parcc claims structure: mathematics the purposes of the parcc mathematics assessments, the major...

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 E: Fluency in applicable grades (3-6)

The student demonstrates fluency as set forth in the Standards for Mathematical

Content in her grade.

PARCC Claims Structure: Mathematics

Sub-Claim C: Highlighted Practices

MP.3,6 with Connections to Content3

(expressing mathematical reasoning)

The student expresses grade/course-level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others, and/or attending to precision

when making mathematical statements.

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).

1

For the purposes of the PARCC Mathematics assessments, the Major Content in a grade/course is determined by that grade level’s Major Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. Note that tasks on PARCC assessments providing evidence for this claim will sometimes require the student to apply the knowledge, skills, and understandings from across several Major Clusters.

2

The Additional and Supporting Content in a grade/course is determined by that grade level’s Additional and Supporting Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. 3

For 3 – 8, Sub-Claim C includes only Major Content. For High School, Sub-Claim C includes Major, Additional and Supporting Content.

PARCC Mathematics Task Types

Selected Evidence Statement Keys, Texts, and Clarifications: Grade 3

Evidence

Statement Key Evidence Statement Text Clarifications MP

3.OA.1 Interpret products of whole numbers, e.g., interpret 5 7

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 .

i) Tasks involve interpreting products in terms of equal groups,

arrays, area, and/or measurement quantities. For more information

see CCSS Table 2, p. 89.

ii) Tasks do not require students to interpret products in terms of

repeated addition, skip-counting, or jumps on the number line.

iii) The italicized example refers to describing a context. But

describing a context is not the only way to meet the standard. For

example, another way to meet the standard would be to identify

contexts in which a total can be expressed as a specified product.

4, 2

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 problem.

i) All products come from the harder three quadrants of the times

table ( where and/or ).

ii) 50% of tasks involve multiplying to find the total number (equal

groups, arrays); 50% involve multiplying to find the area.

iii) For more information see Table 2, p. 89 of the CCSS and

Table 3, p. 23 of Progression for Operations and Algebraic

Thinking.

1, 4

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.

i) Tasks do not involve the number line.

ii) Tasks are limited to fractions with denominators 2, 3, 4, 6 and 8.

(See footnote CCSS, p. 24)

iii) The explanation aspect of 3.NF.3 is not assessed here.

5

3.C.3-1 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 and 3.NF.3d.

i) Tasks may present realistic or quasi-realistic images of a

contextual situation (e.g., a drawing of a partially filled graduated

cylinder). However, tasks do not provide the sort of abstract

drawings that help the student to represent the situation

mathematically (e.g., a number line diagram or other visual fraction

model).

ii) Grade 3 expectations in this domain are limited to fractions with

denominators 2, 3, 4, 6, and 8. (See footnote CCSS, p. 24)

iii) For fractions equal to a whole number, values are limited to 0,

1, 2, 3, 4, and 5.

3, 5, 6

3.D.2 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.OA.B,

2.NBT.A, B, and/or 2.MD.B.

Tasks may have scaffolding if necessary in order to yield a degree

of difficulty appropriate to Grade 3.

4

5 7

a b 5a 5b

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf


http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf





Per the PARCC Calculator Policy, PARCC mathematics assessments for Grades 3 – 5 will not allow for calculator usage.

Evidence

Statement Key Evidence Statement Text Clarifications MP

3.NF.A.Int.1 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.

i) Whole numbers are limited to 0, 1, 2, 3, 4, 5. Fraction

denominators are limited to 2, 3, 4.

2, 4, 5

3.Int.2 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

i. Addition, subtraction, multiplication and division situations in

these problems may involve any of the basic situation types with

unknowns in various positions (see CCSS Table 1, p. 88 and Table

2, p. 89 and the Progression document for Operations and

Algebraic Thinking.

1, 4





Evidence

Statement Key Evidence Statement Text Clarifications MP Calculator

7.NS.1d Apply and extend previous understandings of addition and

subtraction to add and subtract rational numbers; represent

addition and subtraction on a horizontal or vertical number

line.

d. Apply properties of operations as strategies to add and

subtract rational numbers.

i) Tasks do not have a context.

ii) Tasks are not limited to integers.

iii) Tasks may involve sums and differences of 2 or 3

rational numbers.

iv) Tasks require students to represent addition and

subtraction on a horizontal or vertical number line or

compute a sum or difference, or demonstrate

conceptual understanding for example by producing or

recognizing an expression equivalent to a given sum or

difference. For example, given the sum 8.1 7.4, the

student might be asked to recognize or produce the

equivalent expression (8.1 7.4).

