The Pennsylvania System
of School Assessment
Pennsylvania Department of Education Bureau of Curriculum, Assessment and Instruction—September 2021
2021*
*
This is a revised version of the 2017 Item and Scoring Sampler.
Mathematics
Item and Scoring Sampler
2021*
Grade 4
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
ii
TABLE OF CONTENTS
INFORMATION ABOUT MATHEMATICS ..............................................1
Introduction .................................................................1
General Introduction .......................................................1
Pennsylvania Core Standards (PCS) ...........................................1
What Is Included ..........................................................1
Purpose and Uses .........................................................2
Item Format and Scoring Guidelines ..........................................2
Item Alignment ...........................................................2
Testing Time and Mode of Testing Delivery for the PSSA ...........................2
Mathematics Reporting Categories ...........................................3
General Description of Scoring Guidelines for Mathematics Open-Ended Questions .....4
Item and Scoring Sampler Format ............................................5
Grade 4 Protractor ........................................................6
Grade 4 Formula Sheet .....................................................7
Mathematics Test Directions .................................................8
Multiple-Choice Items ........................................................10
Open-Ended Question ........................................................30
Item-Specific Scoring Guideline .............................................32
Mathematics—Summary Data ..................................................44
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
1
INFORMATION ABOUT MATHEMATICS
INTRODUCTION
General Introduction
The Pennsylvania Department of Education (PDE) provides districts and schools with tools to assist
in delivering focused instructional programs aligned with the Pennsylvania Core Standards (PCS).
These tools include Academic Standards, Assessment Anchor documents, assessment handbooks,
and content-based item and scoring samplers. This Item and Scoring Sampler is a useful tool for
Pennsylvania educators in preparing local instructional programs by providing samples of test item
types and scored student responses. The item sampler is not designed to be used as a pretest, a
curriculum, or other benchmark for operational testing.
This Item and Scoring Sampler is available in Braille format. For more information regarding Braille,
call (717)901-2238.
Pennsylvania Core Standards (PCS)
This sampler contains examples of test items (questions) designed to assess the Pennsylvania
Assessment Anchors and Eligible Content aligned to the PCS. The Mathematics, Reading, and
Writing PSSA transitioned to PCS-based operational Mathematics and English Language Arts
assessments starting with the spring 2015 PSSA administration.
The PCS-aligned Assessment Anchors and Eligible Content documents are posted on this portal:
¾ www.education.pa.gov [Hover over “Data and Reporting,” select “Assessment and
Accountability,” and select “PSSA-PA System of School Assessment.” Then select
“Assessment Anchors/Eligible Content” on the right side of the screen.]
What Is Included
This sampler contains test questions (items) that have been written to be aligned with the
Assessment Anchors, which are aligned to the PCS. The test questions provide an idea of the types
of items that will appear on an operational, PCS-based PSSA. Each sample test question has been
through a rigorous review process to ensure alignment with the Assessment Anchors.
Typically an item and scoring sampler is released every year to provide students and educators
with a resource to assist in delivering focused instructional programs aligned to the PCS. However,
due to the cancellation of standardized testing in 2019–2020, the 2021 Item and Scoring Sampler
is a revised version of the previously released 2017 Item and Scoring Sampler. This revised version
ensures that students and educators have an enhanced item and scoring sampler to use during
instruction and/or preparation of students to take the PSSA Exam.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
2
INFORMATION ABOUT MATHEMATICS
Purpose and Uses
The items in this sampler may be used
1
as examples for creating assessment items at the classroom
level, and they may also be copied and used as part of a local instructional program. Classroom
teachers may find it beneficial to have students respond to the open-ended (OE) item in this sampler.
Educators can then use the sampler as a guide to score the responses either independently or
together with colleagues within a school or district.
Item Format and Scoring Guidelines
The multiple-choice (MC) items have four answer choices. Each correct response to an MC item is
worth one point.
Each OE item is designed to take approximately ten to fifteen minutes to complete. During the
administration of the PSSA, students are given additional time as necessary to complete the test
items. Each OE item in mathematics is scored using an item-specific scoring guideline based on a
0–4-point scale. In this sampler, every item-specific scoring guideline is combined with examples of
student responses that represent each score point to form a practical, item-specific scoring guide.
This sampler also includes the General Description of Scoring Guidelines for Mathematics Open-
Ended Questions that students will have access to during a PSSA mathematics administration.
The general description of scoring guidelines may be distributed to students for use during local
assessments and may also be used by educators when scoring local assessments.
1
Item Alignment
All PSSA items are aligned to statements and specifications included in the Assessment Anchors
and Eligible Content Aligned to the Pennsylvania Core Standards. The mathematics content, process
skills, directives, and action statements included in the PSSA mathematics questions align with the
Assessment Anchor Content Standards. The Eligible Content statements represent the limits of the
content of the mathematics questions.
Testing Time and Mode of Testing Delivery for the PSSA
The PSSA is delivered in traditional paper-and-pencil format as well as in an online format. The
estimated time to respond to a test question is the same for both methods of test delivery. During an
official testing administration, students are given additional time as necessary to complete the test
questions. The following table shows the estimated response time for each item type.
