Ohio’s State Tests
PRACTICE TEST ANSWER KEY &
SCORING GUIDELINES
GRADE 4
MATHEMATICS
Table of Contents
Questions 1 – 22: Content Summary and Answer Key ............................................... iii
Question 1: Question and Scoring Guidelines .............................................................. 1
Question 1: Sample Responses ....................................................................................... 5
Question 2: Question and Scoring Guidelines ............................................................ 11
Question 2: Sample Response ...................................................................................... 13
Question 3: Question and Scoring Guidelines ........................................................... 15
Question 3: Sample Responses ..................................................................................... 19
Question 4: Question and Scoring Guidelines ............................................................ 27
Question 4: Sample Responses ..................................................................................... 31
Question 5: Question and Scoring Guidelines ............................................................ 37
Question 5: Sample Responses ..................................................................................... 41
Question 6: Question and Scoring Guidelines ........................................................... 45
Question 6: Sample Responses ..................................................................................... 49
Question 7: Question and Scoring Guidelines ............................................................ 55
Question 7: Sample Responses ..................................................................................... 59
Question 8: Question and Scoring Guidelines ............................................................ 65
Question 8: Sample Response ...................................................................................... 67
Question 9: Question and Scoring Guidelines ............................................................ 69
Question 9: Sample Responses ..................................................................................... 73
Question 10: Question and Scoring Guidelines .......................................................... 87
Question 10: Sample Responses ................................................................................... 91
Question 11: Question and Scoring Guidelines ........................................................ 101
Question 11: Sample Responses ................................................................................. 105
Question 12: Question and Scoring Guidelines ........................................................ 111
Question 12: Sample Responses ................................................................................. 115
Question 13: Question and Scoring Guidelines ........................................................ 123
Question 13: Sample Responses ................................................................................. 127
Question 14: Question and Scoring Guidelines ........................................................ 135
Question 14: Sample Responses ................................................................................. 139
i
Question 15: Question and Scoring Guidelines ........................................................ 145
Question 15: Sample Response .................................................................................. 147
Question 16: Question and Scoring Guidelines ........................................................ 149
Question 16: Sample Responses ................................................................................. 153
Question 17: Question and Scoring Guidelines ........................................................ 159
Question 17: Sample Responses ................................................................................. 161
Question 18: Question and Scoring Guidelines ........................................................ 167
Question 18: Sample Response .................................................................................. 169
Question 19: Question and Scoring Guidelines ........................................................ 171
Question 19: Sample Responses ................................................................................. 175
Question 20: Question and Scoring Guidelines ........................................................ 181
Question 20: Sample Responses ................................................................................. 185
Question 21: Question and Scoring Guidelines ........................................................ 189
Question 21: Sample Responses ................................................................................. 191
Question 22: Question and Scoring Guidelines ........................................................ 197
Question 22: Sample Responses ................................................................................. 201
ii
Grade 4 Math
Practice Test
Content Summary and Answer Key
Question
No.
1
2
3
4
Item
Type
Content
Cluster
Equation
Item
Use the four
operations with
whole numbers
to solve
problems.
Multiple
Choice
Draw and
identify lines
and angles, and
classify shapes
by properties of
their lines and
angles.
Table
Item
Equation
Item
Content
Standard
Multiply or divide to solve word
problems involving multiplicative
comparison, e.g., by using
drawings and equations with a
symbol for the unknown number
to represent the problem,
distinguishing multiplicative
comparison from additive
comparison. (4.OA.2)
Answer
Key
Points
---
1 point
Draw points, lines, line segments,
rays, angles (right, acute,
obtuse), and perpendicular and
parallel lines. Identify these in
two-dimensional figures. (4.G.1)
B
1 point
Solve problems
involving
measurement
and
conversion of
measurements
from a larger
unit to a
smaller unit.
Know relative sizes of
measurement units within one
system of units including km, m,
cm; kg, g; lb, oz.; l, ml; hr, min,
sec. Within a single system of
measurement, express
measurements in a larger unit in
terms of smaller unit. Record
measurement equivalents in a
two-column table. For example,
know that 1 ft is 12 times as long
as 1 in. Express the length of a 4 ft
snake as 48 in. Generate a
conversion table for feet and
inches listing the number pairs
(1, 12), (2, 24), (3, 36), .... (4.MD.1)
---
2 points
Generalize
place value
understanding
for multi-digit
whole numbers.
Recognize that in a multi-digit
whole number, a digit in one
place represents ten times what
it represents in the place to its
right. For example, recognize
that 700 ÷ 70 = 10 by applying
concepts of place value and
division. (4.NBT.1)
---
iii
1 point
Grade 4 Math
Practice Test
Content Summary and Answer Key
Question
No.
5
Item
Type
Graphic
Response
Content
Cluster
Draw and
identify lines
and angles,
and classify
shapes by
properties of
their lines and
angles.
Content
Standard
Answer
Key
Points
Recognize a line of symmetry for
a two-dimensional figure as a line
across the figure such that the
figure can be folded along the
line into matching parts. Identify
line-symmetric figures and draw
lines of symmetry. (4.G.3)
---
1 point
---
1 point
---
1 point
B, D, F
1 point
Explain why a fraction
𝑎
𝑏
is
(𝑛  𝑎)
equivalent to a fraction (𝑛  𝑏) by
6
7
8
Graphic
Response
Extend
understanding
of fraction
equivalence
and ordering.