7, 5 No

7.NS.2a-1

Apply and extend previous understandings of

multiplication and division and of fractions to multiply and

divide rational numbers.

a. Understand that multiplication is extended from

fractions to rational numbers by requiring that operations

continue to satisfy the properties of operations, particularly

the distributive property, leading to products such as

1 1 1 and the rules for multiplying signed

numbers.


ii) Tasks are not computation tasks but rather require

students to demonstrate conceptual understanding, for

example by providing students with a numerical

expression and requiring students to produce or

recognize an equivalent expression using properties of

operations, particularly the distributive property. For

example, given the expression 3 6 4 3 , the

student might be asked to recognize that the given

expression is equivalent to 3 6 4 3 3 .

7 No

7.NS.3 Solve real-world and mathematical problems involving the

four operations with rational numbers.

i) Tasks are one-step word problems.

ii) Tasks sample equally between addition/subtraction

and multiplication/division.

iii) Tasks involve at least one negative number.

iv) Tasks are not limited to integers.

1, 4 No


Evidence


7.C.4 Base explanations/reasoning on a coordinate plane

diagram (whether provided in the prompt or constructed

by the student in her response).

Content Scope: Knowledge and skills articulated in

7.RP.A.

None 2, 3,

5, 6

Yes

7.D.1 Solve multi-step contextual word problems with degree of

difficulty appropriate to grade 7, requiring application of

knowledge and skills articulated in 7.RP.1, 2; 7.NS.1, 2, 3;

and 7.EE.1, 3, 4.

Tasks may have scaffolding if necessary in order to

yield a degree of difficulty appropriate to grade 7.

4, 1,

2, 5,

7

Yes

Selected Evidence Statement Keys, Texts, and Clarifications: Algebra 1

Evidence


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.

See illustrations for F-IF.2 at

http://illustrativemathematics.org

6, 7 Item

Specific

A-SSE.2-4 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.

i) Example: Factor completely 2 21 ( 1)x x . (A first

iteration might give 2( 1)( 1) ( 1)x x x , which could

be rewritten as ( 1)( 1 1)x x x on the way to

factoring completely as 2 ( 1)x x . Or the student might

first expand as 2 21 2 1x x x , rewriting as

22 2x x then factoring as 2 ( 1)x x .

ii) Tasks do not have a context.

7, 1 Neutral

A-REI.4b-1 Solve quadratic equations in one variable.

b) Solve quadratic equations with rational number

coefficients by inspection (e.g., for 2

49x ), taking

square roots, completing the square, the quadratic formula

and factoring, as appropriate to the initial form of the

equation.

i) Tasks should exhibit variety in initial forms. Examples of

quadratic equations with real solutions: 249t , 2

3 4a ,

27 x , 2

0r , 21 1

2 5y , 2

8 15 0y y , 22 16 30 0x x ,

22 1p p , 2

4t t , 27 5 3 0x x ,

3( 1)

4c c c ,

2(3 2) 6 4x x

ii) Methods are not explicitly assessed; strategy is assessed

indirectly by presenting students with a variety of initial

forms.

iii) For rational solutions, exact values are required. For

irrational solutions, exact or decimal approximations may be

required.

iv) Prompts integrate mathematical practices by not

indicating that the equation is quadratic. (E.g., “Find all real

solutions of the equation 2

4t t ”…not, “Solve the quadratic

equation 2

4t t .”)

7, 5 Item

Specific

http://illustrativemathematics.org/


Evidence


A.Int.1 Solve equations that require seeing structure in

expressions.


ii) Equations simplify considerably after appropriate

algebraic manipulations are performed. For example, if 2 2

24 10 ( 5)x x p x , then find the value of p;

solve 2(3 2) 6 4x x .

7, 1 No

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.


ii) Exact answers may be required or decimal

approximations may be given. Students might choose

to take advantage of the graphing utility to find

approximate answers or clarify the situation at hand.

iii) Some examples:

Given the function 2( )f x x x , find all values of k

such that (3 ) (3)f k f . (Exact answers are

required.)

Find a value of c so that the equation 22 1 0x cx

has a double root. Give an answer accurate to the tenths

place.

1, 5,

6

Yes


Evidence


HS.C.12.1 Construct, autonomously, chains of reasoning that will

justify or refute propositions or conjectures about

functions.

Content scope: F-IF.8a

i) Tasks involve using algebra to prove properties of

given functions. For example, prove algebraically that

the function ( ) ( 1)h t t t has minimum value 1/4;

prove algebraically that the graph of 2 1

( )4

g x x x

is symmetric about the line 1

2x ; prove that 2

1x is

never less than 2x .

ii) Scaffolding is provided to ensure tasks have

appropriate level of difficulty. (For example, the

prompt could show the graphs of 21x and 2x on

the same set of axes, and say, “From the graph, it looks

as if 21x is never less than 2x . In this task you

will use algebra to prove it.” And so on, perhaps with

additional hints or scaffolding.