Mathematics Item Type MC OE
Estimated Response Time
(minutes)
2 10 to 15
1
The permission to copy and/or use these materials does not extend to commercial purposes.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
3
INFORMATION ABOUT MATHEMATICS
Mathematics Reporting Categories
The Assessment Anchors are organized into four classifications as listed below.
• A = Numbers and Operations • C = Geometry
• B = Algebraic Concepts • D = Data Analysis and Probability
These four classifications are used throughout the grade levels. In addition to these classifications,
there are five Reporting Categories for each grade level. The first letter of each Reporting Category
represents the classification; the second letter represents the Domain as stated in the Common Core
State Standards for Mathematics. Listed below are the Reporting Categories for Grade 4.
• A-T = Numbers and Operations in Base Ten
• A-F = Numbers and Operations—Fractions
• B-O = Operations and Algebraic Thinking
• C-G = Geometry
• D-M = Measurement and Data
Examples of MC and OE items assessing these categories are included in this sampler.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
4
INFORMATION ABOUT MATHEMATICS
General Description of Scoring Guidelines for Mathematics Open-Ended
Questions
4—The response demonstrates a thorough understanding of the mathematical concepts and
procedures required by the task.
The response provides correct answer(s) with clear and complete mathematical procedures
shown and a correct explanation, as required by the task. Response may contain a minor
“blemish” or omission in work or explanation that does not detract from demonstrating a
thorough understanding.
3—The response demonstrates a general understanding of the mathematical concepts and
procedures required by the task.
The response and explanation (as required by the task) are mostly complete and correct. The
response may have minor errors or omissions that do not detract from demonstrating a general
understanding.
2—The response demonstrates a partial understanding of the mathematical concepts and
procedures required by the task.
The response is somewhat correct with partial understanding of the required mathematical
concepts and/or procedures demonstrated and/or explained. The response may contain some
work that is incomplete or unclear.
1—The response demonstrates a minimal understanding of the mathematical concepts and
procedures required by the task.
0—The response has no correct answer and insufficient evidence to demonstrate any
understanding of the mathematical concepts and procedures required by the task for that
grade level.
Response may show only information copied from the question.
Special Categories within zero reported separately:
BLK (blank).............Is blank, is entirely erased, or gives a written refusal to respond
OT...........................Is off-task
LOE.........................Is in a language other than English
IL.............................Is illegible
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
5
INFORMATION ABOUT MATHEMATICS
Item and Scoring Sampler Format
This sampler includes the test directions and scoring guidelines that appear in the PSSA
Mathematics assessments. Each MC item is followed by a table that includes the alignment, the
answer key, the depth of knowledge (DOK) level, the percentage
2
of students who chose each
answer option, and a brief answer-option analysis or rationale. The OE item is followed by a table
that includes the item alignment, DOK level, and mean student score. Additionally, each of the
included item-specific scoring guidelines is combined with sample student responses representing
each score point to form a practical, item-specific scoring guide. The General Description of Scoring
Guidelines for Mathematics Open-Ended Questions used to develop the item-specific scoring
guidelines should be used if any additional item-specific scoring guidelines are created for use within
local instructional programs.
Example Multiple-Choice Item Information Table
Item Information
Alignment Assigned AAEC
Answer Key Correct Answer
Depth of Knowledge Assigned DOK
p-value A Percentage of students who selected this option
p-value B Percentage of students who selected this option
p-value C Percentage of students who selected this option
p-value D Percentage of students who selected this option
Option Annotations Brief answer-option analysis or rationale
Example Open-Ended Item Information Table
Alignment
Assigned
AAEC
Depth of
Knowledge
Assigned
DOK
Mean Score
2
All p-value percentages listed in the item information tables have been rounded.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
6
INFORMATION ABOUT MATHEMATICS
Grade 4 Protractor
The protractor shown below is not intended to be used to measure. It has been included as a
representation of the protractors that will be provided for students when they take the test. Due to
differences in printers, the protractor in this sampler may not accurately reproduce to scale.
0
180
20
160
30
150
40
140
50
130
60
120
70
110
80
100
100
80
110
70
120
60
130
50
140
40
150
30
160
20
170
10
10
170
180
0
90
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
7
INFORMATION ABOUT MATHEMATICS
Grade 4 Formula Sheet
Formulas and conversions that you may need on this test are found below.
You may refer back to this page at any time during the mathematics test.
2021
Grade 4
1 yard (yd) = 3 feet (ft)
1 foot = 12 inches (in.)
1 pound (lb) = 16 ounces (oz.)
1 kilometer (km) = 1,000 meters (m)
1 meter = 100 centimeters (cm)
1 kilogram (kg) = 1,000 grams (g)
1 liter (L) = 1,000 milliliters (mL)
1 year (yr) = 12 months (mo)
1 year = 52 weeks (wk)
1 year = 365 days
1 week = 7 days
1 day = 24 hours (hr)
1 hour = 60 minutes (min)
1 minute = 60 seconds (sec)
Area = length × width
A =
l × w
Perimeter = length + length + width + width
P =
l + l + w + w
Standard Conversions
Metric Conversions
Time Conversions
Rectangle
w
l
1 gallon (gal) = 4 quarts (qt)
1 quart = 2 pints (pt)
1 pint = 2 cups (c)
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
8
INFORMATION ABOUT MATHEMATICS
Mathematics Test Directions
On the following pages are the mathematics questions.
