Grade 8 Mathematics Item Specification C1 TC Grade 8 Math C1 TC
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and carry out mathematical
procedures with precision and fluency.
Content Domain: Expressions and Equations
Target C [m]: Understand the connections between proportional relationships, lines, and
linear equations. (DOK 2)
Tasks for this target will ask students to graph one or more proportional relationships and
connect the unit rate(s) to the context of the problem.
Other tasks will ask students to apply understanding of the relationship between similar
triangles and slope.**
3
to the right
4
and one unit up puts you back on the line. If you start at a different point on the line and
move to the right 8 units, how many units up do you have to move to be back on the line?
Standards: 8.EE.5, 8.EE.6
DOK Target(s): 1, 2
Evidence Required: 1. The student graphs proportional relationships.
**
For example, a task might say that starting from a point on a line, a move
2. The student interprets the unit rate as the slope of the graph of
a proportional relationship.
3. The student compares two different proportional relationships
represented in different ways.
4. The student solves problems by applying the fact that similar
triangles can be used to explain why the slope m is the same
between any two distinct points on a nonvertical line in the
coordinate plane.
5. The student derives the equation y = mx for a line through the
origin.
Allowable Item Types*:
Task Models:
6. The student derives the equation y = mx + b for a line
intercepting the vertical axis at b.
SR, CR, TE
1. SR (DOK 1, 2)
Prompt Features: The student is prompted to identify the graph
of a given proportional relationship. Or the student is prompted to
identify the proportional relationship represented by a given
graph.
Stimulus: The student is presented with a proportional
relationship that may be represented in a variety of ways,
including graphical, algebraic, tabular, and verbal.
1. CR (DOK 2)
Prompt Features: The student is prompted to describe the
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Grade 8 Mathematics Item Specification C1 TC
proportional relationship represented by a given graph.
Stimulus: The student is presented with a proportional
relationship that is represented graphically.
1. TE (DOK 2)
Prompt Features: The student is prompted to create the graph
of a given proportional relationship.
Stimulus: The student is presented with a proportional
relationship that may be represented in a variety of ways,
including algebraic, tabular, and verbal.
Interaction: The student uses a graphing tool to plot points and
draw a line in the coordinate plane.
2. SR (DOK 1)
Prompt Features: The student is prompted to identify the unit
rate from a graph of a proportional relationship. Or the student is
prompted to identify the graph that shows a given unit rate.
Stimulus 1: The student is presented with a graph of a
proportional relationship.
Stimulus 2: The student is presented with a unit rate.
2. CR (DOK 1)
Prompt Features: The student is prompted to determine the unit
rate from a graph of a proportional relationship.
Stimulus: The student is presented with a graph of a proportional
relationship.
2. TE (DOK 2)
Prompt Features: The student is prompted to create a graph
that shows a given unit rate.
Stimulus: The student is presented with a unit rate.
Interaction: The student uses a graphing tool to plot points and
draw a line in the coordinate plane.
3. SR (DOK 2)
Prompt Features: The student is prompted to identify one or
more correct comparisons between two different proportional
relationships represented in different ways. Or the student is
prompted to identify a proportional relationship that compares to
a given proportional relationship in a certain way.
Stimulus 1: The student is presented with two proportional
relationships that may be represented in a variety of ways,
including graphical, algebraic, tabular, and verbal. The
proportional relationships must be different (not different
representations of the same relationship) and involve different
representations.
Stimulus 2: The student is presented with a comparison of
proportional relationships in addition to one proportional
relationship that may be represented in a variety of ways,
including graphical, algebraic, tabular, and verbal.
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Grade 8 Mathematics Item Specification C1 TC
3. CR (DOK 2)
Prompt Features: The student is prompted to state how two
different proportional relationships represented in different ways
compare to each other. Or the student is prompted to create a
proportional relationship that compares to a given proportional
relationship in a certain way.
Stimulus 1: The student is presented with two proportional
relationships that may be represented in a variety of ways,
including graphical, algebraic, tabular, and verbal. The
proportional relationships must be different (not different
representations of the same relationship) and involve different
representations.