3 Yes

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/

i) F-BF.1a is the primary content; other listed content

elements may be involved in tasks as well.

4, 2 Yes

Evidence Statement Topic Tally: Grade 3

Tally the number of evidence statements for each of the following topics (some evidence

statements may apply to multiple topics).

Note: the number of evidence statements is not equal to the number of questions on each exam.

Topic PBA EOY

Add/subtract whole numbers

Multiply whole numbers

Divide whole numbers

Fractions

Word problems

Area

Other

Tally the number of evidence statements for each of the following domains (some evidence

statements may apply to multiple topics):


Domain PBA EOY

Operations and Algebraic Thinking (OA)

Number and Operations in Base Ten (NBT)

Numbers and Operations – Fractions (NF)

Measurement and Data (MD)

Geometry (G)

Grade 2

PARCC Prototype Tasks: Grade 3

Task #1: Fluency:

Click on all the equations that are true.

CCSS(s): __________________________________

Claim(s) supported: _________ Type: _________

EOY Evidence Statement Key(s): __________________________________

Task #2: Fractions on a Number Line

CCSS(s): __________________________________


EOY Evidence Statement Key(s): __________________________________


Task #3: The Field

CCSS(s): __________________________________

Part a:


PBA/EOY Evidence Statement Key(s): __________

Part b-question 1:

Claim(s) supported: _____Type: _________

PBA/EOY Evidence Statement Key(s):

__________

Part b-question 2:

Claim(s) supported: _____Type: _____

PBA Evidence Statement Key(s): _______


Task #4: Flower Gardens

Part a-question 1:

CCSS(s): __________________________

Claim(s) supported: _____Type: ________


__________

Part a-question 2:

CCSS(s): ___________________________

Claim(s) supported: _____Type: _________

EOY Evidence Statement Key(s):

__________

Part a


Parts b and c:

CCSS(s): __________________________________



Part b

Part c


Part a

Task #5: Fractions on the Number Line

Part a:

CCSS(s): ____________

Claim(s) supported: _______ Type: _______EOY Evidence Statement Key(s):___________

Parts b and c:

CCSS(s): ____________

Claim(s) supported: _______ Type: _______

PBA Evidence Statement Key(s):___________EOY Evidence Statement Key(s):___________

Part b

Part c


Part d-question 1:

CCSS(s): ____________


PBA Evidence Statement Key(s):___________

EOY Evidence Statement Key(s):___________

Part d-question 2 and part e:

CCSS(s): ____________


PBA Evidence Statement Key(s):___________

Part d

Part e

Part d-question 2


Task #6: Mariana’s Fractions

Part a:

CCSS(s): ____________

Claim(s) supported: _______ Type: _______ EOY Evidence Statement Key(s):___________

Parts b and c:

CCSS(s): ____________


Part a

Part b

Part c


Part d:

CCSS(s): ____________

Claim(s) supported: _______ Type: _______ PBA Evidence Statement Key(s):___________

Part e-question a:

CCSS(s): ____________


Part e-part b-part 1:

CCSS(s): ____________

Claim(s) supported: ____Type: _______


_________

Part e-part b-part 2:

CCSS(s): ____________

Claim(s) supported: ____Type: _______

EOY Evidence Statement Key(s):

_________

_

Part d

Part e-question a

Part e-question b


Task #7: School Mural

Part a:

CCSS(s): ________________________________

Claim(s) supported: _________ Type: _______

PBA/EOY Evidence Statement Key(s): ________

EOY Evidence Statement Key(s): ____________

Part a


Task #7: School Mural (continued)

Part b:

CCSS(s): ________________________________

Claim(s) supported: _________ Type: _______

PBA Evidence Statement Key(s): _____________

_________________________________________

Part b

Evidence Statement Topic Tally: Grade 7

Tally the number of evidence statements for each of the following (some evidence statements

may apply to multiple topics):


Topic PBA EOY

Proportional relationships

Add/subtract rational numbers

Multiply/divide rational numbers

Expressions/equations with variables

Geometry

Statistics




Domain PBA EOY

Ratios and Proportional Relationships (RP)

The Number System (NS)

Expressions and Equations (EE)

Geometry (G)

Statistics and Probability (SP)

Grade 6


Task #1: Speed

CCSS(s): _________________




Task #2: School Supplies

CCSS(s): _________________



Part b

Part a


Task #3: Anne’s Family Trip

CCSS(s): __________________________________


PBA/EOY Evidence Statement Key(s): __________________________________

(continued on next page)

Part a


Part b

Part c


Part b

Part a

Task #4: TV Sales

CCSS(s): __________________


EOY Evidence Statement Key(s): _______________

CCSS(s): __________________


PBA Evidence Statement Key(s): _______________


Task #5: Spicy Vegetables

CCSS(s): __________________


PBA/EOY Evidence Statement Key(s): _______________

Part a

Part b

Evidence Statement Topic Tally: Algebra 1

Tally the number of evidence statements for each of the following topics (some evidence

statements may apply to multiple topics).