• You may not use a calculator for question 1. You may use a calculator for all other
questions on this test.
• You may need a protractor for questions on this test.
Directions for Multiple-Choice Questions
Some questions will ask you to select an answer from among four choices.
For the multiple-choice questions:
• First solve the problem on scratch paper.
• Choose the correct answer and record your choice in the answer booklet.
• If none of the choices matches your answer, go back and check your work for
possible errors.
• Only one of the answers provided is the correct response.
Directions for Open-Ended Questions
Some questions will require you to write your response.
For the open-ended questions:
• These questions have more than one part. Be sure to read the directions carefully.
• You cannot receive the highest score for an open-ended question without completing
all tasks in the question. For example, if the question asks you to show your work or
explain your reasoning, be sure to show your work or explain your reasoning in the
space provided.
• If the question does not ask you to show your work or explain your reasoning, you
may use the space provided, but only those parts of your response that the question
specifically asks for will be scored.
• Write your response in the appropriate location within the response box in the
answer booklet. Some answers may require graphing, plotting, labeling, drawing, or
shading. If you use scratch paper, be sure to transfer your final response and any
needed work or reasoning to the answer booklet.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
9
INFORMATION ABOUT MATHEMATICS
THIS PAGE IS
INTENTIONALLY BLANK.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
10
PSSA MATHEMATICS GRADE 4
Question 1 in this sampler is to be solved without the use of a calculator.
MULTIPLE-CHOICE ITEMS
1. Add: 6
2
__
5
+ 3
4
__
5
A. 4
4
__
5
B. 9
1
__
5
C. 10
1
__
5
D. 21
1
__
5
655451655451
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
11
PSSA MATHEMATICS GRADE 4
Item Information
Alignment A-F.2.1.3
Answer Key C
Depth of Knowledge 1
p-value A 4%
p-value B 37%
p-value C 57% (correct answer)
p-value D 2%
Option Annotations
A. multiplies the whole number by the numerator of each fraction and
then adds
12
___
5
+
12
___
5
B. does not add the additional 1 to the whole number when
changing
6
__
5
to
1
__
5
C. Correct: converts each mixed number to an improper fraction by
multiplying the whole part by the denominator (5) and then adding
the product to the numerator to get
3 2
___
5
+
19
___
5
=
5 1
___
5
, and then
converts
5 1
___
5
back to a mixed number by dividing 51 by 5 for the
whole part and leaving the remainder as the new numerator OR
adds the whole parts and the fractional parts separately to get 9 and
6
}
5
, converts the
6
}
5
to 1
1
}
5
, and then adds 9 to 1
1
}
5
D. solves the problem as
62
___
5
+
34
___
5
and then incorrectly converts
96
___
5
to
21
1
__
5
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
12
PSSA MATHEMATICS GRADE 4
A calculator is permitted for use in solving questions 2–17 in this sampler.
2. There are 49,528 people living in a city. What is the value of the 4 in the number of people living
in the city?
A. two times the two in the tens place
B. twenty times the two in the tens place
C. two hundred times the two in the tens place
D. two thousand times the two in the tens place
655469655469
Item Information
Alignment A-T.1.1.1
A-T.1.1.2
Answer Key D
Depth of Knowledge 2
p-value A 15%
p-value B 17%
p-value C 20%
p-value D 48% (correct answer)
Option Annotations
A. does not consider place value
B. uses concept of “10 times the value” but only for 1 place value
C. uses concept of “100 times the value” since there are two digits
between the 2 and the 4
D. Correct: identifies the value of the 4 as 40,000, identifies the value of
the 2 as 20, and recognizes that 40,000 is 2,000 times 20
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
13
PSSA MATHEMATICS GRADE 4
3. The average distance from Earth to the moon is 238,855 miles. What is this distance rounded to
the nearest thousand?
A. 200,000
B. 238,000
C. 238,900
D. 239,000
652724652724
Item Information
Alignment A-T.1.1.4
Answer Key D
Depth of Knowledge 1
p-value A 11%
p-value B 10%
p-value C 12%
p-value D 67% (correct answer)
Option Annotations
A. rounds to the highest place value
B. rounds down (truncates)
C. rounds to the nearest hundred
D. Correct: looks at the digit to the right of the thousands place,
recognizes it as 5 or greater, and rounds the thousands place up
from 8 to 9
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
14
PSSA MATHEMATICS GRADE 4
4. A theater sold $1,048 worth of tickets on Saturday and $424 worth of tickets on Sunday. Each
ticket cost $8. How many tickets were sold altogether on Saturday and Sunday?
