Using PARCC Tools to Develop

Assessments in Grades 6-8

A Workshop Prepared for the Rhode Island Department of Education

by Monique Maynard November 2014

Goals

By utilizing resources from the PARCC assessment system, participants will be prepared to review and evaluate assessment items.

Agenda• Purpose

• PARCC Design

• Tools: Model Content Frameworks, Sub-Claims, and Evidence Tables (Implications for Assessment Design)

• Mock Item Reviewo Type I Itemso Type II and III Items

PARCC Assessment System

Summative Components: Mathematics

Solving multi-step problems that require reasoning and address real world situations

Demonstrating understanding of concepts, fluency, and application of knowledge

Performance-Based Component

(PBA)

End-of-YearComponent

(EOY)

PBA and EOY Combined = Total Score

PARCC Model Content Frameworks

• Key Advances, Fluency Expectations, and Opportunities to Connect Mathematical Content and Mathematical Practices

• Major, Supporting, and Additional

• Key Advances and Fluency Expectations

Model Content Frameworks

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 PracticesThe student solves problems

involving the Major Content1 for her grade/course with

connections to the Standards for Mathematical Practice. 36 - 47

points

Sub-Claim B: Additional & Supporting Content2 with Connections to PracticesThe student solves problems involving the Additional and Supporting Content2 for her

grade/course with connections to the Standards for Mathematical

Practice.

9 - 20 points

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.

14 points

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).

Total Exam :82 points

12 points

Claims Structure*:

Mathematics – Grades 3 - 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 Sub-Claim C includes only Major Content. *Updated September 2014. All points from fluency items in Grades 3 – 6 were reallocated to Sub-Claim A or Sub-Claim B.

Evidence TablesSeveral types of evidence statements are being used to describe what a task should be assessing, including:

1. Those using exact standards language

2. Those transparently derived from exact standards language, e.g., by splitting a content standard

3. Integrative evidence statements that express plausible direct implications of the standards without going beyond the standards to create new requirements

4. Sub-claim C & D evidence statements, which put MP.3, 4, 6 as primary with connections to content

Structure of the Evidence Tables

Exact Standards Language

Derived fromExact Standard Language

Integrative Evidence Statement

Sub-claim C Evidence Statements

Sub-Claim DEvidence Statements

Mock Item Review• Purpose• Life Cycle of a Task• Task Types• Item Review Process• Resources/Materials

o Evidence Tableso CCSS for Mathematical Contento Calculatoro Guiding Questions

• Item Review

Life Cycle of a Task

Item Development

Item Review

Test Construction

Field Test

Rangefinding

Handscoring

Data Review

Operational

Task TypesTask Type I II III

Assesses concepts, skills, and procedures

mathematical reasoning

modeling and applications

Requiresa balance of conceptual

understanding, fluency, and application

written arguments

and/or justifications,

critique of reasoning, or

precision

modeling and applications in

a real-world context

Sub-Claims

A and B C D

Math Practices All MP3, MP6 MP4

ScoringMachine- and Hand-ScoredComponents

Hand- andMachine-Scored

Components

Hand- andMachine-Scored

Components

Test Component

PBA and EOY PBA PBA

Item Review ProcessStep 1. Read the item independently.

Step 2. Ensure that the item meets the evidence statement (e.s.) and standard (std.).

o If the item aligns, continue to Step 3.o If the item does not align, consider two options:

(i) if the item can be edited to align with the indicated e.s./std., note how to do so OR

(ii) align the item, as is, to a more appropriate evidence statement.o If the item cannot be aligned, reject the item.

Step 3. Review the item in terms of other criteria (Guiding Questions). Make notes to reflect needs for revision.

Guiding Questions

• Is the task worthy of high-quality instruction?• Is the task mathematically correct and free of

errors?• Is the task (wording and art) clear, cohesive,

concise, accurate, grade-level appropriate, and free of internal clueing?

• For Type II and Type III tasks only, is the scoring guide/rubric clear, correct, and aligned with the expectations for performance that are expressed in the task?

Record Task OutcomesTask

NumberApprove

dApproved with

EditsRejected. Reasoning

1

2

3

4

5

Evidence Statement TextApply the Pythagorean Theorem in a simple planar case.

