Grade 4 Mathematics Sample SR Item C1 TH
MAT.04.SR.1.000NF.H.213 C1 TH
Sample Item Id:
Grade:
Claim(S):
Assessment Target(S):
Content Domain:
Standard(S):
Mathematical Practice(S):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes
(E.G., Accessibility Issues):
Notes:
MAT.04.SR.1.000NF.H.213
04
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and
carry out mathematical procedures with precision and
fluency.
1 H: Understand decimal notation for fractions, and
compare decimal fractions.
Numbers and Operations—Fractions
04.NF.5
1, 2, 6
1
SR
1
L
C
Which equation is true?
A
7
2
9


100 10 100
B
7
2
9


100 10 10
C
7
2
27


100 10 100
D
7
2
72


100 10 100
Key and Distractor Analysis:
A Added as if both fractions had denominators of 100
B Added as if both fractions had denominators of 10
C Correct
D Multiplied numerator of first fraction by 10 instead of multiplying numerator of second
fraction by 10
Version 1.0
Grade 4 Mathematics Sample SR Item C1 TB
MAT.04.SR.1.000OA.B.023 C1 TB
Sample Item Id:
Grade:
Claim(S):
Assessment Target(S):
Content Domain:
Standard(S):
Mathematical Practice(S):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes
(E.G., Accessibility
Issues):
Notes:
MAT.04.SR.1.000OA.B.023
04
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and
carry out mathematical procedures with precision and
fluency.
1 B: Gain familiarity with factors and multiples.
Operations and Algebraic Thinking
4.OA.4
1, 2
1
SR
1
L
C
Which number is both a factor of 100 and a multiple of 5?
A
004
B
040
C
050
D
500
Key and Distractor Analysis:
A
B
C
D
Did not consider criteria of “multiple of 5”
Did not consider criteria of “factor of 100”
Correct
Multiplied 100 and 5
Version 1.0
Grade 3 Mathematics Sample CR Item C1 T1
Ms. Clancy uses a backpack on a hiking trip. She took about 2
kg of food out of her backpack to make it lighter. The scale
below shows how much the backpack weighed after she took
out the food.
How much did the backpack weigh, in kg, before she took the
food out?
kg
Version 1.0
Grade 03 Mathematics Sample CR Item C1 T1
MAT.03.CR.1.000OA.D.234 C1 T1
Sample Item ID:
Grade:
Claim(s):
Assessment Target(s):
Content Domain:
Standard(s):
Mathematical Practice(s):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes (e.g.,
Accessibility Issues):
Notes:
MAT.03.CR.1.000OA.D.234
03
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts
and carry out mathematical procedures with precision
and fluency.
1 D: Solve problems involving the four operations, and
identify and explain patterns in arithmetic.
Operations and Algebraic Thinking
3.OA.8, 3.OA.5, 3.NBT.3
1, 2, 6
2
CR
1
M
80
Response box will accept up to 4 numeric digits.
A roller skating team has 10 members. Each team member has 2
skates. Each skate has 4 wheels.
What is the total number of skate wheels that the team has?
wheels
Key and Rationale:
80 (10 x 2 x 4)
Version 1.0
Grade 4 Mathematics Sample SR Item C1 TA
MAT.04.SR.1.000OA.A.027 C1 TA
Sample Item Id:
Grade:
Claim(S):
Assessment Target(S):
Content Domain:
Standard(S):
Mathematical Practice(S):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes
(E.G., Accessibility
Issues):
Notes:
MAT.04.SR.1.000OA.A.027
04
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and
carry out mathematical procedures with precision and
fluency.
1 A: Use the four operations with whole numbers to solve
problems.
Operations and Algebraic Thinking
4.OA.2
2, 4
2
SR
2
M
YNY
Multi-part item
Sarah is 12 years old.
• George is g years old.
• Sarah is 3 times as old as George.
For numbers 1a–1c, choose Yes or No to indicate whether each
statement is true.
1a. George’s age, in years, can be represented
by the expression 12 ÷ 3.
Yes
No
1b. George is 15 years old.
Yes
No
1c. George’s age, in years, can be found by
solving the equation 12 = 3 × g.