Stimulus 2: The student is presented with a comparison of
proportional relationships in addition to one proportional
relationship that may be represented in a variety of ways,
including graphical, algebraic, tabular, and verbal.
3. TE (DOK 2)
Prompt Features: The student is prompted to create the
graphical representation of a proportional relationship that
compares to a given proportional relationship in a certain way.
Stimulus: The student is presented with a comparison and a
proportional relationship that may be represented in a variety of
ways, including algebraic, tabular, and verbal. The proportional
relationships must be different (not different representations of
the same relationship).
Interaction: The student uses a graphing tool to plot points and
draw a line in the coordinate plane.
4. SR (DOK 2)
Prompt Features: Given points on a line, the student is
prompted to identify two similar triangles where the segment
between a pair of the points corresponds to the hypotenuse of one
of the triangles. Or the student is prompted to identify correct
statements given two triangles with corresponding sides on a
given line.
Stimulus 1: The student is presented with points on a line in the
coordinate plane.
Stimulus 2: The student is presented with two triangles with
corresponding sides on a given line.
5. SR (DOK 1, 2)
Prompt Features: The student is prompted to identify the slope
and the y-intercept of a line through the origin. Or the student is
prompted to identify the equation of a line through the origin. Or
the student is prompted to identify the graph of a proportional
relationship that may be represented in a variety of ways.
Stimulus 1: The student is presented with the graph of a
proportional relationship.
Stimulus 2: The student is presented with a proportional
relationship that may be represented in a variety of ways,
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Grade 8 Mathematics Item Specification C1 TC
including algebraic, tabular, and verbal.
5. CR (DOK 2)
Prompt Features: The student is prompted to determine the
slope and the y-intercept of a line through the origin. Or the
student is prompted to write the equation of a line through the
origin.
Stimulus: The student is presented with the graph of a line
through the origin.
5. TE (DOK 2)
Prompt Features: The student is prompted to create the graph
of a proportional relationship that may be represented in a variety
of ways.
Stimulus: The student is presented with a proportional
relationship that may be represented in a variety of ways,
including algebraic, tabular, and verbal.
Interaction: The student uses a tool that plots points and draws
line segments between the points to create a figure.
6. SR (DOK 1)
Prompt Features: The student is prompted to identify the slope
and the y-intercept of a line with a nonzero y-intercept. Or the
student is prompted to identify the equation of a line through a
nonzero y-intercept. Or the student is prompted to identify the
graph of a nonproportional relationship that may be represented
in a variety of ways.
Stimulus 1: The student is presented with the graph of a
nonproportional relationship.
Stimulus 2: The student is presented with a nonproportional
relationship that may be represented in a variety of ways,
including algebraic, tabular, and verbal.
6. CR (DOK 2)
Prompt Features: The student is prompted to determine the
slope and the y-intercept of a line with a nonzero y-intercept. Or
the student is prompted to determine the equation of a line
through a nonzero y-intercept.
Stimulus: The student is presented with the graph of a
nonproportional relationship.
Allowable Stimulus
6. TE (DOK 2)
Prompt Features: The student is prompted to create the graph
of an equation given the equation or the slope and nonzero yintercept of the equation.
Stimulus: The student is presented with an equation with a
nonzero y-intercept that may be represented in a variety of ways,
including algebraic, tabular, and verbal.
Interaction: The student uses a tool that plots points and draws
line segments between the points to create a figure.
Graphs, tables, equations, verbal descriptions
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Grade 8 Mathematics Item Specification C1 TC
Materials:
Allowable Disciplinary
Vocabulary:
Allowable Tools:
Target-Specific
Attributes
Key Nontargeted
Constructs:
Accessibility Concerns:
Sample Items:
Proportional relationship, slope, y-intercept, similar triangles,
origin, coordinate plane
Calculator
Proportional relationships may be expressed graphically,
algebraically, numerically in a table, or in a verbal description.
MAT.08.TE.1.000EE.C.200
*SR = selected-response item; CR = constructed-response item; TE = technology-enhanced
item; ER = extended-response item; PT = performance task
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