Reading the Mathematics
Evidence Tables
1
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
•
•
•
•
•
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
•
•
•
•
•
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
•
•
•
•
•
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
Evidence Tables:
Exact Standards Language
Evidence
Statement
Evidence Statement Text
Key
3.OA.1
Interpret products of whole numbers,
e.g., interpret 5x7 as the total number of
objects in 5 groups of 7 objects each.
For example, describe a context in
which a total number of objects can be
expressed as 5x7.
Evidence Tables:
Derived from Exact Standards
Evidence
Evidence Statement Text
Statement Key
3.OA.3-1
Use multiplication within 100 (both factors less than or
equal to 10) to solve word problems in situations
involving equal groups, arrays, or area, e.g., by using
drawings and equations with a symbol for the unknown
number to represent the problems.
3.OA.3: Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and measurement
quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
Evidence Tables:
Derived from Exact Standards
Evidence
Evidence Statement Text
Statement Key
3.NF.3a-1
Explain equivalence of fractions in special cases and
compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they
are the same size.
3.NF.3a:
Explain equivalence of fractions in special cases, and compare fractions
by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same
size, or the same point on a number line.
Evidence Tables:
Sub-claim C Evidence Statement: 3.C.3-1
Evidence
Statement Key
3.C.3-1
Evidence Statement Text
Base arithmetic explanations/reasoning on concrete referents
such as diagrams (whether provided in the prompt or constructed
by the student in her response), connecting the diagrams to a
written (symbolic) method.
Content Scope: Knowledge and skills articulated in 3.NF.3b
3.NF.3b: Explain equivalence of fractions in special cases, and compare
fractions by reasoning about their size.
b. Recognize and generate simple equivalent fractions,
e.g., 1/2 =2/4, 4/6 =2/3. Explain why the fractions are
equivalent, e.g., by using a visual fraction model.
Evidence Tables:
Sub-claim D Evidence Statement: 3.D.2
Evidence
Statement Key
3.D.2
Evidence Statement Text
Solve multi-step contextual problems with degree of difficulty
appropriate to Grade 3, requiring application of knowledge and
skills articulated in 2.OA.A, 2.NBT.A,B, and/or 2.MD.B.
2.OA.A:
Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 100 to solve one- and two-step word
problems involving situations of adding to, taking from, putting together,
taking apart, and comparing, with unknowns in all positions, e.g., by using
drawings and equations with a symbol for the unknown number to represent
the problem.
Evidence Tables:
Sub-claim D Evidence Statement: 3.D.2 (cont.)
2.NBT.A
Understand place value.
1. Understand that the three digits of a three-digit number represent amounts of
hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens—called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one,
two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens
and 0 ones).
2. Count within 1000; skip-count by 5s, 10s, and 100s.
3. Read and write numbers to 1000 using base-ten numerals, number names, and
expanded form.
4. Compare two three-digit numbers based on meanings of the hundreds, tens, and
ones digits, using ¡, =, and symbols to record the results of comparisons.
Evidence Tables:
Sub-claim D Evidence Statement: 3.D.2 (cont.)
2.NBT.B
Use place value understanding and properties of operations to add and subtract.
5. Fluently add and subtract within 100 using strategies based on place value, properties
of operations, and/or the relationship between addition and subtraction.
6. Add up to four two-digit numbers using strategies based on place value and properties
of operations.
7. Add and subtract within 1000, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method. Understand that in adding or
subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and
tens, ones and ones; and sometimes it is necessary to compose or decompose tens or
hundreds.
8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10
or 100 from a given number 100–900.
9. Explain why addition and subtraction strategies work, using place value
and the properties of operations.
Evidence Tables:
Sub-claim D Evidence Statement: 3.D.2 (cont.)
2.MD.B
Relate addition and subtraction to length.
5. Use addition and subtraction within 100 to solve word problems
involving lengths that are given in the same units, e.g., by using
drawings (such as drawings of rulers) and equations with a symbol for
the unknown number to represent the problem.
6. Represent whole numbers as lengths from 0 on a number line
diagram with equally spaced points corresponding to the
numbers 0, 1, 2, . . . , and represent whole-number sums and differences
within 100 on a number line diagram.
Evidence Tables:
Integrated Evidence Statement: 3.NF.A.Int.1
Evidence
Statement Key
3.NF.A.Int.1
Evidence Statement Text
In a contextual situation involving a whole number and
two fractions not equal to a whole number, represent all
three numbers on a number line diagram then choose the
fraction closest in value to the whole number.
Develop understanding of fractions as numbers.
1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is
partitioned into b equal parts; understand a fraction a/b as the quantity
formed by a parts of size 1/b.
2. Understand a fraction as a number on the number line; represent fractions
on a number line diagram.
3. Explain equivalence of fractions in special cases, and compare fractions by
reasoning about their size.
Evidence Tables:
Integrated Evidence Statement: 3.Int.2
Evidence
Statement
Key
3.Int.2
Evidence Statement Text
Solve two-step word problems using the four
operations requiring a substantial addition,
subtraction, or multiplication step, drawing on
knowledge and skills articulated in 3.NBT.
See 3.OA.8, 3.NBT.2, and 3.NBT.3
3.NBT: Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Evidence Tables:
Integrated Evidence Statement: 3.Int.2 (cont.)
3.NBT: Use place value understanding and properties of operations
to perform multi-digit arithmetic.
1. Use place value understanding to round whole numbers to the
nearest 10 or 100.
2. Fluently add and subtract within 1000 using strategies and algorithms
based on place value, properties of operations, and/or the relationship
between addition and subtraction.
3. Multiply one-digit whole numbers by multiples of 10 in the
range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value
and properties of operations.)
Evidence Tables:
Integrated Evidence Statement: 3.Int.2 (cont.)
3.OA.8:
Solve problems involving the four operations, and
identify and explain patterns in arithmetic.
8. Solve two-step word problems using the four
operations. 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.
Familiarizing Yourself with the Evidence Tables
1.Select either Grade 3 or Grade 7.
2.Tally the number of evidence statements
for each of the listed topics.
3.Tally the number of evidence statements
for each listed domain.
16
Connecting the Evidence Tables to PARCC Prototypes
Task #1: Fluency:
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): _______________
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
Questions?
Contact Carrie Piper, Senior Advisor, PARCC Mathematics
cpiper@achieve.org