Grades 6-8, Claim 3
Task Model 1
DOK Level 2
Target A:
Test propositions
or conjectures
with specific
examples
Task Expectations:
The student is asked to give an example that refutes a proposition or conjecture; or
The student is asked to give an example that supports a proposition or conjecture.
[Note: Use appropriate mathematical language in asking students for a single example. While a
single example can be used to refute a conjecture, it cannot be used to prove one is always true.]
Example Item 1 (Grade 6):
Primary Target 3A (Content Domain NF), Secondary Target 1F (CCSS 5.NF.4), Tertiary Target 3F
Sarah claims that for any fraction
multiplied by , the product n will
always be less than .
A. Drag one number into each
box so that the product n is
less than .
B. Drag one number into each
box so that the product n is
not less than .
Rubric: (1 point) The student drags one number into each box to create an equation where n is less than
in Part A, and drags one number into each box to create an equation to show that Sarah’s claim is
incorrect in Part B (e.g., Part A
, Part B
).
This exemplar response represents only one possible solution. Other correct responses are possible.
Response Type: Drag and Drop
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Version 2.0
Grades 6-8, Claim 3
Task Model 1
Example Item 2 (Grade 8):
Primary Target 3A (Content Domain NS), Secondary Target 1A (CCSS 8.NS.1), Tertiary Target 3F
DOK Level 2
Target A:
Test propositions
or conjectures
with specific
examples
Tom claims: “If a rational number is not an integer, then the square root of the number must
be irrational. For example, 3.6 is irrational and 1 is irrational.”
2
Enter a rational number that is not an integer to show Tom’s claim is incorrect.
Rubric: (1 point) The student enters a rational number which has a rational square root (e.g.,
or 2.25).
This exemplar response represents only two possible solutions. Other correct responses are possible.
Response Type: Equation/Numeric
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Version 2.0
Grades 6-8, Claim 3
Task Model 2
Task Expectations: The student is presented with a mathematical phenomenon and a conjecture.
Student is asked to identify or construct reasoning that justifies or refutes a conjecture.
DOK Levels 3, 4
Example Item 1 (Grade 6):
Target B:
Construct,
autonomously,
chains of
reasoning that will
justify or refute
conjectures
Primary Target 3B (Content Domain G), Secondary Target 1H (CCSS 6.G.2), Tertiary Target 3C
Micah constructs a rectangular prism
with a volume of 360 cubic units.
Micah claims that if the height is 10
units, then the base of the prism must
be a square.
Use the Connect Line tool to draw a
base that shows Micah’s claim is
incorrect.
Rubric: (1 point) The student constructs a rectangle that shows Micah’s claim is incorrect (e.g., 4 x 9,
3 x 12, or 2 x 18).
Response Type: Graphing
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Version 2.0
Grades 6-8, Claim 3
Task Model 2
Example Item 2 (Grade 8):
Primary Target 3B (Content Domain G), Secondary Target 1G (CCSS 8.G.2), Tertiary Target 3F
DOK Levels 3, 4
Two figures are shown on the coordinate grid.
Target B:
Construct,
autonomously,
chains of
reasoning that will
justify or refute
conjectures
Prove that Figure A and Figure B are congruent.
Describe three single transformations that, when performed, would transform Figure A to Figure B. In
your response, be sure to identify the transformations in the order they are performed.
Rubric:
(2 points) The student describes three transformations with sufficient detail to prove that Figure A and
Figure B are congruent (e.g., see exemplars).
(1 point) The student either describes all three transformations in general terms, without the degree of
precision necessary to prove congruency (e.g., rotation, reflection, and translation) or correctly describes
two out of three transformations and incorrectly describes the third (e.g., states the rotation is 180°
instead of 90° or translates in the wrong direction or an incorrect number of units).
Exemplars4:
1st Transformation is to reflect over the y-axis. 2nd Transformation is to rotate 90° counter-clockwise
about the origin. 3rd Transformation is to translate right by 2 units.
1st Transformation is to reflect over the x-axis. 2nd Transformation is to rotate 90° clockwise about the
origin. 3rd Transformation is to translate right by 2 units.
Response Type: Short Text (hand scored)
4
Exemplars only represent possible solutions. Typically, many other solutions/responses may receive full credit. The full range of acceptable responses is
determined during rangefinding and/or scoring validation.
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Version 2.0
Grades 6-8, Claim 3
Task Model 3
DOK Levels 2, 3
Target C:
State logical
assumptions being
used
Task Expectations: The student is asked to connect a logical basis to its resulting conjecture. The student
is presented with a mathematical or real-world scenario where an assumption is made in order to find the
solution.
Example Item 1 (Grade 7):
Primary Target 3C (Content Domain NS), Secondary Target 1B (CCSS 7.NS.2), Tertiary Target 3F
In the following equation,
a, b, and c are nonzero
rational numbers.
a
b=c
Given this equation, drag
one value into each box to
complete four true
equations.
Rubric:
(2 points) The student is able to complete all four equations correctly
(e.g., see solution shown at the right).
(1 point) The student is able to complete 3 out of 4 equations correctly.
Response Type: Drag and Drop
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Version 2.0
Grades 6-8, Claim 3
Task Model 4
Task Expectations: The student is given different cases to consider and the student uses or shows
reasoning to support the cases.
DOK Levels 2, 3
Target D:
Use the technique
of breaking an
argument into
cases
Example Item 1 (Grade 7):
Primary Target 3D (Content Domain NS), Secondary Target 1B (CCSS 7.NS.2), Tertiary Target 3F,
Quaternary Target 1C (CCSS 6.NS.4)
Rubric: (2 points) The student identifies all the correct conditions that make the argument true (e. g.,
Statements 1, 3).
