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 6
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:
New York State
Testing Program
2022
Mathematics Test
Session 1
Grade
r
April 26-28, 2022
L
  
RELEASED QUESTIONS
6
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
CONVERSIONS
FORMULAS
Grade 6 Mathematics Reference Sheet
Right Rectangular Prism
1 inch = 2.54 centimeters
1 meter
= 39.37 inches
1 mile
= 5,280 feet
1 mile
= 1,760 yards
1 mile
= 1.609 kilometers
1 kilometer
= 0.62 mile
1 pound
= 16 ounces
1 pound
= 0.454 kilogram
1 kilogram
= 2.2 pounds
1 ton
= 2,000 pounds
1 cup
= 8 fluid ounces
1 pint
= 2 cups
1 quart
= 2 pints
1 gallon
= 4 quarts
1 gallon
= 3.785 liters
1 liter
= 0.264 gallon
1 liter
= 1,000 cubic centimeters
V
= Bh or V = lwh
Triangle
A =
1
bh
2
Session 1
TIPS FOR TAKING THE TEST


            

          

Session 1
Page 1
Which value of makes the inequality true?
A
B
C
D
A farmer places beehives containing bees in her orchard to pollinate the plants. The table
b
elow shows the ratio of the number of beehives to the number of acres in the orchard.
I
f the bees pollinate the plants at a constant rate, how many acres will be pollinated by the
b
ees in 18 beehives?
A
38
B
40
C
44
D
48
1
2
Page 2
GO ON
Session 1
The net of a rectangular prism is shown below.
W
hat is the surface area, in square centimeters, of the rectangular prism?
A
60
B
79
C
158
D
360
3
Page 3
Session 1
GO ON
Jake takes guitar lessons that cost per month. Which equation can be used to
d
etermine the total number of dollars, , that Jake pays for lessons for any number
o
f
months, ?
A
B
C
D
Claire has 6 large envelopes and 11 small envelopes. What is the ratio of large envelopes
t
o the total number of envelopes?
A 5 : 11
B 6 : 11
C 6 : 17
D
11 : 17
4
5
Page 4
GO ON
Session 1
What is the value of the expression shown below when ?
A
B
C
D
A partially shaded rectangle is shown below.
W
hat is the area, in square centimeters, of the shaded part of the rectangle?
A
28
B
44
C
56
D
112
11
12
Page 7
Session 1
GO ON
A group of 10 Science Club students is on a field trip. That number of students represents
2
0% of the total number of students in the Science Club. What is the total number
o
f students in the Science Club?
A 20
B 30
C 50
D 80
Which value of makes the equation true?
A
B
C
D
E
mployees at a construction company are building a fence around the perimeter of a work
s
ite. The perimeter of the work site is mile. The cost of the fence is per yard.
W
hat is the total cost of the fence needed for the perimeter of the work site?
A
B
C
D
15
16
17
Page 9
Session 1
GO ON
R
alph has gallon of paint. He wants to store all of the paint equally among containers.
H
ow much paint, in gallons, will Ralph store in each container?
A
B
C
D
A parallelogram is shown below.
W
hat is the area, in square centimeters, of the parallelogram?
A
8.96
B
10.25
C
11.9
D
13.6
22
23
Page 12
GO ON
Session 1
A number line with points Q, R, S, and T is shown below.
W
hat point represents ?
A
point Q
B
point R
C
point S
D
point T
Ms. Wilson is buying packages of pencils. Each package costs $11.52 and contains
9
6 pencils. What is the unit price of a pencil?
A $0.12
B $0.96
C $1.20
D
$1.92
Three vertices of a rectangle are located at , , and on a coordinate
p
lane. What are the coordinates of the fourth vertex of the rectangle?
A
B
C
D
26
27
28
Page 14
GO ON
Session 1
Grade 6
2022
Mathematics Test
Session 1
April 26–28, 2022
  
Name:
New York State
Testing Program
2022
Mathematics Test
Session
2
Grade
r
April 26-28, 2022
L
  