Yes
No
Version 1.0
Grade 5 Mathematics Sample TE Item C1 TK
Classify the triangles as scalene, right, and/or acute. If a
triangle fits more than one classification, place it in all the boxes
that apply. If none of these classifications apply, leave it outside
the boxes.
Click on a shape and then click inside a box to place a shape in
the box.
Version 1.0
Grade 05 Mathematics Sample ER Item Claim 3
Branden’s teacher said that beginning at age 2, children grow
about 6 centimeters per year. Branden is 125 centimeters tall
and is 9 years old.
In the table below, Branden used his current age and height to
calculate his possible height for each of the previous 3 years.
Branden used the equation 7  6 
 125 to estimate how tall
he was at age 2. Will the equation give him a reasonable
estimate of his height at age 2? Explain your answer by relating
the information in the table to the given equation.
What is a reasonable height for Branden at age 2?
centimeters
Version 1.0
Grade 3 Mathematics Sample ER Item Claim 3
MAT.03.ER.3.000NF.E.216 Claim 3
Sample Item ID:
Grade:
Primary Claim:
Secondary Claim(s):
Primary Content Domain:
Secondary Content Domain(s):
Assessment Target(s):
Standard(s):
Mathematical Practice(s):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes (e.g.,
accessibility issues):
Notes:
MAT.03.ER.3.000NF.E.216
03
Claim 3: Communicating Reasoning
Students can clearly and precisely construct viable
arguments to support their own reasoning and to
critique the reasoning of others.
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts
and carry out mathematical procedures with precision
and fluency.
Number and Operations—Fractions
3 E: Distinguish correct logic or reasoning from that
which is flawed, and—if there is a flaw in the
argument—explain what it is.
1 F: Develop understanding of fractions as numbers.
03.NF.2
1, 2, 4, 5
3, 6
ER
2
L
See Sample Top-Score Response.
2
on the number line. Eva labeled the
4
number line with unit fractions to show how she determined her
answer.
Eva thinks that Q shows
Version 1.0
Grade 3 Mathematics Sample ER Item Claim 3
Is Eva’s drawing correct? Explain your reasoning using words,
numbers, and/or pictures.
Sample Top-Score Response:
Eva’s drawing is not correct. The point that is represented on the number line is
2
4
2
3
.
would be represented on a number-line diagram by marking off 2 lengths, each of
length
1
4
from 0. As shown, the endpoint would be
2
3
because the intervals are in thirds.
Scoring Rubric:
Responses to this item will receive 0–2 points based on the following:
2 points: The student shows thorough communication of distinguishing correct reasoning
from that which is flawed by giving a clear explanation using words, numbers, and/or
pictures of fractions and their representation on the number line.
1 point: The student shows partial communication of distinguishing correct reasoning
from that which is flawed by giving a partial or incomplete explanation that may not
clearly explain fractions and their representation on the number line.
0 points: The student demonstrates little or no communication of distinguishing correct
reasoning from that which is flawed on the number line and representation of the fraction.
Version 1.0
Grade 4 Mathematics Sample ER Item Claim 3
MAT.04.ER.3.000OA.A.512 Claim 3
Sample Item Id:
Grade:
Primary Claim:
Secondary Claim(S):
Primary Content Domain:
Secondary Content Domain(S):
Assessment Target(S):
Standard(S):
Mathematical Practice(S):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes
(E.G., Accessibility Issues):
Notes:
MAT.04.ER.3.000OA.A.512
04
Claim 3: Communicating Reasoning
Students can clearly and precisely construct viable
arguments to support their own reasoning and to
critique the reasoning of others.
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts
and carry out mathematical procedures with precision
and fluency.
Operations and Algebraic Thinking
3A: Test propositions or conjectures with specific
examples.
1B: Gain familiarity with factors and multiples.
4.OA.4
1, 2, 3, 8
2
ER
2
H
See Sample Top-Score Response.
Part of PT set
Peter made the statement shown below.
“The number 32 is a multiple of 8. That means all
of the factors of 8 are also factors of 32.”
Is Peter’s statement correct? In the space below, use numbers
and words to explain why or why not.
