Using PARCC Tools to Develop Assessments in Grades 3  5 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 MP3, 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 18 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 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 Multiply multi-digit whole numbers using the standard algorithm. Clarifications i) Tasks do not have a context. ii) Tasks assess accuracy. iii) The given factors are such as to require an efficient/standard algorithm (e.g., 726 × 48). Factors in the task do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 725 × 40). iv) For purposes of assessment, the possibilities are 1-digit x 2-digit, 1- digit x 3-digit, 2-digit x 3-digit, or 2-digit x 4-digit Item #1Course: Grade 5 Evidence Statement: 5.NBT.5-1 PBA Calculator Code: Math Practice: Major ContentPoints: 1

Enter your answer in the box. 3,472  529 = Item #1Course: Grade 5 Evidence Statement: 5.NBT.5-1 PBA Calculator Code: Math Practice: Major ContentPoints: 1 KEY: 1,836,688

Evidence Statement Text Fluently multiply multi-digit whole numbers using the standard algorithm. Clarifications i) Tasks assess accuracy. ii) The given factors are such as to require an efficient/standard algorithm (e.g., 726 × 4871). Factors in the task do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 7250 × 400). iii) Tasks do not have a context. iv) For purposes of assessment, the possibilities are 1-digit x 2-digit, 1- digit x 3-digit, 2-digit x 3-digit, or 2-digit x 4-digit v) Tasks are not timed. Item #1Course: Grade 5 Evidence Statement: 5.NBT.5 EOY Calculator Code: Math Practice: Major ContentPoints: 1

Evidence Statement Text Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Clarifications None Item #2Course: Grade 4 Evidence Statement: 4.MD.3 EOY Calculator Code: Math Practice: 2, 5 Supporting ContentPoints: 1

A poster is in the shape of a rectangle. The poster has a length of 2.5 feet and an area of 10 square feet. Complete the sentence describing the width and perimeter of the poster. Select from the drop-down menus to correctly complete the sentence. The width of the poster is [IC_1] and the perimeter of the poster is [IC_2]. [IC_1] [IC_2] A.4 feet A. 5 feet B.7.5 feet B. 8 feet C feet C. 15 feet D. 25 feet D. 20 feet Item #2Course: Grade 4 Evidence Statement: 4.MD.3 EOY Calculator Code: Math Practice: 2, 5 Supporting ContentPoints: 1 KEY: [IC_1]: A ; [IC_2]: C

Evidence Statement Text Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides) and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Clarifications i) A trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.” Item #3Course: Grade 3 Evidence Statement: 3.G.1 EOY Calculator Code: Math Practice: Supporting ContentPoints: 1

Shapes may be categorized because of the attributes they share. Categorize the shapes shown as an Irregular Shape or a Regular Shape. Drag and drop each shape into the correct box. Irregular ShapeRegular Shape Item #3Course: Grade 3 Evidence Statement: 3.G.1 EOY Calculator Code: Math Practice: Supporting ContentPoints: 1 KEY: Irregular Shape: A, D, E, G ; Regular Shape: B, C, F

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 Distinguish correct explanations/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed ‘student’ reasoning is presented and the task is to correct and improve it.) Content scope: Knowledge and skills articulated in 5.NF.1-1, 5. NF.1-2, 5.NF.1-3, 5.NF.1-4, 5.NF.1-5 Clarifications None Item #4Course: Grade 5 Evidence Statement: 5.C.7.3 PBA Calculator Code: Math Practice: 3, 6 Major ContentPoints: 3

Item #4Course: Grade 5 Evidence Statement: 5.C.7.3 EOY Calculator Code: Math Practice: 3, 6 Major ContentPoints: 3

Item 4 KEY

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.OA.B, 2.NBT, and/or 2.MD.B. Clarifications i) Tasks may have scaffolding if necessary in order to yield a degree of difficulty appropriate to Grade 3. ii) Multi-step problems must have at least 3 steps. Item #5Course: Grade 3 Evidence Statement: 3.D.2 PBA Calculator Code: Math Practice: 4 Major ContentPoints: 6

This table shows the price of each item that James bought in expanded form. Part A. James bought 1 pair of pants, 1 backpack, and 1 t-shirt. What equation can be used to find the total amount of money, m, that James spent on the three items? A. m = B. m = C. m = D. m = Part B. Did James spend more on the pair of pants or on the backpack? Show your work or explain your answer. Enter your answer and your work or explanation in the space provided.

Part C. Shauna bought two items at a store. The cost of each item is listed in expanded form. The cost, in dollars, of a dress was 4 tens + 18 ones. The cost, in dollars, of a pair of shoes was 3 tens + 9 ones. Explain how to rewrite the cost of each item in standard form. How much more money did Shauna spend on the dress than the shoes? Write your answer in standard form. Enter your explanation, your answer, and your work in the space provided.

Item 5 KEY Student response includes each of the following 6 elements. Correct answer for Part A Correct answer for Part B Correct work or explanation for Part B Correct explanation for rewriting expanded form as standard form for Part C Correct difference for Part C Correct work or explanation for difference for Part C 6-point Sample Student Response Part A. (1 point) Student selects C. Part B. (2 points) Student states that the boy spent the same amount on the pair of pants as he did on the backpack. He explains that, for the pair of pants, the sum of 3 tens and 9 ones is 39. He further explains that, for the backpack, the sum of 2 tens and 19 ones is the same as 3 tens and 9 ones as there is a ten in the 19 ones. Thus, both the pair of pants and the backpack cost $39. Part C. (3 points) Students explains Dress: 4 X X 1 = = X X 1 = = = 58 Shoes: 3 X X 1 = = 39 Student shows that Shauna spent $19 more on the dress than the shoes: 58 – 39 = = = 19 6 points: Student response includes all 6 of the above elements. 5 points: Student response includes 5 of the above elements 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 elements 1 point: Student response includes 1 of the above elements. 0 points: Student response is incorrect or irrelevant.

Record Task Outcomes Task Number ApprovedApproved with EditsRejected. Reasoning 1 Numbers in this item are outside of limits 2 Item is mathematically incorrect 3Item is off grade level 4accept 5 Probably edit – redundant

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?