Clarificationsi) Tasks have “thin context” or no context. ii) Tasks require students to find one side of a right triangle in the plane, given the other two sides. iii) In 50% of tasks, the answer is a whole number and is to be given as a whole number. iv) In 50% of tasks, the answer is irrational and is to be given approximately to three decimal places. v) The testing interface can provide students with a calculation aid of the specified kind for these tasks.

Item #1 Course: Grade 8

Evidence Statement: 8.G.7-1

EOYCalculatorCode: YES

Math Practice:

Additional Content Points: 1

Item #1 Course: Grade 8

Evidence Statement: 8.G.7-1

EOYCalculatorCode: YES

Math Practice:

Additional Content Points: 1

KEY: 29

Evidence Statement Text Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

Clarifications i) Expectations for unit rates in this grade are limited to non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers.

Item #2 Course: Grade 6

Evidence Statement: 6.RP.2

PBA & EOYCalculatorCode: NO

Math Practice: 2 Major Content Points: 1

Steven is using 50 pages of filler paper to make a notebook for each of his 5 school subjects.

Which statement correctly describes the unit rate of filler paper to notebook?

A. There are 50 pages for each notebook.

B. There are 10 pages for each notebook.

C. There are 5 pages for each notebook.

D. There are 2 pages for each notebook.

Item #2 Course: Grade 6

Evidence Statement: 6.RP.2

PBA & EOYCalculatorCode: NO

Math Practice: 2 Major Content Points: 1

KEY: C

Evidence Statement TextApply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Clarificationsi) Tasks may involve issues of strategy, e.g., by providing a factored expression such as y(3 + x + k) and a fully expanded expression 3y + xy + ky, and requiring students to produce or identify a new expression equivalent to both (such as y(3 + x) + yk). ii) Tasks are not limited to integer coefficients.

Item #3 Course: Grade 7

Evidence Statement:

7.EE.1PBA & EOY

CalculatorCode: NO

Math Practice: 7 Major Content Points: 1

Item #3 Course: Grade 7

Evidence Statement:

7.EE.1PBA & EOY

CalculatorCode: NO

Math Practice: 7 Major Content Points: 1

KEY: A, B, C, D, E

Which of the expressions are equivalent to (2x + 1) + 5x?Select all that apply.

A. (x + x) + 1 +(x + x + x + x + x)

B. (2 + 5)x + 1

C. 7x + 1

D. 1 + 5x + 2x

E. 2x + (5x + 1)

F. (2 + 5 + 1)x

Task Types II and IIITask Type II III

Assesses mathematical reasoning

modeling and applications

Requires written arguments and/or justifications,

critique of reasoning, or

precision

modeling and applications in a

real-world context

Sub-Claims C D

Math Practices MP3, MP6 MP4

ScoringHand- and Machine-Scored Components

Hand- and Machine-Scored Components

Test Component PBA PBA

Evidence Statement TextPresent solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 + 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 6.EE.9

Clarifications

i) Tasks that involve writing an equation should not go beyond the equation types described in 6.EE.7 (x+p =q and px = q where p, q, and x are all nonnegative rational numbers).

Item #4 Course: Grade 6

Evidence Statement: 6.C.8.2

PBACalculatorCode: YES

Math Practice: 2, 3, 6 Major Content Points: 4

Item #4 Course: Grade 6

Evidence Statement:

6.C.8.2PBA

CalculatorCode: YES

Math Practice: 2, 3, 6 Major Content Points: 4

Brandon is making a new concrete walkway. Concrete is made using a combination of water and gravel. The amount of water he needs to mix the concrete is directly proportional to how much gravel he will use. This table compares the pounds of gravel used, g, to the quarts of water needed, w.

Pounds of Gravel (g) Quarts of Water (w)

15 6

30 12

40 16

Item #4 Course: Grade 6

Evidence Statement:

6.C.8.2PBA

CalculatorCode: YES

Math Practice: 2, 3, 6 Major Content Points: 4

Part A.

• Write an equation to represent the relationship between the quarts of water needed, w, to the pounds of gravel used, g. Explain how you used the information in the table to write your equation.