A. 53
B. 78
C. 131
D. 184
656381656381
Item Information
Alignment A-T.2.1.3
A-T.2.1.1
Answer Key D
Depth of Knowledge 2
p-value A 7%
p-value B 8%
p-value C 14%
p-value D 71% (correct answer)
Option Annotations
A. divides $424 by $8 (determines the number of tickets sold on
Sunday)
B. subtracts $424 from $1,048 and then divides the difference by $8
C. divides $1,048 by $8 (determines the number of tickets sold on
Saturday)
D. Correct: adds $1,048 to $424 and then divides the sum by $8
OR divides $1,048 by $8, divides $424 by $8, and then adds the
quotients
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
15
PSSA MATHEMATICS GRADE 4
5. Cheryl keeps her marbles in two containers. She has between 177and203marbles in
onecontainer. She has between 157and163marbles in the other container. Which estimate
could be the total number of marbles Cheryl has in bothcontainers?
A. 300
B. 320
C. 360
D. 400
701061701061
Item Information
Alignment A-T.2.1.4
Answer Key C
Depth of Knowledge 2
p-value A 10%
p-value B 20%
p-value C 44% (correct answer)
p-value D 26%
Option Annotations
A. rounds the highest numbers down to the nearest hundred and then
adds 100to200
B. rounds the lowest numbers down to the nearest ten and then adds
170to150
C. Correct: determines the lowest possible total by adding 177 and
157, determines the greatest possible total by adding 203 and
163, and selects a number between these two sums OR selects an
“easy” number between 177 and 203 (e.g., 200), selects an “easy”
number between 157 and 163 (e.g., 160), adds these numbers
together, and selects a value close to this sum
D. rounds both numbers to the nearest hundred and then adds
200to200
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
16
PSSA MATHEMATICS GRADE 4
6. On a vocabulary list,
5
___
10
of the words are nouns and
6
___
12
of the words are verbs. Which pair of
statements correctly compares the fraction of the words on the vocabulary list that are nouns to
the fraction that are verbs?
A. Since 5<6, then
5
___
10
<
6
___
12
.
So, there are fewer nouns than verbs on the vocabulary list.
B. Since
1
___
10
>
1
___
12
, then
5
___
10
>
6
___
12
.
So, there are more nouns than verbs on the vocabulary list.
C. Since
5
___
10
=
7
___
12
and 7>6, then
5
___
10
>
6
___
12
.
So, there are more nouns than verbs on the vocabulary list.
D. Since
5
___
10
=
1
__
2
and
6
___
12
=
1
__
2
, then
5
___
10
=
6
___
12
.
So, there are equal numbers of nouns and verbs on the vocabulary list.
701959701959
Item Information
Alignment A-F.1.1
Answer Key D
Depth of Knowledge 1
p-value A 25%
p-value B 13%
p-value C 8%
p-value D 54% (correct answer)
Option Annotations
A. only compares numerators and does not consider denominators
B. only compares denominators and does not consider numerators
C. incorrectly creates an equivalent fraction by adding 2 to both the
numerator and denominator of
5
___
10
D. Correct: creates equivalent fractions by dividing the numerator
and denominator of
5
___
10
by 5 and by dividing the numerator and
denominator of
6
___
12
by 6
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
17
PSSA MATHEMATICS GRADE 4
7. In September, Mrs. Jones had a full set of pencils. In October, she had
7
___
12
of the full set
remaining. In November, she gave away
2
___
12
of the full set. What fraction of the full set of pencils
did Mrs.Jones have remaining at the end ofNovember?
A.
5
___
24
B.
5
___
12
C.
5
__
6
D.
5
__
0
652758652758
Item Information
Alignment A-F.2.1.1
Answer Key B
Depth of Knowledge 1
p-value A 6%
p-value B 86% (correct answer)
p-value C 5%
p-value D 3%
Option Annotations
A. subtracts the numerators but adds the denominators
B. Correct: subtracts the numerators while leaving the common
denominator
C. subtracts the numerators but “reduces” the 12 to 6 by dividing the
12 by 2
D. subtracts the numerators and the denominators
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
18
PSSA MATHEMATICS GRADE 4
8. Mikalya rode her bike on 4days last week. She rode her bike a total of 2
2
__
3
miles. Which
equation shows how many miles Mikalya could have ridden her bike each day?
A.
1
__
3
+
1
__
3
+ 1 + 1 = 2
2
__
3
B.
2
__
3
+
2
__
3
+ 1 + 1 = 2
2
__
3
C.
1
__
3
+
1
__
3
+
2
__
3
+ 1 = 2
2
__
3
D.
2
__
3
+
2
__
3
+
2
__
3
+ 1 = 2
2
__
3
703508703508
Item Information
Alignment A-F.2.1.2
Answer Key A
Depth of Knowledge 2
p-value A 79% (correct answer)
p-value B 7%
p-value C 7%
p-value D 7%
Option Annotations
A. Correct: uses
1
__
3
+
1
__
3
=
2
__
3
to get
2
__
3
+ 1 + 1 = 2
2
__
3
B. adds only one of the
2
__
3
fractions to 1 + 1
C. uses
1
__
3
+
1
__
3
= 1 to get 1 +
2
__
3
+ 1 = 2
2
__
3
D. uses
2
__
3
+
2
__
3
= 1 to get either
2
__
3
+ 1 + 1 = 2
2
__
3
or 1 +
2
__
3
+ 1 = 2
2
__
3
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
19
PSSA MATHEMATICS GRADE 4
9. In each box of bananas,
2
___
10
of the bananasare already ripe. How many bananasare already ripe
in a box of 30bananas?
