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 Review o Type I Items o 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-Year Component (EOY) PBA and EOY Combined = Total Score

PARCC Model Content Frameworks

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 Content 1 with Connections to Practices The student solves problems involving the Major Content 1 for her grade/course with connections to the Standards for Mathematical Practice points Sub-Claim B: Additional & Supporting Content 2 with Connections to Practices The student solves problems involving the Additional and Supporting Content 2 for her grade/course with connections to the Standards for Mathematical Practice points Sub-Claim C: Highlighted Practices MP.3,6 with Connections to Content 3 (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 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 All points from fluency items in Grades 3 – 6 were reallocated to Sub-Claim A or Sub-Claim B.

Evidence Tables Several 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 from Exact Standard Language

Integrative Evidence Statement

Sub-claim C Evidence Statements

Sub-Claim D Evidence Statements

Mock Item Review Purpose Life Cycle of a Task Task Types Item Review Process Resources/Materials o Evidence Tables o CCSS for Mathematical Content o Calculator o Guiding Questions Item Review

Life Cycle of a Task Item DevelopmentItem ReviewTest ConstructionField TestRangefindingHandscoringData ReviewOperational

Task Types Task TypeIIIIII Assesses concepts, skills, and procedures mathematical reasoning modeling and applications Requires a 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-ClaimsA and BCD Math Practices AllMP3, MP6MP4 Scoring Machine- and Hand-Scored Components Hand- and Machine-Scored Components Hand- and Machine-Scored Components Test Component PBA and EOYPBA

Item Review Process Step 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 Outcomes Task Number ApprovedApproved with EditsRejected. Reasoning

Evidence Statement Text Apply the Pythagorean Theorem in a simple planar case. Clarifications i) 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 #1Course: Grade 8 Evidence Statement: 8.G.7-1 EOY Calculator Code: YES Math Practice: Additional ContentPoints: 1

Item #1Course: Grade 8 Evidence Statement: 8.G.7-1 EOY Calculator Code: YES Math Practice: Additional ContentPoints: 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 #2Course: Grade 6 Evidence Statement: 6.RP.2 PBA & EOY Calculator Code: NO Math Practice: 2 Major ContentPoints: 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 #2Course: Grade 6 Evidence Statement: 6.RP.2 PBA & EOY Calculator Code: NO Math Practice: 2 Major ContentPoints: 1 KEY: C

Evidence Statement Text Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Clarifications i) 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 #3Course: Grade 7 Evidence Statement: 7.EE.1 PBA & EOY Calculator Code: NO Math Practice: 7 Major ContentPoints: 1

Item #3Course: Grade 7 Evidence Statement: 7.EE.1 PBA & EOY Calculator Code: NO Math Practice: 7 Major ContentPoints: 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.( )x

Task Types II and III Task TypeIIIII 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-ClaimsCD Math Practices MP3, MP6MP4 Scoring Hand- and Machine- Scored Components Test Component PBA

Evidence Statement Text Present 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 = , 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 #4Course: Grade 6 Evidence Statement: 6.C.8.2 PBA Calculator Code: YES Math Practice: 2, 3, 6 Major ContentPoints: 4

Item #4Course: Grade 6 Evidence Statement: 6.C.8.2 PBA Calculator Code: YES Math Practice: 2, 3, 6 Major ContentPoints: 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)

Item #4Course: Grade 6 Evidence Statement: 6.C.8.2 PBA Calculator Code: YES Math Practice: 2, 3, 6 Major ContentPoints: 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 KEY

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 Clarifications Task may have scaffolding if necessary in order to yield a degree of difficulty appropriate to Grade 8. Item #5Course: Grade 8 Evidence Statement: 8.D.2 PBA Calculator Code: YES Math Practice: 4, 1, 2, 5, 7 Content: All LevelsPoints: 6

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

Item 5 KEY

Record Task Outcomes ask Number ApprovedApproved 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 5 Reject: 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?