(1 point) The student identifies the correct conditions that make the argument true, but fails to consider
the case of division by zero (e.g., 1, 3, 4).
Response Type: Hot Spot
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Version 2.0
Grades 6-8, Claim 3
Task Model 5
DOK Levels 2, 3
Target E:
Distinguish
correct reasoning
from flawed
reasoning
Task Expectations:
The student is presented with valid or invalid reasoning. If the reasoning is flawed, the student will
explain or correct the flaw.
The student is asked to select the condition(s) for which an argument does or does not always
apply.
Two or more approaches or chains of reasoning are given and the student is asked to identify the
correct method and justification OR identify the incorrect method/reasoning and the justification.
Example Item 1 (Grade 7):
Primary Target 3E (Content Domain RP), Secondary Target 1A (CCSS 6.RP.3), Tertiary Target 3C
Jane wants to buy the following items at a store.
Jeans, $32.99
Earrings, $29.99
T-shirt, $9.99
Shoes, $23.99
Jane will either use coupon A or coupon B to reduce the cost of her purchase. She sees some socks that
cost $4.99. Jane thinks that adding socks to her purchase will cost her less than making the purchase
without socks.
Which option should Jane choose to spend the least amount of money?
A.
B.
C.
D.
Jane
Jane
Jane
Jane
should
should
should
should
add the socks to her purchase and then use Coupon A.
add the socks to her purchase and then use Coupon B.
make the purchase without socks and use Coupon A.
make the purchase without socks and use Coupon B.
Rubric: (1 point) The student selects the statement that represents correct reasoning (e.g., A).
Response Type: Multiple choice, single correct response
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Version 2.0
Grades 6-8, Claim 3
Task Model 5
Example Item 2 (Grade 7):
Primary Target 3E (Content Domain EE), Secondary Target 1D (CCSS 7.EE.3)
DOK Levels 2, 3
Target E:
Distinguish
correct reasoning
from flawed
reasoning
Rubric: (2 points) The student selects the correct steps and plots the correct point on the number line.
(e.g., Part A: 1, 2, 4; Part B: 8).
(1 point) The student either selects the correct steps or plots the correct point on the number line.
Response Type: Hot Spot and Graphing
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Version 2.0
Grades 6-8, Claim 3
Task Model 5
Example Item 3 (Grade 8):
Primary Target 3E (Content Domain RP), Secondary Target 1A (7.RP.3), Tertiary Target 3C
DOK Levels 2, 3
Target E:
Distinguish
correct reasoning
from flawed
reasoning
Rubric: (1 point) The student selects the flawed work (e.g., $90/0.9 = $100 and highlights “The bats are
on sale for 10% off.”).
Response Type: Hot Spot
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Version 2.0
Grades 6-8, Claim 3
Task Model 6
Task Expectations: The student uses concrete referents to help justify or refute an argument.
DOK Levels 2, 3
Example Item 1 (Grade 8):
Primary Target 3F (Content Domain G), Secondary Target 1E (CCSS 7.G.5), Tertiary Target 3D
Target F:
Base arguments
on concrete
referents such as
objects, drawings,
diagrams, and
actions
The base of triangle ABC and the base of triangle DEF lie on line m, as shown in the diagram.
The measure of
is less than the measure of
For each comparison, select the symbol (<, >, =) that
makes the relationship between the first quantity and the second quantity true.
First Quantity
Comparison
Second Quantity
<
>
=
<
>
=
Interaction: The student selects the symbol from a drop down menu of <, >, = .
Rubric: (1 point) The student selects the correct symbol for both comparisons (e.g., >, <)
Response Type: Hot Spot
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Version 2.0
Grades 6-8, Claim 3
Task Model 7
DOK Levels 2, 3
Target G:
Determine
conditions under
which an argument
does and does not
apply
Task Expectations: The student must determine whether a proposition/or conjecture is true for all
cases, true for some cases, or not true for any case. In some problems the student must provide
justification to support the conclusions.
Example Item 1 (Grade 7):
Primary Target 3G (Content Domain G), Secondary Target 1F (CCSS 7.G.5), Tertiary Target 3A
Determine whether each statement is true for all cases, true for some cases, or not true for any case.
Statement
True for
all
True for
some
Not true
for any
Two vertical angles form a linear pair.
If two angles are supplementary and
congruent, they are right angles.
The sum of two adjacent angles is 90°.
If the measure of an angle is 35˚, then the
measure of its complement is 55˚.
The measure of an exterior angle of a
triangle is greater than every interior angle
of the triangle.
Rubric: (1 point) The student can classify each statement correctly (e.g., see table below).
Response Type: Hot Spot
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Version 2.0
Grades 6-8, Claim 3
Task Model 7
Example Item 2 (Grade 8):
Primary Target 3G (Content Domain G), Secondary Target 1G (CCSS 8.G.3)
DOK Levels 2, 3
Target G:
Determine
conditions under
which an argument
does and does not
apply
A sequence of transformations is applied to a polygon. Identify each sequence of transformations where
the resulting polygon has a greater area than the original polygon.
A.
Reflect over the x-axis, dilate about the origin by a scale factor of
, translate up 5 units
B.
Rotate 90° counterclockwise around the origin, dilate about the origin by a scale factor of
C.
Dilate about the origin by a scale factor of
, rotate 180° clockwise around the origin, translate down
2 units
D. Dilate about the origin by a scale factor of 2, reflect over the y-axis, dilate about the origin by a scale
factor of
Rubric: (1 point) The student identifies all the correct conditions that make the argument true (e.g., B,
D)
Response Type: Multiple Choice, multiple correct response
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Version 2.0