A. 2
B. 6
C. 12
D. 20
656705656705
Item Information
Alignment A-F.2.1.7
A-F.2.1.6
Answer Key B
Depth of Knowledge 2
p-value A 9%
p-value B 50% (correct answer)
p-value C 15%
p-value D 26%
Option Annotations
A. uses only the value of the numerator
B. Correct: multiplies the numerator by the number of bananas (2×30)
and then divides the product by the denominator (60 ÷ 10) OR
converts 30 to
30
___
1
, multiplies
2
___
10
by
30
___
1
to get
2 × 30
_______
10 × 1
=
60
___
10
, and then
converts
60
___
10
to 6
C. adds the numerator to the denominator (2 + 10)
D. multiplies the numerator by the denominator (2 × 10) OR subtracts
the denominator from the number of bananas (30 – 10)
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
20
PSSA MATHEMATICS GRADE 4
10. Pauline has two sticks. One is
4
___
10
meter long. The other is
9
___
100
meter long. Which statement
correctly compares the two lengths when written as decimals?
A. 0.04<0.09
B. 0.04<0.90
C. 0.90<0.40
D. 0.09<0.40
671465671465
Item Information
Alignment A-F.3.1.2
A-F.3.1.3
Answer Key D
Depth of Knowledge 1
p-value A 32%
p-value B 17%
p-value C 8%
p-value D 43% (correct answer)
Option Annotations
A. incorrectly converts
4
___
10
B. incorrectly converts both fractions
C. incorrectly converts
9
____
100
and uses the wrong inequality sign for the
given decimals
D. Correct: converts
4
___
10
to 0.4 and includes a 0 placeholder in the
hundredths place to get 0.40, converts
9
____
100
to 0.09, identifies
the comparison symbol as “less than,” and orders the decimals
by comparing place values OR creates an equivalent fraction
of
4
___
10
bymultiplying the numerator and denominator by 10,
converts
40
____
100
to 0.40, converts
9
____
100
to 0.09, identifies the
comparison symbol as “less than,” and orders the decimals by
comparing place values
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
21
PSSA MATHEMATICS GRADE 4
11. Jesse has 4 rows of rocks. There are 6 rocks in each row. Which description shows another way
Jesse can organize all of his rocks?
A. 2 rows with 5 rocks in each row
B. 3 rows with 8 rocks in each row
C. 5 rows with 5 rocks in each row
D. 2 rows with 24 rocks in each row
678033678033
Item Information
Alignment B-O.2.1.1
Answer Key B
Depth of Knowledge 2
p-value A 8%
p-value B 67% (correct answer)
p-value C 11%
p-value D 14%
Option Annotations
A. incorrectly uses 4 + 6 = 10 as the total number of rocks and
matches with 2 × 5 = 10
B. Correct: determines 4 × 6 = 24 and recognizes that 3 × 8 also
equals24
C. incorrectly uses 4 × 6 = 25 as the total number of rocks
D. uses the total number of rocks (24) as the number of rocks in each
row
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
22
PSSA MATHEMATICS GRADE 4
12. The shapes below show a pattern.
shape 1 shape 2 shape 3 shape 4
The pattern continues. How many sides will shape 10 have?
A. 16
B. 22
C. 30
D. 40
702702702702
Item Information
Alignment B-O.3.1
Answer Key B
Depth of Knowledge 2
p-value A 18%
p-value B 60% (correct answer)
p-value C 10%
p-value D 12%
Option Annotations
A. adds 6 to the shape number because 4 + 6 = 10 in shape 4
B. Correct: recognizes that each shape has 2 more sides than the
previous shape, so extends the pattern by adding 2 each time OR
determines the rule to be “multiply the shape number by 2 and then
add 2,” so multiplies 10 by 2 and then adds 2 to 20
C. multiplies 3 by the shape number because 2 × 3 = 6 in shape 2
D. multiplies 4 by the shape number because 1 × 4 = 4 in shape 1
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
23
PSSA MATHEMATICS GRADE 4
13. The shape of Nepal’s flag is shown below.
N
ML
KJ
Which statement about the shape of Nepal’s flag is true?
A. Angle N is a right angle.
B. Angle J is an obtuse angle.
C. Line segment ML and line segment KJ are parallel.
D. Line segment ML and line segment KL are perpendicular.
675118675118
Item Information
Alignment C-G.1.1.1
Answer Key C
Depth of Knowledge 2
p-value A 18%
p-value B 10%
p-value C 52% (correct answer)
p-value D 20%
Option Annotations
A. incorrectly describes the angle (angle is acute, not right)
B. incorrectly describes the angle (angle is acute, not obtuse)
C. Correct: identifies that line segments ML and KJ are both horizontal,
which means they are parallel
D. misidentifies angle KLM as a right angle or does not know that
perpendicular line segments should form a right angle
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
24
PSSA MATHEMATICS GRADE 4
14. The shape of a window in Neal’s house is shown below.
The opposite sides of the window are parallel. No pair of sides is perpendicular. Which term
describes the shape of the window?