Equation
Item
Use the four
operations with
whole numbers
to solve
problems.
MultiSelect
Item
Build fractions
from unit
fractions by
applying and
extending
previous
understandings
of operations
on whole
numbers.
using visual fraction models, with
attention to how the number and
size of the parts differ even
though the two fractions
themselves are the same size. Use
this principle to recognize and
generate equivalent fractions.
(4.NF.1)
Interpret a multiplication equation
as a comparison, e.g., interpret
35 = 5 × 7 as a statement that 35 is
5 times as many as 7 and 7 times
as many as 5. Represent verbal
statements of multiplicative
comparisons as multiplication
equations. (4.OA.1)
Apply and extend previous
understandings of multiplication
to multiply a fraction by a whole
number.
𝑎
b. Understand a multiple of 𝑏 as a
1
multiple of 𝑏, and use this
understanding to multiply a
fraction by a whole number. For
example, use a visual fraction
2
1
model to express 3 × (5) as 6 × (5),
6
recognizing this product as 5. (In
𝑎
𝑏
general, n × ( ) =
iv
(𝑛  𝑎)
.)
𝑏
(4.NF.4b)
Grade 4 Math
Practice Test
Content Summary and Answer Key
Question
No.
9
10
11
Item
Type
Content
Cluster
Content
Standard
Answer
Key
Points
Equation
Item
Geometric
measurement:
understand
concepts of
angle and
measure
angles.
Recognize angle measure as
additive. When an angle is
decomposed into non-overlapping
parts, the angle measure of the
whole is the sum of the angle
measures of the parts. Solve
addition and subtraction problems
to find unknown angles on a
diagram in real world and
mathematical problems, e.g., by
using an equation with a symbol for
the unknown angle measure.
(4.MD.7)
---
2 points
Equation
Item
Use place
value
understanding
and properties
of operations
to perform
multi-digit
arithmetic.
Multiply a whole number of up to
four digits by a one-digit whole
number, and multiply two two-digit
numbers, using strategies based on
place value and the properties of
operations. Illustrate and explain
the calculation by using equations,
rectangular arrays, and/or area
models. (4.NBT.5)
---
1 point
Equation
Item
Build fractions
from unit
fractions by
applying and
extending
previous
understandings
of operations
on whole
numbers.
---
1 point
𝑎
Understand a fraction 𝑏 with a > 1
1
as a sum of fractions 𝑏.
c. Add and subtract mixed
numbers with like denominators,
e.g., by replacing each mixed
number with an equivalent fraction,
and/or by using properties of
operations and the relationship
between addition and subtraction.
(4.NF.3c)
v
Grade 4 Math
Practice Test
Content Summary and Answer Key
Question
No.
12
13
14
Item
Type
Short
Response
Content
Cluster
Use the four
operations with
whole numbers
to solve
problems.
Graphic
Response
Extend
understanding
of fraction
equivalence
and ordering.
Graphic
Response
Draw and
identify lines and
angles, and
classify shapes
by properties of
their lines and
angles.
Content
Standard
Answer
Key
Points
Solve multistep word problems
posed with whole numbers and
having whole-number answers
using the four operations,
including problems in which
remainders must be interpreted.
Represent these problems using
equations with a letter standing
for the unknown quantity. Assess
the reasonableness of answers
using mental computation and
estimation strategies including
rounding. (4.OA.3)
---
1 point
---
2 points
---
1 point
Compare two fractions with
different numerators and
different denominators, e.g., by
creating common denominators
or numerators, or by comparing
to a benchmark fraction such as
1
. Recognize that comparisons
2
are valid only when the two
fractions refer to the same
whole. Record the results of
comparisons with symbols >, =, or
<, and justify the conclusions,
e.g., by using a visual fraction
model. (4.NF.2)
Recognize a line of symmetry for
a two-dimensional figure as a
line across the figure such that
the figure can be folded along
the line into matching parts.
Identify line-symmetric figures
and draw lines of symmetry.
(4.G.3)
vi
Grade 4 Math
Practice Test
Content Summary and Answer Key
Question
No.
Item
Type
15
Multiple
Choice
Generate and
analyze
patterns.
Equation
Item
Understand
decimal
notation for
fractions, and
compare
decimal
fractions.
16
17
18
Content
Cluster
Equation
Item
Solve problems
involving
measurement
and
conversion of
measurements
from a larger
unit to a
smaller unit.
MultiSelect
Item
Draw and
identify lines
and angles, and
classify shapes
by properties of
their lines and
angles.
Content
Standard
Generate a number or shape
pattern that follows a given rule.
Identify apparent features of the
pattern that were not explicit in the
rule itself. For example, given the
rule “Add 3” and the starting
number 1, generate terms in the
resulting sequence and observe
that the terms appear to alternate
between odd and even numbers.
Explain informally why the numbers
will continue to alternate in this
way. (4.OA.5)
Express a fraction with denominator
10 as an equivalent fraction with
denominator 100, and use this
technique to add two fractions with
respective denominators 10 and
3
30
100. For example, express as
,
and add
3
4
34
+
=
.
10 100 100
10
Points
C
1 point
---
1 point
---
1 point
C, F
1 point
100
(4.NF.5)
Use the four operations to solve
word problems involving distances,
intervals of time, liquid volumes,
masses of objects, and money,
including problems involving simple
fractions or decimals, and problems
that require expressing
measurements given in a larger unit
in terms of a smaller unit. Represent
measurement quantities using
diagrams such as number line
diagrams that feature a
measurement scale. (4.MD.2)
Classify two-dimensional figures
based on the presence or absence
of parallel or perpendicular lines, or
the presence or absence of angles
of a specified size. Recognize right
triangles as a category, and
identify right triangles. (4.G.2)
vii
Answer
Key
Grade 4 Math
Practice Test
Content Summary and Answer Key
Question
No.
19
20
21
22
Item
Type
Content
Cluster
Content
Standard
Answer
Key
Points
Equation
Item
Understand
decimal notation
for fractions, and
compare
decimal
fractions.
Compare two decimals to
hundredths by reasoning about
their size. Recognize that
comparisons are valid only when
the two decimals refer to the
same whole. Record the results of
comparisons with the symbols >,
=, or <, and justify the conclusions,
e.g., by using a visual model.
(4.NF.7)
---
1 point
Graphic
Response
Geometric
measurement:
understand
concepts of
angle and
measure angles.
Measure angles in whole-number
degrees using a protractor.
Sketch angles of specified
measure. (4.MD.6)
---
1 point
Equation
Item
Generalize place
value
understanding
for multi-digit
whole numbers.
Use place value understanding to
round multi-digit whole numbers
to any place. (4.NBT.3)
---
1 point
Graphic
Response
Draw and
identify lines and
angles, and
classify shapes
by properties of
their lines and
angles.
Draw points, lines, line segments,
rays, angles (right, acute, obtuse),
and perpendicular and
parallel lines. Identify these in
two-dimensional figures. (4.G.1)
---
1 point
viii
Grade 4
Math
Practice Test
Question 1
Question and Scoring Guidelines
1
Question 1
15664
20512
Points Possible: 1
Content Cluster: Use the four operations with whole numbers to solve
problems.
Content Standard: Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and equations
with a symbol for the unknown number to represent the problem,
distinguishing multiplicative comparison from additive comparison.
(4.OA.2)
2
Scoring Guidelines
Exemplar Response

