Reading the Mathematics
Evidence Tables
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Claims Structure: Mathematics
Master Claim: On-Track for college and career readiness. The degree to which a student is college and career ready
(or “on-track” to being ready) in mathematics. The student solves grade-level /course-level problems in
mathematics as set forth in the Standards for Mathematical Content with connections to the Standards for
Mathematical Practice.
Sub-Claim A: Major Content1 with
Connections to Practices
The student solves problems
involving the Major Content1 for her
grade/course with connections to
the Standards for Mathematical
Practice.
Sub-Claim B: Additional & Supporting
Content2 with Connections to
Practices
The student solves problems involving
the Additional and Supporting
Content2 for her grade/course with
connections to the Standards for
Mathematical Practice.
Sub-Claim D: Highlighted Practice MP.4 with Connections to Content
(modeling/application)
The student solves real-world problems with a degree of difficulty appropriate to the
grade/course by applying knowledge and skills articulated in the standards for the
current grade/course (or for more complex problems, knowledge and skills articulated
in the standards for previous grades/courses), engaging particularly in the Modeling
practice, and where helpful making sense of problems and persevering to solve them
(MP. 1),reasoning abstractly and quantitatively (MP. 2), using appropriate tools
strategically (MP.5), looking for and making use of structure (MP.7), and/or looking for
and expressing regularity in repeated reasoning (MP.8).
Sub-Claim C: Highlighted Practices
MP.3,6 with Connections to Content3
(expressing mathematical reasoning)
The student expresses grade/courselevel appropriate mathematical
reasoning by constructing viable
arguments, critiquing the reasoning of
others, and/or attending to precision
when making mathematical statements.
Sub-Claim E: Fluency in applicable
grades (3-6)
The student demonstrates fluency as set
forth in the Standards for Mathematical
Content in her grade.
Overview of PARCC Mathematics Task
Types
Task Type
Description of Task Type
I. Tasks assessing
concepts, skills and
procedures
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Balance of conceptual understanding, fluency, and application
Can involve any or all mathematical practice standards
Machine scoreable including innovative, computer-based formats
Will appear on the End of Year and Performance Based Assessment components
Sub-claims A, B and E
II. Tasks assessing
expressing
mathematical
reasoning
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Each task calls for written arguments / justifications, critique of reasoning, or precision in
mathematical statements (MP.3, 6).
Can involve other mathematical practice standards
May include a mix of machine scored and hand scored responses
Included on the Performance Based Assessment component
Sub-claim C
III. Tasks assessing
modeling /
applications
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Each task calls for modeling/application in a real-world context or scenario (MP.4)
Can involve other mathematical practice standards
May include a mix of machine scored and hand scored responses
Included on the Performance Based Assessment component
Sub-claim D
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For more information see PARCC Task Development ITN Appendix D.
Evidence Statement:
Exact Standards Language
Evidence
Statement
Evidence Statement Text
Key
F-IF.2
Use function notation, evaluate
functions for inputs in their domains,
and interpret statements that use
function notation in terms of a
context.
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Evidence Statement:
Derived from Exact Standards Language
Evidence
Statement
Key
A-SSE.2-4
Evidence Statement Text
Use the structure of a numerical expression or
polynomial expression in one variable to
rewrite it, in a case where two or more
rewriting steps are required.
Interpret the structure of expressions.
2. Use the structure of an expression to identify ways to rewrite
it. For example, see x4 - y4 as (x2)2 - (y2)2 , thus recognizing it as
a difference of squares that can be factored as (x2 - y2) (x2 + y2).
Evidence Statement:
Derived from Exact Standards Language
Evidence
Statement Key
A-REI.4b-1
Evidence Statement Text
Solve quadratic equations in one variable.
b) Solve quadratic equations with rational number coefficients
by inspection (e.g., for
), taking square roots,
completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation.