RELEASED QUESTIONS
6
CONVERSIONS
FORMULAS
Grade 6 Mathematics Reference Sheet
Right Rectangular Prism
1 inch = 2.54 centimeters
1 meter
= 39.37 inches
1 mile
= 5,280 feet
1 mile
= 1,760 yards
1 mile
= 1.609 kilometers
1 kilometer
= 0.62 mile
1 pound
= 16 ounces
1 pound
= 0.454 kilogram
1 kilogram
= 2.2 pounds
1 ton
= 2,000 pounds
1 cup
= 8 fluid ounces
1 pint
= 2 cups
1 quart
= 2 pints
1 gallon
= 4 quarts
1 gallon
= 3.785 liters
1 liter
= 0.264 gallon
1 liter
= 1,000 cubic centimeters
V
= Bh or V = lwh
Triangle
A =
1
bh
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 mathematics tools (a ruler, a protractor, and a calculator)
and a reference sheet to use during the test. It is up to you to decide when each tool and
the reference sheet will be helpful. You should use mathematics tools and the reference
sheet whenever you think they will help you to answer the question.
• Be sure to show your work when asked.
Page 1
Session 2
There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3 : 5. There
a
re 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
A 18
B 20
C 30
D
48
What is the surface area, in square inches, of the rectangular prism formed by folding the
n
et below?
A 1,300
B 2,232
C 2,416
D 2,600
32
33
Page 2
GO ON
Session 2
Jasmine goes to the store to buy some fruit to make a fruit salad. The list below shows the
a
mount and the price of each type of fruit she buys.
3 pounds of apples for $4.05
2 pounds of grapes for $4.80
5 pounds of oranges for $7.50
3 pounds of peaches for $4.65
W
hich type of fruit costs $1.55 per pound?
A
apples
B
grapes
C
oranges
D
peaches
The outside temperature in a town is degrees Fahrenheit. What change in
t
emperature, in degrees Fahrenheit, would bring the outside temperature to
degrees Fahrenheit?
A
B
C
D
34
35
Page 3
Session 2
GO ON
A diagram of Joe’s living room wall with a geometric design is shown. Joe painted the
s
haded triangle on the living room wall.
W
hat is the area, in square feet, of the shaded triangle that Joe painted?
A
20
B
28
C
48
D
96
There was a total of 640 students at a school on Friday. Every student either walked or
r
ode in a bus to the school. If 45% of the total number of students walked to the school
o
n Friday, how many of the students rode in a bus to the school?
A 288
B 352
C 585
D 595
36
37
Page 4
GO ON
Session 2
Josh has
coins. Nick has fewer than times as many coins as Josh. Which expression can
b
e used to show how many coins Nick has?
A
B
C
D
38
Page 5
Session 2
GO ON
T
wo students, Student A and Student B, claim to know the correct representation of the
e
xpression .
Student A represents the expression as the product of and times
the product of and .
Student B represents the expression as the quotient of and times
the sum of and .
B
oth students’ claims are incorrect. What makes each representation incorrect?
EE
x
x
p
p
l
l
a
a
i
i
n
n
y
y
o
o
u
u
r
r
a
a
n
n
s
s
w
w
e
e
r
r
.
.
39
Page 6
GO ON
Session 2
A restaurant owner orders new plates and spoons based on the information below.
plates are sold in packages of 9
spoons are sold in packages of 12
T
he restaurant owner orders an equal number of plates and spoons. What is the l
l
e
e
a
a
s
s
t
t
n
umber of packages of plates and packages of spoons she should order to have an
e
qual number of plates and spoons?
SS
h
h
o
o
w
w
y
y
o
o
u
u
r
r
w
w
o
o
r
r
k
k
.
.
A
A
n
n
s
s
w
w
e
e
r
r
packages of plates
packages of spoons
41
Page 8
GO ON
Session 2
A
cereal box has dimensions of inches, inches, and inches. A pastry box
h
as dimensions of inches, inches, and inches. What is the difference
i
n volume, in cubic inches, between the two boxes?
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
cubic inches
42
Page 9
Session 2
GO ON
Two students evaluate the expression .
Student A evaluates the expression by adding the product of and to the
product of and .
Student B evaluates the expression by determining the product of and .