• Enter your equation and your explanation in the space provided.

Part B.

• Use the equation that you wrote in part A to determine how many quarts of water Brandon will need if he uses 215 pounds of gravel. Show or explain how you found your answer.

• Enter your answer and your work or explanation in the space provided.

Item 4 KEYStudent response includes each of the following 4 elements.

• Student indicates correct equation.• Student correctly justifies each component of the equation using data from the table.• Student correctly determines the number of quarts of water needed.• Student correctly shows his work or gives a correct explanation of how he solved the problem.

4-point Sample Student Response

Part A. (2 points)

1 point w = 2/5 g

1 point Student explains and/or demonstrates that the unit rate is needed as the rate of change in this equation. The student uses any pair of values from the table to find .

Part B. (2 points)

1 point 86

1 pointw = 2/5 gw = 2/5 (215)w= 430/5w= 86

4 points: Student response includes 4 of the above elements.3 points: Student response includes 3 of the above elements.2 points: Student response includes 2 of the above elements1 point: Student response includes 1 of the above elements.0 points: Student response is incorrect or irrelevant. Note: If student has an incorrect equation in Part A but correctly solves it and provides the needed work in Part B, the student is awarded two points.

Solve multi-step contextual problems with degree of difficulty appropriate to Grade 8, requiring application of knowledge and skills articulated in 7.RP.A, 7.NS.3, 7.EE, 7.G, and 7.SP.B

ClarificationsTask may have scaffolding if necessary in order to yield a degree of difficulty appropriate to Grade 8.

Item #5 Course: Grade 8

Evidence Statement:

8.D.2PBA

CalculatorCode: YES

Math Practice: 4, 1, 2, 5, 7

Content: All Levels

Points: 6

The circle graph shows the five most popular snacks of 120 people between the ages of 20 and 24.

Part A. What fractional amount of people like fruit? Show your work or explain your answer.

Enter your answer and work or explanation in the space provided.

Part B. If of the people who like tortilla chips indicated that they prefer them with salsa, how many actual people prefer tortilla chips with salsa? Show your work or explain your answer.Enter your answer and work or explanation in the space provided.

Part C. The publishers of the survey realized their computer incorrectly counted people whose favorite snack is an energy bar among the third whose favorite snack is chips. If the correct fractional amount of people who like chips is , what is the fractional change in the people whose favorite snack is chips? Show your work or explain your answer.

Enter your answer and work or explanation in the space provided.

Item 5 KEYStudent response includes each of the following 6 elements.

• Correct answer for Part A.• Correct work or explanation for Part A: consisting of (i) finding the correct the correct sum of the parts using a common denominator and (ii) the correct difference.• Correct answer for Part B • Correct work or explanation for Part B: consisting of (i) finding the part of the part and (ii) the portion of the whole.• Correct answer for Part C.• Correct work or explanation for Part C:

6-point Sample Student ResponsePart A. (2 points)1 point. Student indicates

1 point. Student (i) adds fractions upon finding a common denominator and (ii) then subtracts from 1, the whole.

Part B. (2 points) 1 point. Student indicates 20 people.1 point. Student (i) multiplies the part by the part and (ii) and then multiplies by the whole to find the actual number of people who prefer tortilla chips with salsa.

Part C. (2 points)1 point. Student indicates

1 point. Student (i) writes an equation to model the question and (ii) solves for the fractional change.

, where x is the change

6 points: Student response includes all 6 of the above elements.5 points: Student response includes 5 of the above elements4 points: Student response includes 4 of the above elements.3 points: Student response includes 3 of the above elements2 points: Student response includes 2 of the above elements1 point: Student response includes 1 of the above elements.0 points: Student response is incorrect or irrelevant.

Record Task Outcomesask

NumberApprove

dApproved with

EditsRejected. Reasoning

1

Item aligned to incorrect evidence statement - revise evidence statement key

2 Item has wrong key - correct the key

3 Accept as is

4 Accept as is

5Reject: circle graphs are not assessed in CCSS

Next Steps• What are your key take-aways from today’s

session?

• How will you communicate what you learned today?

• What protocols/structures can help you in your practice?

• What additional questions/concerns would you like addressed?