a product greater than a
Number and Operations- given factor and identify the fraction that can be
16 20 5.NF.B.5 SR B,E,F;A
Fractions multiplied by a whole number to get a product less
than that whole number.
Given an ordered pair, select the statement that
correctly describes the location of the point
17 21 Geometry 5.G.A.1 SR B
represented by the ordered pair in relation to the
origin on a coordinate plane.
Number and Operations- Determine the product of a fraction and a whole
18 21 5.NF.B.4 SR C
Fractions number.
Operations and Algebraic Determine the value of a given expression with
19 22 5.OA.A.1 SR D
Thinking parentheses.
Find the volume of a figure by counting cubes with
20 23 Measurement and Data 5.MD.C.4 SA 12
given dimensions.

* Mathematics item types are: selected-response (SR), short-answer (SA), and constructed-response (CR).
**Answers are provided here for selected-response and short-answer items only. Sample responses and scoring guidelines for any constructed-
response items will be posted to the Department’s website later this year.

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 Grade 5 Mathematics
Spring 2021 Unreleased Operational Items

PBT
Reporting Item
Item Standard Item Description
Category Type*
No.
Determine which triangle meets specified criteria based on the given side
21 Geometry 5.G.B.3 SR
lengths of each triangle.
Operations and Algebraic Determine which expression with parentheses has an equivalent value if
22 5.OA.A.1 SR
Thinking the parentheses are removed.
Number and Operations- Identify which expression can be used to solve an addition problem by
23 5.NF.A.1 SR
Fractions replacing given fractions with equivalent fractions with like denominators.
Given several expressions, determine whether the product of each
Number and Operations-
24 5.NF.B.5 SR expression is greater than or less than the value of a given factor of the
Fractions
expression.
Number and Operations
25 5.NBT.B.7 SR Divide a decimal to hundredths by a whole number.
in Base Ten
Write an equation to find the volume of a given prism, find the total
26 Measurement and Data 5.MD.C.5 CR volume of two prisms placed together, and determine a set of dimensions
that will result in a given volume.
Number and Operations- Determine which division equation involving a whole number and a unit
27 5.NF.B.7 SR
Fractions fraction can be used to solve a word problem.
Number and Operations- Estimate the sum of two fractions that are less than one to solve a word
28 5.NF.A.2 SR
Fractions problem.
Number and Operations Match decimal numbers in number form with decimals in expanded form
29 5.NBT.A.3 SR
in Base Ten and compare two decimal numbers to thousandths.
Number and Operations
30 5.NBT.B.5 SA Determine the product of two three-digit numbers.
in Base Ten
Operations and Algebraic
31 5.OA.A.2 SR Identify the word form of a given numerical expression.
Thinking
Number and Operations- Determine the quotient of a whole number divided by a fraction in a real-
32 5.NF.B.7 SA
Fractions world context.
33 Geometry 5.G.B.4 SR Classify triangles based on angle and side properties.
Identify which graph shows three points correctly plotted in the first
34 Geometry 5.G.A.2 SR
quadrant of the coordinate plane.
Write an equation to solve a real-world problem, critique another student’s
Number and Operations
35 5.NBT.B.6 CR reasoning of the problem, and solve a similar problem using division with
in Base Ten
whole numbers.
Number and Operations Determine the relationship of the value of a digit in one number compared
36 5.NBT.A.1 SR
in Base Ten to the value of that digit in another number.
Number and Operations- Determine the product of a mixed number and a fraction to solve a real-
37 5.NF.B.6 SR
Fractions world problem.
38 Geometry 5.G.B.3 SR Identify shapes that have two pairs of opposite angles that are congruent.
Operations and Algebraic Select the numerical expression, with parentheses, that represents a given
39 5.OA.A.2 SR
Thinking word expression.
Number and Operations-
40 5.NF.B.3 SR Determine the fraction that represents a given word problem.
Fractions

* Mathematics item types are: selected-response (SR), short-answer (SA), and constructed-response (CR).

26