New York State administered the Mathematics Tests in May 2022
and is now making approximiately 75% of the questions
from these tests available for review and use.
New York State Testing Program
Grade 3
Mathematics Test
Released Questions
2022
THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234
New York State Testing Program
Grades 3–8 Mathematics
Released Questions from 2022 Exams
Background
As in past years, SED is releasing large portions of the 2022 NYS Grades 3–8 English Language Arts
and Mathematics test materials for review, discussion, and use.
For 2022, included in these released materials are at least 75 percent of the test questions that appeared on
the 2022 tests (including all constructed-response questions) that counted toward students’ scores.
Additionally, SED is also providing a map that details what each released question measures and the correct
response to each question. These released materials will help students, families, educators, and the public
better understand the tests and the New York State Education Department’s expectations for students.
Understanding Math Questions
Multiple-Choice Questions
Multiple-choice questions are designed to assess the New York State P–12 Learning Standards
for Mathematics. Mathematics multiple-choice questions will be used mainly to assess standard
algorithms and conceptual standards. Multiple-choice questions incorporate both the grade-level
standards and the “Standards for Mathematical Practices.” Many questions are framed within the
context of real-world applications or require students to complete multiple steps. Likewise, many of these
questions are linked to more than one standard, drawing on the simultaneous application of multiple skills
and concepts.
Short-Response Questions
Short-response questions require students to complete tasks and show their work. Like multiple-
choice questions, short-response questions will often require multiple steps, the application of multiple
mathematics skills, and real-world applications. Many of the short-response questions will cover conceptual
and application standards.
Extended-Response Questions
Extended-response questions ask students to show their work in completing two or more tasks or a
more extensive problem. Extended-response questions allow students to show their understanding of
mathematical procedures, conceptual understanding, and application. Extended-response questions may also
assess student reasoning and the ability to critique the arguments of others. The scoring rubric for short
and extended constructed-response questions can be found in the grade-level Educator
Guides at http://www.nysed.gov/state-assessment/grades-3-8-ela-and-math-test-manuals.
New York State P–12 Learning Standards Alignment
The alignment(s) to the New York State P–12 Learning Standards for Mathematics is/are intended to
identify the primary analytic skills necessary to successfully answer each question. However, some questions
measure proficiencies described in multiple standards, including a balanced combination of procedure and
conceptual understanding. For example, two-point and three-point constructed-response questions require
students to show an understanding of mathematical procedures, concepts, and applications.
These Released Questions Do Not Comprise a “Mini Test”
To ensure it is possible to develop future tests, some content must remain secure. This document is not
intended to be representative of the entire test, to show how operational tests look, or to provide information
about how teachers should administer the test; rather, its purpose is to provide an overview of how the
test reflects the demands of the New York State P–12 Learning Standards.
The released questions do not represent the full spectrum of the standards assessed on the State tests, nor
do they represent the full spectrum of how the standards should be taught and assessed in the classroom. It
should not be assumed that a particular standard will be measured by an identical question in future
assessments.
Name:
2022
Mathematics Test
Session 1
Grade
r
April 26-28, 2022
L
RELEASED QUESTIONS
3
Developed and published under contract with the New York State Education Department by Questar Assessment Inc., 5550 Upper 147th
Street West, Minneapolis, MN 55124. Copyright © 2022 by the New York State Education Department.
Session 1
Mr. Green buys packages of cups. Each package has cups. Which expression can
b
e used to find the number of cups that Mr. Green buys?
A
B
C
D
Which fraction is represented by point M on the number line shown below?
A
B
C
D
1
2
Page 2
GO ON
Session 1
A student made the shape shown below by combining two rectangles.
W
hat is the area, in square centimeters, of the shape the student made?
A 22
B 37
C 45
D 52
A worker has 3 bags of pebbles to use in a garden. The mass of each bag is
9
kilograms. What is the total mass, in kilograms, of all of the bags of pebbles?
A 3
B 6
C 12
D 27
3
4
Page 3
Session 1
GO ON
Which expression is equivalent to ?
A
B
C
D
9
Page 5
Session 1
GO ON
Zach earns the same amount of money each week doing yard work. If he earns $36
a
t the end of 4 weeks, how much money does Zach earn each week?
A $9
B $32
C $40
D $144
What is the value of ?
A
B
C
D
A student draws a rectangle on a sheet of paper. He labels two of the sides 1 unit
a
nd the other two sides 2 units. What is the area of the rectangle?
A 2 square units
B 4 units
C 4 square units
D 6 units
10
11
12
Page 6
GO ON
Session 1
What number makes the equation below true?
?
A
B
C
D
The shaded part of the model below represents a fraction.