A-REI.4b
Solve quadratic equations in one variable.
b) Solve quadratic equations with rational number coefficients by inspection
(e.g., for
), taking square roots, completing the square, the quadratic
formula and factoring, as appropriate to the initial form of the equation.
Recognize when the quadratic formula gives complex solutions and write
them as a +- bi for real numbers a and b.
Evidence Tables:
Integrative Evidence Statements
Evidence
Statement
Evidence Statement Text
Key
A.Int.1
Solve equations that require seeing
structure in expressions.
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Seeing Structure in Expressions
Arithmetic with Polynomials and Rational Expressions
Creating Equations
Reasoning with Equations and Inequalities
Evidence Tables:
Integrative Evidence Statements
Evidence
Statement
Evidence Statement Text
Key
HS-Int.2
Solve multi-step mathematical
problems with degree of difficulty
appropriate to the course that require
analyzing quadratic functions and/or
writing and solving quadratic
equations.
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Evidence Tables:
Sub-claim C Evidence Statement
Evidence
Evidence Statement Text
Statement Key
HS.C.12.1
Construct, autonomously, chains of reasoning that will
justify or refute propositions or conjectures about
functions.
Content scope: F-IF.8a
F-IF. Analyze functions using different representations.
8. Write a function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a
quadratic function to show zeros, extreme values, and symmetry of
the graph, and interpret these in terms of a context.
Evidence Tables:
Sub-claim D Evidence Statement: HS.D.2-9
Evidence
Statement
Evidence Statement Text
Key
HS.D.2-9
Solve multi-step contextual word problems with
degree of difficulty appropriate to the course,
requiring application of course-level knowledge
and skills articulated in the following standards
but limited to linear and quadratic functions:
F-BF.1a, F-BF.3, A-CED.1, A-SSE.3,F-IF.4-6,
and F-IF.7.
Evidence Tables:
Sub-claim D Evidence Statement: HS.D.2-9
F-BF.1: Build a function that models a relationship between two quantities.
1. Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation
from a context.
F-BF.3: Build new functions from existing functions.
3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and
f(x + k) for specific values of k (both positive and negative); find the value of k
given the graphs. Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing even and odd
functions from their graphs and algebraic expressions for them.
A-CED.1:Create equations that describe numbers or relationships.
1. Create equations and inequalities in one variable and use them to solve
problems. Include equations arising from linear and quadratic functions,
and simple rational and exponential functions.★
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Evidence Tables:
Sub-claim D Evidence Statement: HS.D.2-9
F-IF.4-6 Interpret functions that arise in applications in terms of the context
4. For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing
key features given a verbal description of the relationship. Key features include:
intercepts; intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end behavior; and
periodicity.★
5. Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. For example, if the function h(n) gives the
number of person-hours it takes to assemble n engines in a factory, then the
positive integers would be an appropriate domain for the function.★
6. Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change
from a graph.★
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Evidence Tables:
Sub-claim D Evidence Statement: HS.D.2-9
F-IF.7 Analyze functions using different representations.
Graph functions expressed symbolically and show key features of the graph, by
hand in simple cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and
minima.★
b. Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions.★
c. Graph polynomial functions, identifying zeros when suitable factorizations are
available, and showing end behavior.★
d. Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.★
e. Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude.★
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Familiarizing Yourself with the Evidence Tables
1.Tally the number of evidence statements
for each of the listed topics.
2.Tally the number of evidence statements
for each listed domain.
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Connecting the Evidence Tables to PARCC Prototypes
Task #1: Speed
CCSS: ______
Claims: _____
Type: ____
PBA/EOY
Evidence Key:
___________
Instructional Uses
• To see ways to combine standards naturally
when designing instructional tasks
• To determine and create instructional
scaffolding (to think through which
individual, simpler skills can be taught first
to build to more complex skills)
• To develop rubrics and scoring tools for
instructional tasks
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Questions?
Contact Carrie Piper, Senior Advisor, PARCC Mathematics
cpiper@achieve.org
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