A. parallelogram
B. rectangle
C. square
D. trapezoid
702995702995
Item Information
Alignment C-G.1.1.2
Answer Key A
Depth of Knowledge 1
p-value A 63% (correct answer)
p-value B 4%
p-value C 15%
p-value D 18%
Option Annotations
A. Correct: identifies a quadrilateral with opposite sides parallel as a
parallelogram
B. does not associate “perpendicular” with right angles
C. thinks parallel sides mean all sides are equal length; does not
associate “perpendicular” with right angles
D. thinks only one pair of opposite sides are parallel
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
25
PSSA MATHEMATICS GRADE 4
THIS PAGE IS
INTENTIONALLY BLANK.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
26
PSSA MATHEMATICS GRADE 4
15. Erin sorted some shapes based on the number of lines of symmetry each shapehas.
Group A Group B
Which shape belongs in Group B?
A.
B.
C.
D.
701390701390
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
27
PSSA MATHEMATICS GRADE 4
Item Information
Alignment C-G.1.1.3
Answer Key D
Depth of Knowledge 2
p-value A 25%
p-value B 12%
p-value C 7%
p-value D 56% (correct answer)
Option Annotations
A. identifies a shape with only one line of symmetry
B. identifies a shape with only one line of symmetry
C. identifies a shape with no lines of symmetry
D. Correct: recognizes that the shapes in Group B each have 2 lines of
symmetry, so identifies a shape with 2 lines of symmetry
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
28
PSSA MATHEMATICS GRADE 4
16. On the street map shown below, Elm Street and Oak Street meet at a right angle.
Oak Street
Maple Street
Elm Street
50°
Which equation shows how to find the measure of the angle formed by Maple Street and
OakStreet?
A. 90°–50° = 40°
B. 180°–50° = 130°
C. 90° + 50° = 140°
D. 180° + 50° = 230°
656529656529
Item Information
Alignment D-M.3.1.2
Answer Key A
Depth of Knowledge 2
p-value A 63% (correct answer)
p-value B 14%
p-value C 17%
p-value D 6%
Option Annotations
A. Correct: recognizes that a right angle is 90° and uses subtraction
since the unknown angle and the labeled angle form the right angle
B. uses 180° as the sum of the two angles (straight angle) instead of
90° (right angle)
C. uses addition instead of subtraction
D. uses 180° instead of 90° and uses addition instead of subtraction
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
29
PSSA MATHEMATICS GRADE 4
THIS PAGE IS
INTENTIONALLY BLANK.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
30
PSSA MATHEMATICS GRADE 4
OPEN-ENDED QUESTION
17. A construction crew is paving a highway.
One morning, the crew starts work at 10 minutes past 6
a.m. and finishes at
20 minutes to noon.
A. How many hours and minutes does the crew work in the morning?
The crew can extend the length of the highway by 200 feet each hour.
B. What is the length, in feet, of the new part of the highway when the crew
finishes working in the morning? Show or explain all your work.
Go to the next page to finish question 17.
GO ON
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
31
PSSA MATHEMATICS GRADE 4
17. Continued. Please refer to the previous page for task explanation.
After lunch, the crew will extend the length of the highway by another 300 yards.
They will start at 1:30
p.m.
C. At what time will they complete the 300 yards?
After you have checked your work, close your answer booklet
and test booklet so your teacher will know you are finished.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
32
PSSA MATHEMATICS GRADE 4
Item-Specific Scoring Guideline
#17 Item Information
Alignment D-M.1
Depth of
Knowledge
2 Mean Score 0.74
Assessment Anchor this item will be reported under:
M04.D-M.1—Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
Specific Anchor Descriptor addressed by this item:
M04.D-M.1.1—Solve problems involving length, weight (mass), liquid volume, time, area, and
perimeter.
Scoring Guide
Score
In this item, the student . . .
4
Demonstrates a thorough understanding of solving problems involving measurement
and conversion of measurements from a larger unit to a smaller unit by correctly solving
problems and clearly explaining procedures.
3
Demonstrates a general understanding of solving problems involving measurement and
conversion of measurements from a larger unit to a smaller unit by correctly solving
problems and clearly explaining procedures with only minor errors or omissions.
2
Demonstrates a partial understanding of solving problems involving measurement and
conversion of measurements from a larger unit to a smaller unit by correctly performing a
significant portion of the required task.
1
Demonstrates minimal understanding of solving problems involving measurement and
conversion of measurements from a larger unit to a smaller unit.
0
The response has no correct answer and insufficient evidence to demonstrate any
understanding of the mathematical concepts and procedures as required by the task.
Response may show only information copied from the question.
Top-Scoring Student Response and Training Notes
Score
Description
4
Student earns 4 points.
3 Student earns 3 points.
2 Student earns 2 points.
1
Student earns 1 point.