Topic PBA EOY

Linear equations/functions

Quadratic equations/functions

Exponential functions

Other functions:

Square root, cube root, piecewise, absolute value,

rational, cubic with linear and quadratic roots

Polynomial expressions/equations

Inequalities

Other




Domain PBA EOY

Real Number System (N-RN)

Quantities (N-Q)

Seeing Structure in Expressions (A-SSE)

Arithmetic w/Polynomials and Rational Expression (A-APR)

Creating Equations (A-CED)

Reasoning w/Equations and Inequalities (A-REI)

Interpreting Functions (F-IF)

Building Functions (F-BF)

Linear, Quadratic, and Exponential Models (F-LE)

Interpreting Categorical and Quantitative Data (S-ID)

7th

/8th

grade

PARCC Prototype Tasks: Algebra 1

Task #1: Functions

CCSS(s): __________________________________


EOY Evidence Statement Key(s): ______________


Task #2: Seeing Structure in an Equation

CCSS(s): __________________________________



Task #3: Seeing Structure in a Quadratic Equation

CCSS(s): __________________________________


PBA/EOY Evidence Statement Key(

s): __________


Task #4: Quadratic Transformation

Part a

CCSS(s): ______________

Claim(s) supported: _____ Type: ________

EOY Evidence Statement Key(s): ________

Part a


Task #4: Quadratic Transformation (continued)

Part b-questions a and b

CCSS(s): ______________


EOY Evidence Statement Key(s): ________

Part b-question c


PBA Evidence Statement Key(s): ________

Part b


Task #5: Rabbit Populations

Part a:

CCSS(s): __________________________________



Part a


Task #5: Rabbit Populations (continued)

Part b:

CCSS(s): __________________________________



Part b


Task #5: Rabbit Populations (continued)

Part c:

CCSS(s): __________________________________



Part c


Task #6: Isabella’s Credit Card

CCSS(s): __________________



(continued on next page)

Part a


Task #6: Isabella’s Credit Card (continued)

Part b

Part c


Task #7: Golf Balls in Water

CCSS(s): _____________________________________


PBA Evidence Statement Key(s): _________________

Part a


Part b


Part c

PARCC Prototyping Project “Golf Balls in Water – High School”

Tom is doing an experiment adding golf balls to a glass jar containing water. The picture and the

table show what happens to the height of the water as Tom adds golf balls.

Part a:

Use the following options to complete the sentences and the equation below based on the results

of Tom’s experiment.

golf balls change glass jars water height 1.16

1.2 1.3 9.0 12.0 13.8

The height of the water changes at an average rate of about _______________centimeters per

golf ball. If these data were graphed with the number of golf balls as their independent variable,

the y-intercept for the graph would be about _______________centimeters. This means that for

zero _______________, the _______________is 9 centimeters. Tom’s table and graph can be

represented by the trend line with the equation y = _______________x+______________.

Part b:

There are several ways that Tom could modify the conditions of his experiment. What

modifications would increase the rate of change in the height of the water level with respect to

the number of golf balls? Select all that apply.

Use larger golf balls Add 5 cm of water to the glass jar

Decrease the diameter of the glass jar Drop the golf balls into the glass jar

two at a time

Drop the golf balls into the glass jar at a

faster rate

Number of golf balls, x Height of water in centimeters, y

0 9.0

1 10.2

2 11.5

3 12.7

4 13.8

PARCC Prototyping Project “Golf Balls in Water – High School”

Tom repeats his experiment with a different glass jar. The new glass jar, B, has a smaller

radius than the original glass jar, A.

Data from Experiment with Glass Jar A

Number of golf balls, x Height of water in centimeters, y

0 9.0

1 10.2

2 11.5

3 12.7

4 13.8

Tom forgot to write down the initial height of the water in glass jar B, but he measured the

water height at 9 centimeters after adding two golf balls.

Question a: When Tom creates graphs of the data from both experiments, how will the

y-intercepts of the graphs be different for glass jar A versus glass jar B? Explain how you

know.

Question b: How will the rate of change in the experiment using glass jar B be different than

the rate of change in the experiment using glass jar A? Explain how you know.

Question c: Suppose glass jar B has a water height of 5 centimeters with no golf balls, and

the water height increases at a rate of 2 centimeters per golf ball added. Tom continues to add

golf balls to each glass jar. He discovers that there is a number of golf balls at which the

height of the water in each glass jar is the same. How many golf balls will be in each jar

when the water in each reaches the same height?

parcc claims structure: mathematics the purposes of the parcc mathematics assessments, the major...

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