45
Other Correct Responses

Any equivalent value
For this item, a full-credit response includes:

The correct value (1 point).
3
Grade 4
Math
Practice Test
Question 1
Sample Responses
5
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the number of stickers Kiara has.
 The student may have used repeated addition or
multiplication.
15 + 15 + 15 = 45
3 × 15 = 45
6
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the number of stickers Kiara has.
 The student may have used repeated addition or
multiplication.
15.0 + 15.0 + 15.0 = 45.0
3 × 15.0 = 45.0
While decimals are introduced in the standards in grade 4, students
are not expected to be able to perform calculations using the four
operations until grade 5. A student can earn credit in grade 4 by
identifying an equivalent value to a correct response.
7
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the number of stickers Kiara has.
 The student may have misread the number of stickers
Jayla has as 5 and used the incorrect number when
he/she multiplied.
3 × 5 = 15
8
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the number of stickers Kiara has.
 The student may have thought Jayla’s 15 stickers were
3 times the number of stickers Kiara has and incorrectly
set up the multiplication problem.
3 ×  = 15
15 ÷ 3 = 
15 ÷ 3 = 5
9
Grade 4
Math
Practice Test
Question 2
Question and Scoring Guidelines
11
Question 2
16301
Points Possible: 1
Content Cluster: Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Content Standard: Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel lines. Identify
these in two-dimensional figures. (4.G.1)
12
Scoring Guidelines
Rationale for Option A: This is incorrect. The student may have thought that a
line segment is an exact location in space.
Rationale for Option B: Key – The student identified that a line segment is part of
a line with two endpoints.
Rationale for Option C: This is incorrect. The student may have thought that a
line segment is a line with one endpoint that continues indefinitely in the other
direction.
Rationale for Option D: This is incorrect. The student may have thought that a
line segment is a straight path of points that has no endpoints.
Sample Response: 1 point
13
Grade 4
Math
Practice Test
Question 3
Question and Scoring Guidelines
15
Question 3
15666
20512
Points Possible: 2
Content Cluster: Solve problems involving measurement and
conversion of measurements from a larger unit to a smaller unit.
Content Standard: Know relative sizes of measurement units within
one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min,
sec. Within a single system of measurement, express measurements
in a larger unit in terms of smaller unit. Record measurement
equivalents in a two-column table. For example, know that 1 ft is 12
times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number
pairs (1, 12), (2, 24), (3, 36), .... (4.MD.1)
16
Scoring Guidelines
Exemplar Response
Other Correct Responses

Any equivalent value
For this item, a full-credit response includes:

The correct number of cups of orange juice (1 point);
AND

The correct number of cups of pineapple juice (1 point).
17
Grade 4
Math
Practice Test
Question 3
Sample Responses
19
Sample Response: 2 points
Notes on Scoring
This response earns full credit (2 points) because the student correctly identified the
number of cups of orange juice and pineapple juice Sara needs for the picnic.
 The student may have used a two-column table to convert from larger to
smaller units of measurement.
Orange Juice
Pineapple Juice
Pineapple Juice
1 pint = 2 cups
1 quart = 2 pints
1 pint = 2 cups
2 pints = 4 cups
2 quarts = 4 pints
2 pints = 4 cups
3 pints = 6 cups
3 pints = 6 cups
4 pints = 8 cups
5 pints = 10 cups
4 pints = 8 cups
6 pints = 12 cups
20
Sample Response: 2 points
Notes on Scoring
This response earns full credit (2 points) because the student correctly identified the
number of cups of orange juice and pineapple juice Sara needs for the picnic.
 The student may have used a two-column table to convert from larger to
smaller units of measurement.
Orange Juice
Pineapple Juice
Pineapple Juice
1.0 pint = 2.0 cups
1.0 quart = 2.0 pints
1.0 pint = 2.0 cups
2.0 pints = 4.0 cups
2.0 quarts = 4.0 pints
2.0 pints = 4.0 cups
3.0 pints = 6.0 cups
3.0 pints = 6.0 cups
4.0 pints = 8.0 cups
5.0 pints = 10.0 cups
4.0 pints = 8.0 cups
6.0 pints = 12.0 cups
While decimals are introduced in the standards in grade 4, students are not expected to
be able to perform calculations using the four operations until grade 5. A student can earn
credit in grade 4 by identifying an equivalent value to a correct response.
21
Sample Response: 1 point
Notes on Scoring
This response earns partial credit (1 point) because the student correctly identified
the number of cups of pineapple juice but did not correctly identify the number of
cups of orange juice Sara needs for the picnic.
 The student may have used a two-column table to convert between units of
measurement but incorrectly converted from larger to smaller units of orange
juice.
Orange Juice
Pineapple Juice
Pineapple Juice
1 cup ≠ 2 pints
1 quart = 2 pints
1 pint = 2 cups
2 cups ≠ 4 pints
2 quarts = 4 pints
2 pints = 4 cups
3 cups ≠ 6 pints
3 pints = 6 cups
3 cups ≠ 6 pints
4 pints = 8 cups
22
Sample Response: 1 point
Notes on Scoring
This response earns partial credit (1 point) because the student correctly identified the
number of cups of orange juice but did not correctly identify the number of cups of
pineapple juice Sara needs for the picnic.
 The student may have used a two-column table to convert between units of
measurement but incorrectly converted from larger to smaller units of
pineapple juice.
Orange Juice
Pineapple Juice
1 pint = 2 cups
1 quart = 2 pints
2 pints = 4 cups
2 quarts = 4 pints
3 pints = 6 cups
4 pints = 8 cups
2 quarts ≠ 4 cups
5 pints = 10 cups
6 pints = 12 cups
23
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly identify
the number of cups of orange juice and pineapple juice Sara needs for the picnic.
 The student may have used a two-column table to convert between units of
measurement but incorrectly converted from larger to smaller units.
Orange Juice
Pineapple Juice
1 pint ≠ 0.25 cup
1 quart = 0.25 gallons
2 pints ≠ 0.5 cup
2 quarts = 0.5 gallons
3 pints ≠ 0.75 cup
3 quarts = 0.75 gallons
4 pints ≠ 1.0 cup
4 quarts = 1.0 gallon
5 pints ≠ 1.25 cups
6 pints ≠ 1.5 cups
2 quarts ≠ 0.5 cups
6 pints ≠ 1.5 cups
24
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly identify
the number of cups of orange juice and pineapple juice Sara needs for the picnic.
 The student may have used a two-column table to convert between units of
measurement but incorrectly converted from larger to smaller units.
Orange Juice
Pineapple Juice
1 gallon = 4 quarts
1 quart = 2 pints
2 gallons = 8 quarts
2 quarts = 4 pints
3 gallons = 12 quarts
4 gallons = 16 quarts
2 quarts ≠ 4 cups
5 gallons = 20 quarts
6 gallons = 24 quarts
6 pints ≠ 24 cups
25
Grade 4
Math
Practice Test
Question 4
Question and Scoring Guidelines
27
Question 4
16304
20512
Points Possible: 1
Content Cluster: Generalize place value understanding for multi-digit
whole numbers.
Content Standard: Recognize that in a multi-digit whole number, a
digit in one place represents ten times what it represents in the place
to its right. For example, recognize that 700 ÷ 70 = 10 by applying
concepts of place value and division. (4.NBT.1)
28
Scoring Guidelines
Exemplar Response

3,695
Other Correct Responses

Any whole number between 1,000 and 10,000 where one digit is 6, and
the 6 is in the hundreds place
For this item, a full-credit response includes:

A correct value (1 point).
29
Grade 4
Math
Practice Test
Question 4
Sample Responses
31
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified a number Camilla could have written.
32
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified a number Camilla could have written.
33
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify a number Camilla could have
written.
 The student may have thought that there could be
more than one 6 in the number.
34
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify a number Camilla could have
written.
 The student may have thought that the 6 in Abby’s
number was supposed to be 10 times the value of
the 6 in Camilla’s number.
35
Grade 4
Math
Practice Test
Question 5
Question and Scoring Guidelines
37
Question 5
16299
20512
Points Possible: 1
Content Cluster: Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Content Standard: Recognize a line of symmetry for a
two-dimensional figure as a line across the figure such that
the figure can be folded along the line into matching parts.
Identify line-symmetric figures and draw lines of symmetry. (4.G.3)
38
Scoring Guidelines
Exemplar Response
Other Correct Responses

Any two lines of symmetry correctly drawn on the figure
For this item, a full-credit response includes:

Two correct lines of symmetry (1 point).
39
Grade 4
Math
Practice Test
Question 5
Sample Responses
41
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student correctly identified two
lines of symmetry on the figure.
 The student may have recognized the figure as a rotated octagon. The
student may have found the lines of symmetry in an octagon without any
rotation and then transferred the lines of symmetry onto the octagon with a
rotation.
Octagon Without a Rotation
Octagon With a Rotation
42
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
only identified one correct line of symmetry on the figure. The
student did not identify a second line of symmetry.
43
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify two lines of symmetry on the figure.
 The student may have thought that any two lines
drawn on the figure would be symmetrical.
44
Grade 4
Math
Practice Test
Question 6
Question and Scoring Guidelines
45
Question 6
16294
20512
Points Possible: 1
Content Cluster: Extend understanding of fraction equivalence and
ordering.
𝑎
Content Standard: Explain why a fraction 𝑏 is equivalent to a fraction
(𝑛  𝑎)
(𝑛  𝑏)
by using visual fraction models, with attention to how the
number and size of the parts differ even though the two fractions
themselves are the same size. Use this principle to recognize and
generate equivalent fractions. (4.NF.1)
46
Scoring Guidelines
Exemplar Response
Other Correct Responses

Any equivalent model
For this item, a full-credit response includes:

A correct model (1 point).
47
Grade 4
Math
Practice Test
Question 6
Sample Responses
49
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student correctly shaded a
10
fraction model that represents a fraction equivalent to 12 .

The student may have divided
10
12

10 ÷ 2
5
10
12
2
2
by to find an equivalent fraction to
10
12
= 12 ÷ 2 = 6
The student may have created equivalent fraction models.
10
∶
12
5
6
:
While the example shows the lower right tile unshaded, the student could have
shaded any 5 out of the 6 tiles.
50
.
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student correctly shaded a
10
fraction model that represents a fraction equivalent to 12 .

10
10
12

2
10
The student may have divided 12 by 2 to find an equivalent fraction to 12 .
10 ÷ 2
5
= 12 ÷ 2 = 6
The student may have created equivalent fraction models.
10
12
:
5
6
:
While the example shows the bottom middle tile unshaded, the student could have
shaded any 5 out of the 6 tiles.
51
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly shade the fraction model to represent a
10
fraction equivalent to 12 .

The student may have thought that the fraction model
12
shown represented a portion of a whole model of 12
6
instead of a whole model of 6 . The student may have
6
labeled all 6 squares or 12 of an incomplete model
because he/she thought there was another part of the
model not being shown.
52
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly shade the fraction model to represent a
10
fraction equivalent to 12 .

The student may have thought that the fraction model
5
shown was supposed to represent 6 unshaded.
53
Grade 4
Math
Practice Test
Question 7
Question and Scoring Guidelines
55
Question 7
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Points Possible: 1
Content Cluster: Use the four operations with whole numbers to solve
problems.
Content Standard: Interpret a multiplication equation as a
comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times
as many as 7 and 7 times as many as 5. Represent verbal statements
of multiplicative comparisons as multiplication equations. (4.OA.1)
56
Scoring Guidelines
Exemplar Response

1160 = 8 × d
Other Correct Responses

Any equivalent multiplication equation
For this item, a full-credit response includes:

A correct equation (1 point).
57
Grade 4
Math
Practice Test
Question 7
Sample Responses
59
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
created a correct multiplication equation that can be
used to find out how many donations the school collected
last year.
60
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
created a correct multiplication equation that can be
used to find out how many donations the school collected
last year.
61
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not provide a multiplication equation that can be used to
find out how many donations the school collected last year.
 The student may have thought that he/she was
supposed to solve for the unknown value instead of to
provide the multiplication equation.
8 ×  = 1160
1160 ÷ 8 = 
1160 ÷ 8 = 145
62
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not provide a multiplication equation that can be used to
find out how many donations the school collected last year.
 The student may have thought that he/she was
supposed to set up a division equation to find out how
many donations the school collected last year.
63
Grade 4
Math
Practice Test
Question 8
Question and Scoring Guidelines
65
Question 8
15665
Points Possible: 1
Content Cluster: Build fractions from unit fractions by applying and
extending previous understandings of operations on whole numbers.
Content Standard: Apply and extend previous understandings of
multiplication to multiply a fraction by a whole number.
𝑎
1
b. Understand a multiple of 𝑏 as a multiple of 𝑏, and use this
understanding to multiply a fraction by a whole number. For
2
1
example, use a visual fraction model to express 3 × (5) as 6 × (5),
6
𝑎
recognizing this product as 5. (In general, n × (𝑏 ) =
66
(𝑛  𝑎)
.)
𝑏
(4.NF.4b)
Scoring Guidelines
Rationale for First Option: This is incorrect. The student may have thought that both
the numerator and the denominator should be multiplied by the whole number.
Rationale for Second Option: Key – The student correctly identified an expression
with the given product.
Rationale for Third Option: This is incorrect. The student may have thought that the
expression in the numerator represented addition instead of multiplication.
Rationale for Fourth Option: Key – The student correctly identified an expression with
the given product.
Rationale for Fifth Option: This is incorrect. The student may have thought that both
the numerator and the denominator should be multiplied by the whole number.
Rationale for Sixth Option: Key – The student correctly identified an expression with
the given product.
Sample Response: 1 point
67
Grade 4
Math
Practice Test
Question 9
Question and Scoring Guidelines
69
Question 9
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Points Possible: 2
Content Cluster: Geometric measurement: understand concepts of
angle and measure angles.
Content Standard: Recognize angle measure as additive. When an
angle is decomposed into non-overlapping parts, the angle
measure of the whole is the sum of the angle measures of the parts.
Solve addition and subtraction problems to find unknown angles on
a diagram in real world and mathematical problems, e.g., by using
an equation with a symbol for the unknown angle measure. (4.MD.7)
70
Scoring Guidelines
Exemplar Response


A. 155 degrees
B. 25 degrees
Other Correct Responses


Any equivalent values
Partial credit is given for a correct Part B based on an incorrect Part A, i.e.
Part B = 180 – (Part A)
For this item, a full-credit response includes:

One correct value (1 point);
AND

Another correct value (1 point).
71
Grade 4
Math
Practice Test
Question 9
Sample Responses
73
Sample Response: 2 points
74
Notes on Scoring
This response earns full credit (2 points) because the student correctly identified the
sum of ∠QRT and ∠URS and the measure of ∠TRU.
 The student may have found the sum of ∠QRT and ∠URS using addition.
∠QRT = 20° and ∠URS = 135°
20° + 135° = 155°
 The student may have used mathematical reasoning about lines to figure out
the measure of ∠QRS and then set up a multi-step equation to find the
measure of ∠TRU.
A line is 180°. The first sentence states, ∠QRS is a line; therefore, the measure of
∠QRS = 180°.
∠QRS = 180° ; ∠QRT = 20° ; ∠URS = 135° ; ∠TRU = 
20° +  + 135° = 180°
20° + 135° +  = 180°
e 155° +  = 180°
 = 180° – 155°
 = 25°
Measure of ∠TRU = 25°
75
Sample Response: 1 point
76
Notes on Scoring
This response earns partial credit (1 point) because the student correctly identified
the sum of ∠QRT and ∠URS but not the measure of ∠TRU.
 The student may have found the sum of ∠QRT and ∠URS using addition.
∠QRT = 20° and ∠URS = 135°
20° + 135° = 155°
 The student may have used incorrect reasoning to determine that the
measure of ∠QRS was equal to the measure of ∠TRU.
A line is 180°. The first sentence states, ∠QRS is a line; therefore, the measure of
∠QRS = 180°.
∠QRS ≠ ∠TRU
180° = 
180° = 180°
Measure of ∠TRU ≠ 180°
77
Sample Response: 1 point
78
Notes on Scoring
This response earns partial credit (1 point) because the student did not correctly identify
the sum of ∠QRT and ∠URS but correctly identified the measure of ∠TRU.
 The student may have used mathematical reasoning about lines to figure out the
measure of ∠QRS but used incorrect reasoning to determine that the measure of
∠QRS was equal to the sum of ∠QRT and ∠URS.
A line is 180°. The first sentence states, ∠QRS is a line; therefore, the measure of
∠QRS = 180°.
∠QRS ≠ ∠QRT + ∠URS
180° = 
180° = 180°
∠QRT + ∠URS ≠ 180°
 The student may have used mathematical reasoning about lines to figure out the
measure of ∠QRS and then set up a multi-step equation to find the measure of
∠TRU.
∠QRS = 180° ; ∠QRT = 20° ; ∠URS = 135° ; ∠TRU = 
20° +  + 135° = 180°
20° + 135° +  = 180°
155° +  = 180°
 = 180° – 155°
 = 25°
Measure of ∠TRU = 25°
79
Sample Response: 1 point
80
Notes on Scoring
This response earns partial credit (1 point) because the student did not correctly identify
the sum of ∠QRT and ∠URS but correctly identified the measure of ∠TRU based on the
error carried through from Part A.
 The student may have found the incorrect sum of ∠QRT and ∠URS using
addition.
∠QRT ≠ 10° and ∠URS = 135°
10° + 135° = 145°
∠𝐐𝐑𝐓 + ∠𝐔𝐑𝐒 ≠145°
 The student may have used mathematical reasoning about lines to figure out the
measure of ∠QRS and then set up a multi-step equation to find the measure of
∠TRU, using a value based on an error carried through from Part A.
∠QRS = 180° ; ∠QRT ≠ 10° ; ∠URS = 135° ; ∠TRU = 
10° +  + 135° = 180°
10° + 135° +  = 180°
145° +  = 180°
 = 180° – 145°
 = 35°
Measure of ∠TRU = 35°
81
Sample Response: 0 points
82
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly identify
the sum of ∠QRT and ∠URS and did not correctly identify the measure of ∠TRU.
 The student may have used mathematical reasoning about lines to figure out
the measure of ∠QRS but used incorrect reasoning to determine that the
measure of ∠QRS was equal to the sum of ∠QRT and ∠URS.
A line is 180°. The first sentence states, ∠QRS is a line; therefore, the measure of
∠QRS = 180°.
∠QRS = 180° and ∠QRT + ∠URS = 
∠QRS = ∠QRT + ∠URS
180° = 
180° = 180°
Sum of ∠QRT + ∠URS = 180°
 The student may have used addition to find the sum of ∠QRT and ∠URS and
incorrectly identified the sum of ∠QRT and ∠URS as equal to the measure of
∠TRU.
∠QRT = 20° ; ∠URS = 135° ; ∠TRU = 
∠QRT + ∠URS = ∠TRU
20° + 135° = 
155° = 
155° = ∠TRU
Measure of ∠TRU ≠ 155°
83
Sample Response: 0 points
84
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly identify
the sum of ∠QRT and ∠URS and did not correctly identify the measure of ∠TRU.
 The student may have subtracted ∠QRT from ∠URS, instead of finding the
sum.
∠QRT = 20° and ∠URS = 135°
135° – 20° = 115°
 The student may have used mathematical reasoning about lines to figure out
the measure of ∠QRS and then set up an incorrect addition equation to find
the measure of ∠TRU, omitting the measure of ∠QRT.
A line is 180°. The first sentence states, ∠QRS is a line; therefore, the measure of
∠QRS = 180°.
∠QRS = 180° ; ∠URS = 135° ; ∠TRU = 
∠URS + ∠TRU = ∠QRS
135° +  = 180°
135° +  = 180° – 135°
135° +  = 45°
Measure of ∠TRU ≠ 45°
85
Grade 4
Math
Practice Test
Question 10
Question and Scoring Guidelines
87
Question 10
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Points Possible: 1
Content Cluster: Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Content Standard: Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using equations, rectangular
arrays, and/or area models. (4.NBT.5)
88
Scoring Guidelines
Exemplar Response

625
Other Correct Responses

Any equivalent value
For this item, a full-credit response includes:

A correct value (1 point).
89
Grade 4
Math
Practice Test
Question 10
Sample Responses
91
Sample Response: 1 point
92
Notes on Scoring
This response earns full credit (1 point) because the student correctly identified the product
represented by the model.
 The student may have solved the problem by using the area model to find partial
products and then found the sum of the partial products.
20
5
400
25
5
×5
×5
100
× 25
100
25
100
625
+ 25
625
20
20
20
× 20
×5
400
100
20
5
93
Sample Response: 1 point
94
Notes on Scoring
This response earns full credit (1 point) because the student correctly identified the product
represented by the model.
 The student may have solved the problem by finding partial products and the sum of
the partial products without using the area model.
25.0 = (20 + 5)
400.0
25.0 × 25.0 = 625.0
× 25.0 = (20 + 5)
100.0
25.0 = 5.0 × 5.0
100.0
100.0 = 5.0 × 20.0
+ 25.0
100.0 = 20.0 × 5.0
625.0
400.0 = 20.0 × 20.0
While decimals are introduced in the standards in grade 4, students are not expected to be able
to perform calculations using the four operations until grade 5. A student can earn credit in
grade 4 by identifying an equivalent value to a correct response.
95
Sample Response: 0 points
96
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly identify the
product represented by the model.
 The student may have solved the problem by using the area model to find partial
products but omitted two of the partial products.
5
400
5
×5
+ 25
25
425
20
25 × 25 ≠ 425
× 20
20
400
20
5
97
Sample Response: 0 points
98
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly identify the
product represented by the model.
 The student may have solved the problem by using the area model to find the sum of
each rectangle and adding the sums together.
20
5
40
5
+5
+5
25
25
10
25
+10
100
20
20
+ 20
+5
25 × 25 ≠ 100
20
40
25
20
5
99
Grade 4
Math
Practice Test
Question 11
Question and Scoring Guidelines
101
Question 11
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Points Possible: 1
Content Cluster: Build fractions from unit fractions by applying and
extending previous understandings of operations on whole numbers.
𝑎
Content Standard: Understand a fraction 𝑏 with a > 1 as a sum of
1
fractions 𝑏.
c. Add and subtract mixed numbers with like denominators, e.g., by
replacing each mixed number with an equivalent fraction, and/or
by using properties of operations and the relationship between
addition and subtraction. (4.NF.3c)
102
Scoring Guidelines
Exemplar Response

1
13 cups
Other Correct Responses

Any equivalent fraction
For this item, a full-credit response includes:

A correct fraction (1 point).
103
Grade 4
Math
Practice Test
Question 11
Sample Responses
105
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the number of cups Theresa has left.
 The student may have solved the problem using
subtraction.
2
1
1
2 3 – 13 = 13
106
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the number of cups Theresa has left.
 The student may have converted the mixed numbers
into improper fractions and solved the problem using
subtraction.
2
8
1
4
2 3 = 3 and 13 = 3
8
3
4
4
–3=3
While it may be convenient for students to place fractions in
simplest form to help with problem solving, students are not
required to place fractions in simplest form. A student can
earn credit by identifying an equivalent value to a correct
response.
107
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the number of cups Theresa has left.
 The student may have solved the problem by
subtracting incorrectly.
2
1
1
2 3 – 13 ≠ 10
108
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the number of cups Theresa has left.
 The student may have converted the mixed numbers
to improper fractions, and then solved the problem by
subtracting incorrectly.
2
8
1
4
2 3 = 3 and 13 = 3
8
4
4
– ≠0
3 3
109
Grade 4
Math
Practice Test
Question 12
Question and Scoring Guidelines
111
Question 12
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Points Possible: 1
Content Cluster: Use the four operations with whole numbers to solve
problems.
Content Standard: Solve multistep word problems posed with whole
numbers and having whole-number answers using the four
operations, including problems in which remainders must be
interpreted. Represent these problems using equations with a letter
standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies
including rounding. (4.OA.3)
112
Scoring Guidelines
Correct Responses
For example, the response may include:

5 pans. I divided 36 by 8 and got 4 with a remainder of 4. So she can
make 4 whole pans of banana bread and part of another pan to make all
36 loaves.

5 pans.
36
8
=4
R
4, so Corinna needs to use 5 pans.
Score Point
Description
1 point
The focus of this item is to divide 36 by 8 and
interpret the remainder in the context of the word
problem. The response determines how many pans
are needed to make 36 loaves of banana bread
with supporting work or an explanation.
0 points
The response does not meet the criteria required to
earn one point. The response indicates inadequate or
no understanding of the task and/or the idea or
concept needed to answer the item. It may only
repeat information given in the test item. The response
may provide an incorrect solution/response and the
provided supportive information may be irrelevant to
the item, or possibly, no other information is shown.
The student may have written on a different topic or
written, “I don’t know.”
113
Grade 4
Math
Practice Test
Question 12
Sample Responses
115
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the least number of pans Corinna could
have used and explained his/her thinking.
116
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the least number of pans Corinna could
have used and explained his/her thinking.
117
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified the least number of pans Corinna could
have used and explained his/her thinking.
118
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the least number of pans Corinna
could have used.
 The student may have misunderstood the meaning of
the remainder.
119
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the least number of pans Corinna
could have used.
 The student may have overlooked that Corinna uses
each pan only one time.
120
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly identify the least number of pans Corinna
could have used.
 The student may have misunderstood the meaning of
the remainder.
121
Grade 4
Math
Practice Test
Question 13
Question and Scoring Guidelines
123
Question 13
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Points Possible: 2
Content Cluster: Extend understanding of fraction equivalence and
ordering.
Content Standard: Compare two fractions with different numerators
and different denominators, e.g., by creating common
denominators or numerators, or by comparing to a benchmark
1
fraction such as 2. Recognize that comparisons are valid only when
the two fractions refer to the same whole. Record the results of
comparisons with symbols >, =, or <, and justify the conclusions, e.g.,
by using a visual fraction model. (4.NF.2)
124
Scoring Guidelines
Exemplar Response
Other Correct Responses

Part B: Any 3 sections in the first model and any 4 sections in the second
model can be selected.
For this item, a full-credit response includes:

A correct comparison (1 point);
AND

Two correct fraction models (1 point).
125
Grade 4
Math
Practice Test
Question 13
Sample Responses
127
Sample Response: 2 points
Notes on Scoring
This response earns full credit (2 points) because the student
correctly identified the symbol to complete the comparison
of the two fractions and correctly modeled the comparison
from Part A in Part B.
While the example in Part B shows the red fraction model on
the left with the upper-right piece unshaded, the student
could have shaded any 3 out of the 4 pieces.
While the example in Part B shows the blue fraction model on
the right with the left-middle and the right-middle pieces
unshaded, the student could have shaded any 4 out of the
6 pieces.
128
Sample Response: 2 points
Notes on Scoring
This response earns full credit (2 points) because the student
correctly identified the symbol to complete the comparison
of the two fractions and correctly modeled the comparison
from Part A in Part B.
While the example in Part B shows the red fraction model on
the left with the lower-left piece unshaded, the student could
have shaded any 3 out of the 4 pieces.
While the example in Part B shows the blue fraction model on
the right with the left-lower and the right-lower pieces
unshaded, the student could have shaded any 4 out of the
6 pieces.
129
Sample Response: 1 point
Notes on Scoring
This response earns partial credit (1 point) because the
student did not identify the correct symbol to complete the
comparison of the two fractions but correctly modeled the
fractions from Part A in Part B.
3
4
 The student may have thought 4 < 6 because the
numerator in
4
6
3
is greater than the numerator in 4 .
While the example in Part B shows the red fraction model on
the left with the upper-right piece unshaded, the student
could have shaded any 3 out of the 4 pieces.
While the example in Part B shows the blue fraction model on
the right with the left-middle and the right-middle pieces
unshaded, the student could have shaded any 4 out of the
6 pieces.
130
Sample Response: 1 point
Notes on Scoring
This response earns partial credit (1 point) because the
student correctly identified the symbol to complete the
comparison of the two fractions but incorrectly modeled the
comparison from Part A in Part B.
3
4
 The student may have thought the fractions 4 and 6
represented the unshaded amount of the models.
131
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student did not identify
the correct symbol to complete the comparison of the two fractions and
incorrectly modeled the comparison from Part A in Part B.
 The student may have incorrectly solved the problem by using
1
subtraction to get 2 .
4
6