W
hich figure is shaded to represent a fraction equivalent to the model shown?
A
B
C
D
15
16
Page 8
GO ON
Session 1
Grade 3
2022
Mathematics Test
Session 1
April 26 – 28, 2022
Name:
2022
Mathematics Test
Session 2
Grade
r
April 26-28, 2022
L
RELEASED QUESTIONS
3
Developed and published under contract with the New York State Education Department by Questar Assessment Inc., 5550 Upper 147th
Street West, Minneapolis, MN 55124. Copyright © 2022 by the New York State Education Department.
Session 2
Session 2
TIPS FOR TAKING THE TEST
Here are some suggestions to help you do your best:
• Read each question carefully and think about the answer before making your choice or
writing your response.
• You have been provided with a ruler to use during the test. Use the ruler whenever you
think it will help you to answer the question.
• Be sure to show your work when asked.
Page 1
Session 2
Which rectangle is divided into 4 equal parts?
A
B
C
D
A pet store has 4 fish tanks of the same size. A worker puts 10 liters of water in
e
ach fish tank. What is the total number of liters of water the worker puts in
a
ll of the fish tanks?
A 4
B 6
C 14
D 40
26
27
Page 2
GO ON
Session 2
Which array represents ?
A
B
C
D
Which number pattern uses the rule add 3 ?
A 2, 6, 18, 48, . . .
B 3, 7, 11, 15, . . .
C 3, 9, 27, 54, . . .
D 4, 7, 10, 13, . . .
28
29
Page 3
Session 2
GO ON
W
hich fraction is less than ?
A
B
C
D
Mica has gumballs. He gives all of them to friends. Each friend gets the same
n
umber of gumballs. Which expression can be used to find the number of gumballs
M
ica gives each friend?
A
B
C
D
30
31
Page 4
GO ON
Session 2
The figure below is made up of unit squares. Some of the unit squares are shaded
a
nd some of the unit squares are unshaded.
W
hich process describes one way to find the area, in square units, of the shaded
p
art of the figure?
A count all of the unit squares in the entire figure
B count only the unit squares that are shaded in the figure
C add up all of the side lengths in the entire figure
D add up only the side lengths of the shaded part in the figure
32
Page 5
Session 2
GO ON
The number line below shows a point.
W
hich equivalent fraction is represented by the location of the point on the
n
umber line?
A
B
C
D
33
Page 6
GO ON
Session 2
Three classes are on a field trip at the zoo. The number of students in each class is
l
isted below.
Class A has 24 students.
Class B has 23 students.
Class C has 25 students.
A
t the zoo, all the students are placed into 8 equal groups. How many students are
i
n each group?
SS
h
h
o
o
w
w
y
y
o
o
u
u
r
r
w
w
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o
r
r
k
k
.
.
AA
n
n
s
s
w
w
e
e
r
r
students
34
Page 7
Session 2
GO ON
A figure is shown below.
O
ne more row of 6 unit squares is added to the figure. What is the total area of
t
he new figure after the unit squares are added?
SS
h
h
o
o
w
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u
r
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k
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.
AA
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s
s
w
w
e
e
r
r
square units
35
Page 8
GO ON
Session 2
The manager at a movie theater needs to order 267 new seats. If the seats are
s
old only in groups of 10, what is the l
l
e
e
a
a
s
s
t
t
number of seats that the manager
s
hould order?
EE
x
x
p
p
l
l
a
a
i
i
n
n
h
h
o
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w
w
y
y
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k
k
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.
36
Page 9
Session 2
GO ON
Sam needs to solve the problem shown below.
?
H
e uses the equation ? to find the unknown number. Will this process
h
elp Sam solve the problem?
EE
x
x
p
p
l
l
a
a
i
i
n
n
h
h
o
o
w
w
y
y
o
o
u
u
k
k
n
n
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w
w
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u
u
r
r
a
a
n
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s
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w
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c
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r
r
r
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c
c
t
t
.
.
37
Page 10
GO ON
Session 2
The figure shown below is made up of unit squares.
W
rite and solve one addition equation a
a
n
n
d
d
one multiplication equation that can b
e
u
sed to find the area of the figure.
SS
h
h
o
o
w
w
y
y
o
o
u
u
r
r
w
w
o
o
r
r
k
k
.
.
38
Page 11
Session 2
GO ON
W
rite a fraction that has a value greater than using as the numerator. Be sure
t
o include what you know about fractions in your answer.
EE
x
x
p
p
l
l
a
a
i
i
n
n
h
h
o
o
w
w
y
y
o
o
u
u
k
k
n
n
o
o
w
w
y
y
o
o
u
u
r
r
a
a
n
n
s
s
w
w
e
e
r
r
i
i
s
s
c
c
o
o
r
r
r
r
e
e
c
c
t
t
.