OR
Student demonstrates minimal understanding of solving problems involving
measurement and conversion of measurements from a larger unit to a smaller unit.
0
Response is incorrect or contains some correct work that is irrelevant to the skill or
concept being measured.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
33
PSSA MATHEMATICS GRADE 4
Top-Scoring Response
Part A (1 point):
1 point for correct answer
What?
Why?
5 hours and 30 minutes
Part B (2 points):
1 point for correct answer
1 point for complete support
What?
Why?
1,100 (feet)
[Note: Carry over
any error from
Part A]
Sample Work:
5 hours and 30 minutes = 5.5 hours
5.5 × 200 = 1,100
OR
Sample Explanation:
The crew can cover 200 feet each hour, so they can cover 100 feet in a
half-hour. In 5 hours, they can cover 5 × 200 = 1,000 feet. In the other half-
hour, they can cover 100 feet. So they cover 1,000 + 100 = 1,100 feet in all.
Part C (1 point):
1 point for correct answer
What?
Why?
6:00 (
p.m.)
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
34
PSSA MATHEMATICS GRADE 4
STUDENT RESPONSE
Response Score: 4 points
17. A construction crew is paving a highway.
One morning, the crew starts work at 10 minutes past 6
a.m. and finishes at
20 minutes to noon.
A. How many hours and minutes does the crew work in the morning?
The crew can extend the length of the highway by 200 feet each hour.
B. What is the length, in feet, of the new part of the highway when the crew
finishes working in the morning? Show or explain all your work.
Go to the next page to finish question 17.
GO ON
The student has given the correct answer (5 hours and 30 minutes) by correctly calculating
the time difference between 6:10 a.m. and 11:40 a.m. [1 point]
The student has given the correct answer (1,100 feet) with complete support. The student first multiplies
200 (feet) by 5 (hours) to find that the crew completed 1,000 feet in 5 hours. To find how many feet the crew
completed in 30 minutes, the student took the number of feet completed in one hour and divided by 2
(200÷2=100). The student then added 1,000 and 100 to find the complete length of highway completed
(1,100 feet). [2 points]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
35
PSSA MATHEMATICS GRADE 4
17. Continued. Please refer to the previous page for task explanation.
After lunch, the crew will extend the length of the highway by another 300 yards.
They will start at 1:30
p.m.
C. At what time will they complete the 300 yards?
The student has given the correct answer (6:00). The student most likely converted from yards to feet by
multiplying 300 by 3 to get 900 feet, divided 900 by 200 (the number of feet the crew can complete each hour)
to get 4.5 hours, and then added 4.5 hours to 1:30 p.m. to get a finish time of 6:00. [1 point]
After you have checked your work, close your answer booklet
and test booklet so your teacher will know you are finished.
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
36
PSSA MATHEMATICS GRADE 4
STUDENT RESPONSE
Response Score: 3 points
PART A
Question 17
Page 1 of 2
The student has given the correct answer (5 hrs 30 mins) by correctly calculating the time difference between
6:10 a.m. and 11:40 a.m. [1 point]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
37
PSSA MATHEMATICS GRADE 4
PART B
Question 17
Page 2 of 2
The student has given the correct answer (1100 feet) with complete support. The student first multiplies 5 and
200 = 1000, which is the number of hrs times number of feet per hour to find the total length completed in
5hours. The student then performs mental math to figure out that the crew can do 100 feet in 30 minutes (plus
100 feet because they only worked another 30 mins). The student then added 1,000 and 100 (1000 . . . plus
100) to find the complete length of highway completed (1100 feet). [2 points]
The student has given an incorrect answer (The crew will stop
at 4:10). It is unclear how the student derived this answer since
no support (work or explanation) is required. [0 points]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
38
PSSA MATHEMATICS GRADE 4
STUDENT RESPONSE
Response Score: 2 points
17. A construction crew is paving a highway.
One morning, the crew starts work at 10 minutes past 6
a.m. and finishes at
20 minutes to noon.
A. How many hours and minutes does the crew work in the morning?
The crew can extend the length of the highway by 200 feet each hour.
B. What is the length, in feet, of the new part of the highway when the crew
finishes working in the morning? Show or explain all your work.
Go to the next page to finish question 17.
GO ON
The student has given the correct answer (5 hours and 30 mintes) by correctly calculating
the time difference between 6:10 a.m. and 11:40 a.m. [1 point]
The student has given the correct answer (1100 ft.) but the support is incorrect. While the student starts out
with calculating the length of the highway completed in 5 hours (200[lenght] × 5 [hours] = 1000 [ft.] ), the
second part of the support given is unclear (+
1
__
2
[minutes] ). There is no support showing how the student
calculated the length for the remaining 30 minutes of work. Students must show correct support for both
hours and minutes for credit. The support is both incorrect and written as a run-on equation; either results in
no credit for the support. [1 point]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
39
PSSA MATHEMATICS GRADE 4
17. Continued. Please refer to the previous page for task explanation.
After lunch, the crew will extend the length of the highway by another 300 yards.
They will start at 1:30
p.m.
