Report

Reading the Mathematics Evidence Tables 1 Claims Structure: Mathematics 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 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). Sub-Claim C: Highlighted Practices MP.3,6 with Connections to Content3 (expressing mathematical reasoning) The student expresses grade/courselevel appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others, and/or attending to precision when making mathematical statements. 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. Overview of PARCC Mathematics Task Types Task Type Description 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 3 For more information see PARCC Task Development ITN Appendix D. Evidence Statement: Exact Standards Language Evidence Statement Evidence Statement Text Key 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. 4 Evidence Statement: Derived from Exact Standards Language Evidence Statement Key A-SSE.2-4 Evidence Statement Text 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. Interpret the structure of expressions. 2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2 , thus recognizing it as a difference of squares that can be factored as (x2 - y2) (x2 + y2). Evidence Statement: Derived from Exact Standards Language Evidence Statement Key A-REI.4b-1 Evidence Statement Text Solve quadratic equations in one variable. b) Solve quadratic equations with rational number coefficients by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. A-REI.4b Solve quadratic equations in one variable. b) Solve quadratic equations with rational number coefficients by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a +- bi for real numbers a and b. Evidence Tables: Integrative Evidence Statements Evidence Statement Evidence Statement Text Key A.Int.1 Solve equations that require seeing structure in expressions. • • • • Seeing Structure in Expressions Arithmetic with Polynomials and Rational Expressions Creating Equations Reasoning with Equations and Inequalities Evidence Tables: Integrative Evidence Statements Evidence Statement Evidence Statement Text Key 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. 8 Evidence Tables: Sub-claim C Evidence Statement Evidence Evidence Statement Text Statement Key HS.C.12.1 Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures about functions. Content scope: F-IF.8a F-IF. Analyze functions using different representations. 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Evidence Tables: Sub-claim D Evidence Statement: HS.D.2-9 Evidence Statement Evidence Statement Text Key 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. Evidence Tables: Sub-claim D Evidence Statement: HS.D.2-9 F-BF.1: Build a function that models a relationship between two quantities. 1. Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. F-BF.3: Build new functions from existing functions. 3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. A-CED.1:Create equations that describe numbers or relationships. 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.★ 11 Evidence Tables: Sub-claim D Evidence Statement: HS.D.2-9 F-IF.4-6 Interpret functions that arise in applications in terms of the context 4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★ 6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ 12 Evidence Tables: Sub-claim D Evidence Statement: HS.D.2-9 F-IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.★ b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.★ c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.★ d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.★ e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.★ 13 Familiarizing Yourself with the Evidence Tables 1.Tally the number of evidence statements for each of the listed topics. 2.Tally the number of evidence statements for each listed domain. 14 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 16 Questions? Contact Carrie Piper, Senior Advisor, PARCC Mathematics [email protected] 17