I
s each student’s evaluation correct or incorrect?
EE
x
x
p
p
l
l
a
a
i
i
n
n
y
y
o
o
u
u
r
r
a
a
n
n
s
s
w
w
e
e
r
r
.
.
43
Page 10
GO ON
Session 2
Ryan delivers flowers to two customers. He drives for 12 minutes at an average speed of
4
0 miles per hour to reach his first customer. He then drives for 15 minutes at an average
s
peed of 50 miles per hour to reach his second customer. During the 27 minutes of driving
t
ime, how many total miles does Ryan drive?
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
miles
44
Page 11
Session 2
GO ON
Johnny is 21 years old. He is 3 times as old as Becky. Write and solve an equation to
d
etermine Becky’s age,
a
.
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
a
=
45
Page 12
GO ON
Session 2
An office supply store sells boxes of pencils. Each box contains pencils. Write an
e
quation that represents the total number of pencils,
, in boxes.
EE
q
q
u
u
a
a
t
t
i
i
o
o
n
n
I
f for one day of sales, use your equation to find the total number of pencils the
s
upply store sells.
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
pencils
46
Page 13
Session 2
STOP
Grade 6
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 A 1 CCSS.Math.Content.6.EE.B.5 Expressions and Equations 0.68
2 Multiple Choice D 1 CCSS.Math.Content.6.RP.A.3a
Ratios and Proportional
Relationships
0.53
3 Multiple Choice C 1 CCSS.Math.Content.6.G.A.4 Geometry 0.54
4 Multiple Choice A 1 CCSS.Math.Content.6.EE.C.9 Expressions and Equations 0.71
5 Multiple Choice C 1 CCSS.Math.Content.6.RP.A.1
Ratios and Proportional
Relationships
0.55
11 Multiple Choice C 1 CCSS.Math.Content.6.EE.A.2c Expressions and Equations 0.49
12 Multiple Choice C 1 CCSS.Math.Content.6.G.A.1 Geometry 0.5
15 Multiple Choice C 1 CCSS.Math.Content.6.RP.A.3c
Ratios and Proportional
Relationships
0.63
16 Multiple Choice B 1 CCSS.Math.Content.6.EE.B.5 Expressions and Equations 0.62
17 Multiple Choice B 1 CCSS.Math.Content.6.RP.A.3d
Ratios and Proportional
Relationships
0.54
22 Multiple Choice A 1 CCSS.Math.Content.6.NS.A.1 The Number System 0.55
23 Multiple Choice C 1 CCSS.Math.Content.6.G.A.1 Geometry 0.33
26 Multiple Choice B 1 CCSS.Math.Content.6.NS.C.6c The Number System 0.51
27 Multiple Choice A 1 CCSS.Math.Content.6.RP.A.2
Ratios and Proportional
Relationships
0.59
THE STATE EDUCATION DEPARTMENT
THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234
2022 Mathematics Tests Map to the Standards
Grade 6 Released Questions
Constructed Response
Questions
Session 1
Question Type Key Points Standard Cluster
28 Multiple Choice B 1 CCSS.Math.Content.6.G.A.3 Geometry 0.56
32 Multiple Choice A 1 CCSS.Math.Content.6.RP.A.3a
Ratios and Proportional
Relationships
0.53
33 Multiple Choice D 1 CCSS.Math.Content.6.G.A.4 Geometry 0.43
34 Multiple Choice D 1 CCSS.Math.Content.6.RP.A.2
Ratios and Proportional
Relationships
0.79
35 Multiple Choice D 1 CCSS.Math.Content.6.NS.C.5 The Number System 0.72
36 Multiple Choice C 1 CCSS.Math.Content.6.G.A.1 Geometry 0.53
37 Multiple Choice B 1 CCSS.Math.Content.6.RP.A.3c
Ratios and Proportional
Relationships
0.38
38 Multiple Choice A 1 CCSS.Math.Content.6.EE.B.6 Expressions and Equations 0.61
39 Constructed Response 2 CCSS.Math.Content.6.EE.A.2a Expressions and Equations 0.8 0.4
40 Constructed Response 2 CCSS.Math.Content.6.NS.C.8 The Number System 0.93 0.46
41 Constructed Response 2 CCSS.Math.Content.6.NS.B.4 The Number System 1.09 0.54
42 Constructed Response 2 CCSS.Math.Content.6.G.A.2 Geometry 0.44 0.22
43 Constructed Response 2 CCSS.Math.Content.6.EE.A.3 Expressions and Equations 0.73 0.36
44 Constructed Response 2 CCSS.Math.Content.6.RP.A.3b
Ratios and Proportional
Relationships
0.25 0.12
45 Constructed Response 2 CCSS.Math.Content.6.EE.B.7 Expressions and Equations 1.04 0.52
46 Constructed Response 3 CCSS.Math.Content.6.EE.C.9 Expressions and Equations 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.
Session 2