3
1
–4≠2
1
The student may have created equivalent fractions to 2 and incorrectly
1
compared those equivalent fractions to 2 .
1
2
4
6

2
=4
and
1
2
3
=6
3
≠4
4
3
The student may have incorrectly identified 6 and 4 as fractions
1
equivalent to 2 , therefore equal to each other.
3
4
1
≠2
and
4
6
≠
1
2
132
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify the correct symbol to complete the
comparison of the two fractions and incorrectly modeled the
comparison from Part A in Part B.
3
4
 The student may have thought the fractions 4 and 6
represented the unshaded amount of the models
and made the comparison based on the unshaded
amount of both models.
133
Grade 4
Math
Practice Test
Question 14
Question and Scoring Guidelines
135
Question 14
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Points Possible: 1
Content Cluster: Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Content Standard: Recognize a line of symmetry for a
two-dimensional figure as a line across the figure such that
the figure can be folded along the line into matching parts.
Identify line-symmetric figures and draw lines of symmetry. (4.G.3)
136
Scoring Guidelines
Exemplar Response
Other Correct Responses


Any rectangle or rhombus that is not a square
The student may draw the lines of symmetry
For this item, a full-credit response includes:

A correct quadrilateral (1 point).
137
Grade 4
Math
Practice Test
Question 14
Sample Responses
139
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified a quadrilateral with exactly two lines of
symmetry.
140
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified a quadrilateral with exactly two lines of
symmetry.
A student can earn credit for a correct response that includes
lines of symmetry marked; however, students are not required
to include lines of symmetry in their response.
141
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify a quadrilateral with exactly two lines of
symmetry.
 The student may have thought that a square has only
two lines of symmetry instead of four.
Line 1
Line 2
Line 3
142
Line 4
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify a quadrilateral with exactly two lines of
symmetry.
 The student may have thought that a quadrilateral has
six sides.
143
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify a quadrilateral with exactly two lines of
symmetry.
 The student created a quadrilateral that has only one
line of symmetry.
144
Grade 4
Math
Practice Test
Question 15
Question and Scoring Guidelines
145
Question 15
16305
Points Possible: 1
Content Cluster: Generate and analyze patterns.
Content Standard: Generate a number or shape pattern that follows
a given rule. Identify apparent features of the pattern that were not
explicit in the rule itself. For example, given the rule “Add 3” and the
starting number 1, generate terms in the resulting sequence and
observe that the terms appear to alternate between odd and even
numbers. Explain informally why the numbers will continue to
alternate in this way. (4.OA.5)
146
Scoring Guidelines
Rationale for Option A: This is incorrect. The student may have thought that the
next number in the pattern is 12.
Rationale for Option B: This is incorrect. The student may have thought that the
next number in the pattern is 13.
Rationale for Option C: Key – The student identified the next number in the
pattern.
Rationale for Option D: This is incorrect. The student may have thought that the
next number in the pattern is 16.
Sample Response: 1 point
147
Grade 4
Math
Practice Test
Question 16
Question and Scoring Guidelines
149
Question 16
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Points Possible: 1
Content Cluster: Understand decimal notation for fractions, and
compare decimal fractions.
Content Standard: Express a fraction with denominator 10 as an
equivalent fraction with denominator 100, and use this technique to
add two fractions with respective denominators 10 and 100. For
3
30
3
4
34
example, express 10 as 100, and add 10 + 100 = 100. (4.NF.5)
150
Scoring Guidelines
Exemplar Response
Other Correct Responses

A. Any equivalent values, but must be a sum
B. Any equivalent value
For this item, a full-credit response includes:

A correct expression and a correct value (1 point).
151
Grade 4
Math
Practice Test
Question 16
Sample Responses
153
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
created a correct addition expression that represented the
model and the student found the correct sum of the two
fractions.
While it may be convenient for students to place fractions in
simplest form to help with problem solving, students are not
required to place fractions in simplest form. A student can
earn credit by identifying an equivalent value to a correct
response.
154
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
created a correct addition expression that represented the
model and the student found the correct sum of the two
fractions.
While it may be convenient for students to place fractions in
simplest form to help with problem solving, students are not
required to place fractions in simplest form. A student can
earn credit by identifying an equivalent value to a correct
response.
155
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because although the
student created a correct addition expression that
represented the model, he/she did not provide the correct
sum of the two fractions.
 The student may have been unable to identify
12
2
equivalent fractions for 100 and 10 in order to add the
two fractions.
12
12
100
12
100
= 100
20
and
2
10
32
+ 100 = 100
156
20
= 100
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because although the student
created a correct addition expression that represented the model,
he/she found the incorrect sum of the two fractions.
 The student may have been unable to identify equivalent
12
2
fractions for 100 and 10 before adding the two fractions together.
12
100

12
= 100
and
2
10
20
= 100
The student may have added the two fractions without finding
common denominators and creating equivalent fractions.
12
2
14
+ 10 ≠ 110
100
157
Grade 4
Math
Practice Test
Question 17
Question and Scoring Guidelines
159
Question 17
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Points Possible: 1
Content Cluster: Solve problems involving measurement and
conversion of measurements from a larger unit to a smaller unit.
Content Standard: Use the four operations to solve word problems
involving distances, intervals of time, liquid volumes, masses of
objects, and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements given
in a larger unit in terms of a smaller unit. Represent measurement
quantities using diagrams such as number line diagrams that feature
a measurement scale. (4.MD.2)
Scoring Guidelines
Exemplar Response

94 inches
Other Correct Responses

Any equivalent value
For this item, a full-credit response includes:

The correct value (1 point).
160
Grade 4
Math
Practice Test
Question 17
Sample Responses
161
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student correctly
identified the height in inches of Charles Austin’s jump.

