Reading the Mathematics Evidence Tables 1

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. 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. 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. Claims Structure: Mathematics 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. 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).

Overview of PARCC Mathematics Task Types Task TypeDescription 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 Key Evidence Statement Text 3.OA.1Interpret 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 Statement Key Evidence Statement Text 3.OA.3-1Use 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 Statement Key Evidence Statement Text 3.NF.3a-1Explain 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 Evidence Statement Text 3.C.3-1Base 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 Evidence Statement Text 3.D.2Solve 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.

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– 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: Sub-claim D Evidence Statement: 3.D.2 (cont.)

Evidence Tables: Integrated Evidence Statement: 3.NF.A.Int.1 Evidence Statement Key Evidence Statement Text 3.NF.A.Int.1In 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 Evidence Statement Text 3.Int.2Solve 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.

1.Use place value understanding to round whole numbers to the nearest 10 or 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. Evidence Tables: Integrated Evidence Statement: 3.Int.2 (cont.)

Familiarizing Yourself with the Evidence Tables 16 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.

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