New York State Testing Program

Grade 4
Mathematics Test

Released Questions

June 2019

New York State administered the Mathematics Tests in May 2019

and is now making approximately 75% of the
questions from these tests available for review and use.
 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 2019 Exams
Background

In 2013, New York State began administering tests designed to assess student performance in accordance with
the instructional shifts and rigor demanded by the new New York State P-12 Learning Standards in
Mathematics. To help in this transition to new assessments, the New York State Education Department (SED)
has been releasing an increasing number of test questions from the tests that were administered to students
across the State in the spring. This year, SED is again releasing large portions of the 2019 NYS Grades 3-8
English Language Arts and Mathematics test materials for review, discussion, and use.

For 2019, included in these released materials are at least 75 percent of the test questions that appeared on
the 2019 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
of the 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 https://www.engageny.org/resource/test-guides-english-language-arts-andmathematics.

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 future valid and reliable tests, some content must remain secure for possible use on future exams.
As such, 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. Specific criteria for writing test questions, as well as additional assessment information, are
available at http://www.engageny.org/common-core-assessments.
RELEASED QUESTIONS
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 © 2019 by the New York State Education Department.

Session 1
 Session 1

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.
•  Y
 ou have been provided with mathematics tools (a ruler and a protractor) to use
during the test. It is up to you to decide when each tool will be helpful. You should use
mathematics tools whenever you think they will help you to answer the question.

Session 1 Page 1
 There are three different sections to sit in at a baseball park. The number of people
4
who can sit in each section is described below.

red section seats 200 people

blue section seats 20 fewer people than the red section

green section seats 2 times as many people as the blue section

What is the total number of people who can sit in the baseball park?

A 260

B 380

C 640

D 740

Which figure is an example of a line segment?

5

A C

B D

GO ON
Session 1 Page 3
8 Which fraction model has a shaded area equivalent to ?

A C

B D

The measure of angle EFG shown below is 106 degrees.

9

What is the measure, in degrees, of angle EFH ?

A 34

B 56

C 72

D 140

GO ON
Session 1 Page 5
 What is the value of the expression below?
15

What is the quotient for the expression ?

16

B r

D r

A teacher buys the folders listed below.

17
5 boxes of red folders with 36 folders in each box

6 boxes of blue folders with 32 folders in each box

Which number is closest to the total number of red and blue folders that the
teacher buys?

A 275

B 380

C 440

D 550

GO ON
Page 8 Session 1
 Which two numbers both round to 1,500 when rounded to the nearest hundred?
20

A 1,399 and 1,599

B 1,449 and 1,549

C 1,457 and 1,547

D 1,489 and 1,589

Mr. Fuller wants to put fencing around his rectangular-shaped yard. The width
21
of the yard is 55 feet and the length is 75 feet. How many feet of fencing does
Mr. Fuller need?

A 130

B 260

C 3,905

D 4,125

GO ON
Page 10 Session 1
 The three models below are each shaded to represent a different fraction.
27

What is the sum of the fractions represented by the shaded parts of the models?

What is the greatest number of lines of symmetry that can be drawn on the figure
28
shown below?

A 0

B 1

C 2

D 4

GO ON
Session 1 Page 13
29 What is the measure, in degrees, of an angle that is equivalent to of a circle?

Which comparison statement describes the model below?

30

A 6 is 24 times as many as 4

B 24 is 4 times as many as 6

C 4 times as many as 24 is 6

D 6 times as many as 6 is 24

STOP
Page 14 Session 1
Grade 4
2019
Mathematics Test
Session 1
May 1 – 3, 2019
SESSION 2

RELEASED QUESTIONS
SESSION 2
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 © 2019 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.
•  Y
 ou have been provided with mathematics tools (a ruler and a protractor) to use
during the test. It is up to you to decide when each tool will be helpful. You should use
mathematics tools whenever you think they will help you to answer the question.
•  Be sure to show your work when asked.

Session 2 Page 1
31 In which model could the shaded parts represent ?

A C

B D

A truck is parked next to a tree. The height of the truck is feet. The height of the
32
tree is times the height of the truck. Which equation can be used to find the
height of the tree?

GO ON
Page 2 Session 2
 Which expression can be used to solve the equation below?
33

Which statement about an object turning degrees around in a circle is true?

34

A It turns of the way around in a circle.

B It turns of the way around in a circle.

C It turns of the way around in a circle.

D It turns of the way around in a circle.

Which statement represents the number sentence below?

35

A is times as many as

B is times as many as

C is times as many as

D is times as many as

GO ON
Session 2 Page 3
 The picture below shows line segments of different lengths, in inches.
38

Measure each line segment. Which line plot correctly shows the lengths of the
line segments?

A C

B D

GO ON
Session 2 Page 5
 The shaded part of the model below represents the fraction of a candy bar that
39
Jill ate.

Tom has the same size candy bar. He eats 2 times the amount that Jill ate. What
fraction of the candy bar does Tom eat?

Show your work.

Answer of the candy bar

GO ON
Page 6 Session 2
 Use each digit shown below to create a 5-digit number with the greatest value and
40
a 5-digit number with the least value. Each digit can only be used once in each
number. Then write a number sentence using or to compare the two
numbers you created.

2, 9, 1, 3, 8

Show your work.

GO ON
Session 2 Page 7
 The diagram below shows line AB, line CD, and line EF.
41

Identify two lines on the diagram that appear to be perpendicular to each other.

Explain how you determined your answer.