The student may have found the correct answer by recognizing 7 feet
10 inches is 2 inches less than 8 feet. The student could have set up a
two-column table to find the total number of inches in 8 feet and then
subtracted 2 inches to find the total number of inches in 7 feet 10
inches.
1 foot = 12 inches
8 feet = 96 inches
2 feet = 24 inches
96 inches – 2 inches = 94 inches
3 feet = 36 inches
4 feet = 48 inches
5 feet = 60 inches
6 feet = 72 inches
7 feet = 84 inches
8 feet = 96 inches
162
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student correctly
identified the height in inches of Charles Austin’s jump.
 The student may have found the correct answer by setting up a twocolumn table to convert 7 feet to inches and then added 10 inches to
the total.
1.0 foot = 12.0 inches
7.0 feet + 10.0 inches = 84.0 inches + 10.0 inches
2.0 feet = 24.0 inches
84.0 inches + 10.0 inches = 94.0 inches
3.0 feet = 36.0 inches
4.0 feet = 48.0 inches
5.0 feet = 60.0 inches
6.0 feet = 72.0 inches
7.0 feet = 84.0 inches
While decimals are introduced in the standards in grade 4, students are not
expected to be able to perform calculations using the four operations until
grade 5. A student can earn credit in grade 4 by identifying an equivalent
value to a correct response.
163
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly
identify the height in inches of Charles Austin’s jump.
 The student may have used an incorrect unit conversion of
1 foot ≠ 10 inches when creating a two-column table.
1 foot ≠ 10 inches
2 feet ≠ 20 inches
3 feet ≠ 30 inches
4 feet ≠ 40 inches
5 feet ≠ 50 inches
6 feet ≠ 60 inches
7 feet ≠ 70 inches
7 feet 10 inches ≠ 70 inches + 10 inches
70 inches + 10 inches = 80 inches
164
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student did not correctly
identify the height in inches of Charles Austin’s jump.
 The student may not have recognized that he/she needed to first
convert the 7 feet into inches and then add the 10 inches to find how
high, in inches, Charles Austin jumped.
165
Grade 4
Math
Practice Test
Question 18
Question and Scoring Guidelines
167
Question 18
16298
Points Possible: 1
Content Cluster: Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Content Standard: Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular lines, or the
presence or absence of angles of a specified size. Recognize right
triangles as a category, and identify right triangles. (4.G.2)
168
Scoring Guidelines
Rationale for First Option: This is incorrect. The student may have identified that
a parallelogram can have right angles, but did not consider that not all
parallelograms have right angles.
Rationale for Second Option: This is incorrect. The student may have identified
that a trapezoid can have a right angle, but did not consider that not all
trapezoids have a right angle.
Rationale for Third Option: Key – The student correctly chose a rectangle,
which always has 4 right angles.
Rationale for Fourth Option: This is incorrect. The student may have identified
the special case of the rhombus when it is a square.
Rationale for Fifth Option: This is incorrect. The student may have identified that
a right triangle always has a right angle, but did not consider that other types
of triangles do not have right angles.
Rationale for Sixth Option: Key – The student correctly chose a square, which
always has 4 right angles.
Sample Response: 1 point
169
Grade 4
Math
Practice Test
Question 19
Question and Scoring Guidelines
171
Question 19
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Points Possible: 1
Content Cluster: Understand decimal notation for fractions, and
compare decimal fractions.
Content Standard: Compare two decimals to hundredths by
reasoning about their size. Recognize that comparisons are valid
only when the two decimals refer to the same whole. Record the
results of comparisons with the symbols >, =, or <, and justify the
conclusions, e.g., by using a visual model. (4.NF.7)
172
Scoring Guidelines
Exemplar Response

2.1
Other Correct Responses

Any value between 2.07 and 2.3, exclusive
For this item, a full-credit response includes:

A correct value (1 point).
173
Grade 4
Math
Practice Test
Question 19
Sample Responses
175
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified a number that is less than 2.3 and greater
than 2.07.
176
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified a number that is less than 2.3 and greater
than 2.07.
While decimals beyond hundredths are not introduced in the
standards until grade 5, a student can earn credit at grade 4
by identifying a decimal beyond hundredths that is
equivalent to a correct response.
177
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify a number that is less than 2.3 and 2.07.
 The student may have thought that 2.03 is greater
than 2.07.
178
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify a number that is greater than 2.3 and 2.07.
 The student may have thought that 2.92 is less than 2.3.
179
Grade 4
Math
Practice Test
Question 20
Question and Scoring Guidelines
181
Question 20
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Points Possible: 1
Content Cluster: Geometric measurement: understand concepts of
angle and measure angles.
Content Standard: Measure angles in whole-number degrees using a
protractor. Sketch angles of specified measure. (4.MD.6)
182
Scoring Guidelines
Exemplar Response
Other Correct Responses

The correct angle does not need to be on the protractor in Part A
For this item, a full-credit response includes:

The correct angle (1 point).
183
Grade 4
Math
Practice Test
Question 20
Sample Responses
185
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly selected the letter that matches the angle label for
the angle with a measure of 50 degrees.
186
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not select the correct letter that matches the angle label
to the angle with a measure of 50 degrees.
187
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not select the correct letter that matches the angle label
to the angle with a measure of 50 degrees.
 The student may have incorrectly measured the angle
using the protractor.
188
Grade 4
Math
Practice Test
Question 21
Question and Scoring Guidelines
189
Question 21
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Points Possible: 1
Content Cluster: Generalize place value understanding for multi-digit
whole numbers.
Content Standard: Use place value understanding to round
multi-digit whole numbers to any place. (4.NBT.3)
Scoring Guidelines
Exemplar Response

26,000
Other Correct Responses

Any equivalent value
For this item, a full-credit response includes:

The correct value (1 point).
190
Grade 4
Math
Practice Test
Question 21
Sample Responses
191
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly rounded the number 25,632 to the nearest
thousand.
192
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly rounded the number 25,632 to the nearest
thousand.
While interpreting a fraction as division is not in the standards until
grade 5, a student can earn credit in grade 4 by identifying an
equivalent value to a correct response.
193
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly round the number 25,632 to the nearest
thousand.
 The student may have thought that 25,632 rounded
down to 25,000.
194
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not correctly round the number 25,632 to the nearest
thousand.
 The student may have thought that 25,632 was
supposed to be rounded to the nearest ten thousand.
195
Grade 4
Math
Practice Test
Question 22
Question and Scoring Guidelines
197
Question 22
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Points Possible: 1
Content Cluster: Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Content Standard: Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel lines. Identify
these in two-dimensional figures. (4.G.1)
198
Scoring Guidelines
Exemplar Response
Other Correct Responses

N/A
For this item, a full-credit response includes:

Two correctly marked angles (1 point).
199
Grade 4
Math
Practice Test
Question 22
Sample Responses
201
Sample Response: 1 point
Notes on Scoring
This response earns full credit (1 point) because the student
correctly identified all of the angles that appear to be acute.
 The student may have recognized that acute angles
are less than 90° and identified all of the angles that
appear to be less than 90°.
202
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify all of the angles that appear to be acute.
 The student may have thought that acute angles are
greater than 90° and identified all of the angles that
appear to be greater than 90°.
203
Sample Response: 0 points
Notes on Scoring
This response earns no credit (0 points) because the student
did not identify all of the angles that appear to be acute.
 The student may have thought that acute angles are
greater than 90° and identified two angles that appear
to be greater than 90°.
204
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