C. At what time will they complete the 300 yards?
After you have checked your work, close your answer booklet
and test booklet so your teacher will know you are finished.
The student has given an incorrect answer (3:00 p.m.). It is unclear how
the student derived this answer since no support (work or explanation)
is required. The student may not have converted the 300 yards to feet
and then proceeded to divide 300 by 200 to get 1.5 hours and add
1.5hours to 1:30 p.m. [0 points]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
40
PSSA MATHEMATICS GRADE 4
STUDENT RESPONSE
Response Score: 1 point
PART A
Question 17
Page 1 of 2
The student has given an incorrect answer (4 hours and
30mins.) by miscalculating the time difference between
6:10a.m. and 11:40 a.m. [0 points]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
41
PSSA MATHEMATICS GRADE 4
PART B
Question 17
Page 2 of 2
The student has given an incorrect answer (There would be
800 feet of the new part of the highway in length) and incorrect
support (4 hours × 200 feet = 800 feet). The student has only
carried over part of the answer from Part A (4 hours), and
without addressing both the hours and minutes from Part A in
Part B, no credit is given for the support. [0 points]
The student has given the correct answer (6:00 is when they
finish). The student most likely converted from yards to feet
by multiplying 300 by 3 to get 900 feet, divided 900 by 200
(the number of feet the crew can complete each hour) to get
4.5hours, and then added 4.5 hours to 1:30 p.m. to get a
finish time of 6:00. [1 point]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
42
PSSA MATHEMATICS GRADE 4
STUDENT RESPONSE
Response Score: 0 points
17. A construction crew is paving a highway.
One morning, the crew starts work at 10 minutes past 6
a.m. and finishes at
20 minutes to noon.
A. How many hours and minutes does the crew work in the morning?
The crew can extend the length of the highway by 200 feet each hour.
B. What is the length, in feet, of the new part of the highway when the crew
finishes working in the morning? Show or explain all your work.
Go to the next page to finish question 17.
GO ON
The student has given an incorrect answer (They work 6 hours and 10 minutes) by
miscalculating the time difference between 6:10 a.m. and 11:40 a.m. [0 points]
The student has given an incorrect answer (1,200 feet) and incorrect support (200 feet × 6 hours = 1,200 feet).
The student has only carried over part of the answer from Part A (6 hours), and without addressing both the
hours and minutes from Part A in Part B, no credit is given for the support. [0 points]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
43
PSSA MATHEMATICS GRADE 4
17. Continued. Please refer to the previous page for task explanation.
After lunch, the crew will extend the length of the highway by another 300 yards.
They will start at 1:30
p.m.
C. At what time will they complete the 300 yards?
After you have checked your work, close your answer booklet
and test booklet so your teacher will know you are finished.
The student has given an incorrect answer (they will complete 300Yards
at 2:10). It is unclear how the student derived this answer since no
support (work or explanation) is required. The student may not have
converted the 300 yards to feet and then proceeded to divide 200 by
300 to get
2
__
3
hour, convert
2
__
3
hour to 40 minutes, and add 40 minutes to
1:30 p.m. [0 points]
PSSA Grade 4 Mathematics Item and Scoring Sampler—September 2021
44
PSSA MATHEMATICS GRADE 4
MATHEMATICS—SUMMARY DATA
Multiple-Choice
Sample
Number
Alignment Answer Key
Depth of
Knowledge
p-value
A
p-value
B
p-value
C
p-value
D
1 A-F.2.1.3 C 1 4% 37% 57% 2%
2
A-T.1.1.1
A-T.1.1.2
D 2 15% 17% 20% 48%
3 A-T.1.1.4 D 1 11% 10% 12% 67%
4
A-T.2.1.3
A-T.2.1.1
D 2 7% 8% 14% 71%
5 A-T.2.1.4 C 2 10% 20% 44% 26%
6 A-F.1.1 D 1 25% 13% 8% 54%
7 A-F.2.1.1 B 1 6% 86% 5% 3%
8 A-F.2.1.2 A 2 79% 7% 7% 7%
9
A-F.2.1.7
A-F.2.1.6
B 2 9% 50% 15% 26%
10
A-F.3.1.2
A-F.3.1.3
D 1 32% 17% 8% 43%
11 B-O.2.1.1 B 2 8% 67% 11% 14%
12 B-O.3.1 B 2 18% 60% 10% 12%
13 C-G.1.1.1 C 2 18% 10% 52% 20%
14 C-G.1.1.2 A 1 63% 4%
15% 18%
15 C-G.1.1.3 D 2 25% 12% 7% 56%
16 D-M.3.1.2 A 2 63% 14% 17% 6%
Open-Ended
Sample
Number
Alignment Points
Depth of
Knowledge
Mean Score
17 D-M.1 4 2 0.74
PSSA MATHEMATICS GRADE 4
PSSA Grade 4 Mathematics
Item and Scoring Sampler
Copyright © 2021 by the Pennsylvania Department of Education. The materials contained in
this publication may be duplicated by Pennsylvania educators for local classroom use. This
permission does not extend to the duplication of materials for commercial use.