GO ON
Page 8 Session 2
42 Mick and Jackie buy a large sandwich to share. They each eat of the sandwich.

How much of the sandwich is remaining?

Show your work.

Answer of the sandwich

GO ON
Session 2 Page 9
 How does the value of the digit 3 in the number 63,297 compare to the value of
43
the digit 3 in the number 60,325 ? Be sure to include what you know about place
value in your answer.

Explain your answer.

GO ON
Page 10 Session 2
 Ms. Peterson wants to replace all the floor tiles in her kitchen. The kitchen floor is
44
12 feet long and 7 feet wide. If Ms. Peterson already has 45 one-foot square tiles,
how many more one-foot square tiles does she need to completely cover the
kitchen floor?

Show your work.

Answer more tiles

GO ON
Session 2 Page 11
 The height of Mountain P is 1,086 feet. The height of Mountain Q is 4 times the
45
height of Mountain P. The area model shown below represents one way to find
the height of Mountain Q.

What are the missing values for A, B, and C in the area model?

Show your work.

Answer A ,B , and C

What is the height, in feet, of Mountain Q ?

Show your work.

Answer feet

STOP
Page 12 Session 2
Grade 4
2019
Mathematics Test
Session 2
May 1 – 3, 2019
 THE STATE EDUCATION DEPARTMENT
THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234
2019 Mathematics Tests Map to the Standards
Grade 4 Released Questions on EngageNY

Multiple Choice Questions: Constructed Response Questions:

Question Type Key Points Standard Cluster Percentage of Students Average P-Value
Who Answered Correctly Points (Average Points Earned
(P-Value) Earned ÷ Total Possible Points)
Session 1
0.79
1 Multiple Choice B 1 CCSS.Math.Content.4.NF.B.4c Number and Operations - Fractions
0.84
2 Multiple Choice B 1 CCSS.Math.Content.4.OA.B.4 Operations and Algebraic Thinking
0.68
3 Multiple Choice A 1 CCSS.Math.Content.4.NF.A.2 Number and Operations - Fractions
0.55
4 Multiple Choice D 1 CCSS.Math.Content.4.OA.A.2 Operations and Algebraic Thinking

5 Multiple Choice A 1 CCSS.Math.Content.4.G.A.1 Geometry 0.67

0.6
8 Multiple Choice B 1 CCSS.Math.Content.4.NF.A.1 Number and Operations - Fractions

9 Multiple Choice C 1 CCSS.Math.Content.4.MD.C.7 Measurement and Data 0.74

0.71
15 Multiple Choice D 1 CCSS.Math.Content.4.NBT.B.5 Number and Operations in Base Ten
0.7
16 Multiple Choice D 1 CCSS.Math.Content.4.NBT.B.6 Number and Operations in Base Ten
0.68
17 Multiple Choice B 1 CCSS.Math.Content.4.OA.A.3 Operations and Algebraic Thinking
0.64
20 Multiple Choice C 1 CCSS.Math.Content.4.NBT.A.3 Number and Operations in Base Ten

21 Multiple Choice B 1 CCSS.Math.Content.4.MD.A.3 Measurement and Data 0.48

0.68
27 Multiple Choice D 1 CCSS.Math.Content.4.NF.B.3a Number and Operations - Fractions

28 Multiple Choice C 1 CCSS.Math.Content.4.G.A.3 Geometry 0.59

29 Multiple Choice A 1 CCSS.Math.Content.4.MD.C.5a Measurement and Data 0.41
0.63
30 Multiple Choice B 1 CCSS.Math.Content.4.OA.A.1 Operations and Algebraic Thinking

Session 2
0.83
31 Multiple Choice B 1 CCSS.Math.Content.4.NF.B.4a Number and Operations - Fractions
0.92
32 Multiple Choice B 1 CCSS.Math.Content.4.OA.A.2 Operations and Algebraic Thinking
0.76
33 Multiple Choice D 1 CCSS.Math.Content.4.NBT.B.6 Number and Operations in Base Ten
 34 Multiple Choice A 1 CCSS.Math.Content.4.MD.C.5b Measurement and Data 0.63
0.58
35 Multiple Choice D 1 CCSS.Math.Content.4.OA.A.1 Operations and Algebraic Thinking

36 Multiple Choice A 1 CCSS.Math.Content.4.MD.C.6 Measurement and Data 0.59

0.74
37 Multiple Choice D 1 CCSS.Math.Content.4.NF.A.1 Number and Operations - Fractions

38 Multiple Choice C 1 CCSS.Math.Content.3.MD.B.4 Measurement and Data 0.58

1.46 0.73
39 Constructed Response 2 CCSS.Math.Content.4.NF.B.4b Number and Operations - Fractions
1.04 0.52
40 Constructed Response 2 CCSS.Math.Content.4.NBT.A.2 Number and Operations in Base Ten

41 Constructed Response 2 CCSS.Math.Content.4.G.A.2 Geometry 0.97 0.49

1.22 0.61
42 Constructed Response 2 CCSS.Math.Content.4.NF.B.3d Number and Operations - Fractions
1.04 0.52
43 Constructed Response 2 CCSS.Math.Content.4.NBT.A.1 Number and Operations in Base Ten

44 Constructed Response 2 CCSS.Math.Content.4.MD.A.3 Measurement and Data 1.13 0.57

1.32 0.44
45 Constructed Response 3 CCSS.Math.Content.4.NBT.B.5 Number and Operations in Base Ten
*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.