.
39
Page 12
GO ON
Session 2
Selena is training for a race. Last week, she ran 4 miles each day on 3 different
d
ays. Use the symbol X to make an array that represents the total number of miles
S
elena ran last week.
SS
h
h
o
o
w
w
y
y
o
o
u
u
r
r
w
w
o
o
r
r
k
k
.
.
T
his week, Selena plans to run a total of 20 miles. If she runs 4 miles each day, how
m
any days will she need to run this week?
SS
h
h
o
o
w
w
y
y
o
o
u
u
r
r
w
w
o
o
r
r
k
k
.
.
AA
n
n
s
s
w
w
e
e
r
r
days
40
Page 13
Session 2
STOP
Grade 3
2022
Mathematics Test
Session 2
April 26 – 28, 2022
Multiple Choice Questions
Percentage of Students
Who Answered Correctly
(P-Value)
Average
Points
Earned
P-Value
(Average Points
Earned
÷ Total Possible
Points)
1 Multiple Choice D 1 CCSS.Math.Content.3.OA.A.1 Operations and Algebraic Thinking 0.78
2 Multiple Choice D 1 CCSS.Math.Content.3.NF.A.2b Number and Operations - Fractions 0.62
3 Multiple Choice B 1 CCSS.Math.Content.3.MD.C.7d Measurement and Data 0.35
4 Multiple Choice D 1 CCSS.Math.Content.3.MD.A.2 Measurement and Data 0.79
9 Multiple Choice D 1 CCSS.Math.Content.3.OA.B.5 Operations and Algebraic Thinking 0.63
10 Multiple Choice A 1 CCSS.Math.Content.3.OA.A.3 Operations and Algebraic Thinking 0.63
11 Multiple Choice C 1 CCSS.Math.Content.3.NBT.A.3
Number and Operations in Base
Ten
0.68
12 Multiple Choice A 1 CCSS.Math.Content.3.MD.C.5b Measurement and Data 0.4
15 Multiple Choice A 1 CCSS.Math.Content.3.OA.A.4 Operations and Algebraic Thinking 0.75
16 Multiple Choice D 1 CCSS.Math.Content.3.NF.A.3b Number and Operations - Fractions 0.41
22 Multiple Choice B 1 CCSS.Math.Content.3.NF.A.2a Number and Operations - Fractions 0.51
26 Multiple Choice B 1 CCSS.Math.Content.3.G.A.2 Geometry 0.96
27 Multiple Choice D 1 CCSS.Math.Content.3.MD.A.2 Measurement and Data 0.82
THE STATE EDUCATION DEPARTMENT
THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234
2022 Mathematics Tests Map to the Standards
Grade 3 Released Questions
Session 2
Constructed Response
Questions
Session 1
Question Type Key Points Standard Cluster
28 Multiple Choice C 1 CCSS.Math.Content.3.OA.A.1 Operations and Algebraic Thinking 0.93
29 Multiple Choice D 1 CCSS.Math.Content.3.OA.D.9 Operations and Algebraic Thinking 0.57
30 Multiple Choice D 1 CCSS.Math.Content.3.NF.A.3d Number and Operations - Fractions 0.45
31 Multiple Choice B 1 CCSS.Math.Content.3.OA.A.2 Operations and Algebraic Thinking 0.75
32 Multiple Choice B 1 CCSS.Math.Content.3.MD.C.5b Measurement and Data 0.5
33 Multiple Choice B 1 CCSS.Math.Content.3.NF.A.3a Number and Operations - Fractions 0.36
34 Constructed Response 2 CCSS.Math.Content.3.OA.D.8 Operations and Algebraic Thinking 1.09 0.55
35 Constructed Response 2 CCSS.Math.Content.3.MD.C.6 Measurement and Data 1.2 0.6
36 Constructed Response 2 CCSS.Math.Content.3.NBT.A.1
Number and Operations in Base
Ten
0.45 0.22
37 Constructed Response 2 CCSS.Math.Content.3.OA.B.6 Operations and Algebraic Thinking 0.88 0.44
38 Constructed Response 2 CCSS.Math.Content.3.MD.C.7a Measurement and Data 1.18 0.59
39 Constructed Response 2 CCSS.Math.Content.3.NF.A.3d Number and Operations - Fractions 0.8 0.4
40 Constructed Response 3 CCSS.Math.Content.3.OA.A.3 Operations and Algebraic Thinking 1.64 0.55
*This item map is intended to identify the primary analytic skills necessary to successfully answer each question. However, some questions measure proficiencies described in multiple standards, including
a balanced combination of procedural and conceptual understanding.