Version 1.0
Grade 8 Mathematics Sample SR Item
MAT.08.SR.1.000EE.B.203
Sample Item ID:
Grade:
Claim(s):
Assessment Target(s):
Content Domain:
Standard(s):
Mathematical Practice(s):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes
(e.g., accessibility issues):
Notes:
MAT.08.SR.1.000EE.B.203
08
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and
carry out mathematical procedures with precision and
fluency.
1 B: Work with radicals and integer exponents.
Equations and Expressions
8.EE.1
1, 5, 7
1
SR
1
M
A, C, D
Students may not use calculators for this target.
Multiple correct keys
Select all of the expressions that have a value between 0 and 1.
A
8 7 ⋅ 8 − 12
B
74
7 −3
C
1 1
3 ⋅ 3
   
D
( −5)
10
( −5)
2
9
6
Key and Distractor Analysis:
A. Key. Students may think that a negative exponent means that the number is
negative, not that the number is between 0 and 1.
B. The expression is equal to 77, so it is greater than 1. Students may make mistakes
when finding the exponent of the equivalent expression.
C. Key. Students may think that since the base is raised to such a high exponent it
will be greater than 1, but since the base is between 0 and 1, the value of the
expression is between 0 and 1.
D. Key. Students may miscalculate the exponent of the equivalent expression or
forget that the expression will be positive because the exponent is even.
Version 1.0
HS Mathematics Sample TE Item C1 TI
Match each inequality in items 1 – 3 with the number line in
items A – F that represent the solution to the inequality.
To connect an inequality to its number line, first click the
inequality. Then click the number line it goes with. A line will
automatically be drawn between them.
1
−4x < −12
A
B
2
2(x + 2) < 8
C
D
3
5 − 2x < 2 − x
E
F
Key and Distractor Analysis:
1. Key F; Students that match this inequality correctly have demonstrated an
understanding of how the inequality symbol is affected when dividing by a negative
number.
2. Key B; Students that match this inequality correctly have demonstrated an
Version 1.0
Grade 6 Mathematics Sample TE Item C1 TF
MAT.06.TE.1.000EE.F.170 C1 TF
Sample Item ID:
Grade:
Claim(s):
Assessment Target(s):
Content Domain:
Standard(s):
Mathematical Practice(s):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes
(e.g., accessibility issues):
Notes:
MAT.06.TE.1.000EE.F.170
06
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and
carry out mathematical procedures with precision and
fluency.
1 F: Reason about and solve one-variable equations and
inequalities.
Expressions and Equations
6.EE.6
2, 4
1
TE
1
M
3b+5 (see others below)
Tab entry will be used in place of click and drag for students
that need this accommodation.
TE Template: Select and Order
Let b represent a number.
Click and drag the objects (numbers, operation symbols, letter)
to the line below to create an expression that represents the
following:
“5 more than the product of 3 and the number b”
Not all objects will be used.
3
5
b
+
–
x
÷
Version 1.0
HS Mathematics Sample CR Item Claim 2
Hannah makes 6 cups of cake batter. She pours and levels all
the batter into a rectangular cake pan with a length of 11 inches,
a width of 7 inches, and a depth of 2 inches.
One cubic inch is approximately equal to 0.069 cup.
What is the depth of the batter in the pan when it is completely
1
poured in? Round your answer to the nearest
of an inch.
8
Key:
Correct responses to this item will receive 1 point.
1 point: For correct answer 1
1
or 1.125 inches.
8
Version 1.0
HS Mathematics Sample CR Item Claim 2
Jaime randomly surveyed some students at his school to see
what they thought of a possible increase to the length of the
school day. The results of his survey are shown in the table
below.
Part A
A newspaper reporter will randomly select a Grade 11 student
from this survey to interview. What is the probability that the
student selected is opposed to lengthening the school day?
Part B
The newspaper reporter would also like to interview a student in
favor of lengthening the school day. If a student in favor is
randomly selected, what is the probability that this student is
also from Grade 11?
Version 1.0
Grade 8 Mathematics Sample CR Item Form Claim 2
Juan needs a right cylindrical storage tank that holds between
110 and 115 cubic feet of water.
Using whole numbers only, provide the radius and height for 3
different tanks that hold between 110 and 115 cubic feet of
water.
Tank #1
Tank #2
Tank #3
radius =
ft.
radius =
ft.
radius =
ft.
height =
ft.
height =
ft.
height =
ft.
Sample Top-Score Response:
Tank #1: r = 2, h = 9
Tank #2: r = 3; h = 4
Tank #3: r = 6; h = 1
Scoring Rubric:
Responses to this item will receive 0-3 points, based on the following:
3 points: The student shows a thorough understanding of the volume of cylinders. The
student provides 3 correct sets of dimensions.
2 points: The student shows a partial understanding of the volume of cylinders. The
student provides 2 correct sets of dimensions.
1 point: The student shows a limited understanding of the volume of cylinders. The
student provides 1 correct set of dimensions.
0 points: The student shows inconsistent or no understanding of the volume of cylinders.
Version 1.0
Grade 8 Mathematics Sample ER Item Form Claim 3
Part A
Triangle STV has sides with lengths of 7, 11, and 14 units.
Determine whether this triangle is a right triangle.
Show all work necessary to justify your answer.
Part B
A right triangle has a hypotenuse with a length of 15. The
lengths of the legs are whole numbers. What are the lengths of
the legs?
Sample Top-Score Response:
Part A
72 + 112 does not equal 142 because 49 + 121 = 170, not 196.
Therefore, it is not a right triangle because the side lengths do not satisfy the Pythagorean
theorem.
Part B
9, 12
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Grade 6 Mathematics Sample ER Item Claim 3
The areas, in square kilometers, of 10 countries in South America
are shown in the table.
The data is also summarized in the box plot.
Which measure of center, the mean or the median, is best to use
when describing this data? Thoroughly explain your reasoning for
choosing one measure over the other measure.
Version 1.0
Grade 7 Mathematics Sample ER Item
MAT.07.ER.3.000NS.A.293
Sample Item ID:
Grade:
Primary Claim:
Secondary Claim(s):
Primary Content Domain:
Secondary Content Domain(s):
Assessment Target(s):
MAT.07.ER.3.000NS.A.293
07
Claim 3: Communicating Reasoning
Students can clearly and precisely construct viable
arguments to support their own reasoning and to
critique the reasoning of others.
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts
and carry out mathematical procedures with precision
and fluency.
The Number System
3 A: Test propositions or conjectures with specific
examples.
3 E: Distinguish correct logic or reasoning from that
which is flawed and—if there is a flaw in the argument—
explain what it is.
Standard(s):
Mathematical Practice(s):
DOK:
Item Type:
Score Points:
Difficulty:
Key:
Stimulus/Source:
Target-Specific Attributes (e.g.,
accessibility issues):
Notes:
1 B: Apply and extend previous understandings of
operations with fractions to add, subtract, multiply, and
divide rational numbers.
7.NS.2, 6.NS.4
1, 3
3
ER
2
H
See Sample Top-Score Response.
Part of PT set
Two of these statements are true in all cases:
• Statement 1: The greatest common factor of any two
distinct prime numbers is 1.
• Statement 2: The greatest common factor of any two
distinct composite numbers is 1.
• Statement 3: The product of any two integers is a rational
number.
• Statement 4: The quotient of any two integers is a rational
number.
Version 1.0
Grade 7 Mathematics Sample ER Item
Part A:
Which two statements are true in all cases?
Part B: For both statements that you did not choose in Part A,
provide one clear reason and/or example for each statement
that proves the statement can be false.
Statement
Reason/example
Statement
Reason/example
Sample Top-Score Response:
a. Statements 1 and 3 are true.
b. Statement 2 is not true because the G.C.F. of 12 and 16 is 4.
Statement 4 is not true because 1/0 is not a rational number.
Scoring Rubric:
Responses to this item will receive 0–2 points, based on the following:
2 points: The student shows thorough understanding of how to test propositions with
specific examples. The student identifies the 2 true statements and provides
counterexamples for the 2 statements that are not true.
1 point: The student shows partial understanding of how to test propositions with specific
examples. The student identifies the 2 true statements, but neither
counterexample for the false statements is accurate. OR The student provides
a least one correct counterexample for 1 of the true statements.
0 points: The student shows limited or no understanding of how to test propositions with
specific examples.
Version 1.0