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Common Core Mathematics 6 Unit 1: Ratios and Proportional Relationships PARCC Exam Notes Unit 1: Assessment Clarifications Standard M/S/A 6.RP.A.1 Major 6.RP.A.2 6.RP.A.3a Major Major PBA/ EOY? PBA Yes Calc? MP Notes No 2 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Yes 2, 3, 6 EOY Yes No 2 PBA Yes No 2 Connected to Evidence Statement 6.C.8.1 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 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.RP.A i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. 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. 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. Yes 2, 3, 6 EOY Yes No 2 PBA Yes Yes 2, 4, 5, 7, 8 Yes 2, 3, 6 Connected to Evidence Statement 6.C.8.1 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 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.RP.A i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. 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. 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. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. i) The testing interface can provide students with a calculation aid of the specified kind for these tasks. ii) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42) The initial numerator and denominator should be whole numbers. Connected to Evidence Statement 6.C.8.1 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 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.RP.A i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and 6.RP.A.3b 6.RP.A.3c 6.RP.A.3d Major Major Major EOY Yes Yes 2, 4, 5, 7, 8 Yes (for Sub-C) Yes 2, 3, 6 EOY Yes Yes 2, 5, 8 Yes (for Sub-C) Yes 2, 3, 6 EOY Yes Yes 2, 7, 5, 8 Yes 2, 7, 5, 8 Yes 2, 3, 6 Yes (for Sub-C) denominator should be whole numbers. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. The testing interface can provide students with a calculation aid of the specified kind for these tasks. i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Connected to Evidence Statement 6.C.8.1 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 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.RP.A i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. b. Solve unit rate problems including those involving unit pricing and constant speed. i) See ITN Appendix F, Table F.c, “Minimizing or avoiding common drawbacks of selected response,” specifically, Illustration 1 (in contrast to the problem “A bird flew 20 miles in 100 minutes. At that speed, how long would it take the bird to fly 6 miles?”) ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks. iii) 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. Connected to Evidence Statement 6.C.8.1 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 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.RP.A i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity). i) The testing interface can provide students with a calculation aid of the specified kind for these tasks. ii) Pool should contain tasks with and without contexts iii) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. c. Solve problems involving finding the whole, given a part and the percent. i) The testing interface can provide students with a calculation aid of the specified kind for these tasks. ii) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Connected to Evidence Statement 6.C.8.1 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 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.RP.A i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. EOY Yes Yes 2, 6, 7, 5, 8 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. i) Pool should contain tasks with and without contexts ii) Tasks require students to multiply and/or divide dimensioned quantities iii) 50% of tasks require students to correctly express the units of the result. The testing interface can provide students with a calculation aid of the specified kind for these tasks. iv) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Other Integrative Tasks that may be linked to Unit 1 Evidence Statement Reach Back? PBA/ EOY? Calc? MP Notes 6.D.1 N/A PBA Yes 4, 1, 2, 5, 7 Solve multi-step contextual word problem with degree of difficulty appropriate to Grade 6, requiring application of knowledge and skills articulated in the Evidence Statements on the PBA (excludes Reasoning Evidence Statements). Tasks may have scaffolding if necessary in order to yield a degree of difficulty appropriate to Grade 6. Grade 6 Sub-Claim A Performance Level Descriptors applicable to Unit 1 Ratios 6.RP.1 6.RP.2 6.RP.3a 6.RP.3b 6.RP.3c-1 6.RP.3c-2 6.RP.3d Grade 6 Math: Sub-Claim A The student solves problems involving the Major Content for grade/course with connections to the Standards for Mathematical Practice. Level 5: Distinguished Command Level 4: Strong Command Level 3: Moderate Command Level 2: Partial Command Uses ratio and rate reasoning to solve Uses ratio and rate reasoning to solve Uses ratio and rate reasoning to solve Uses ratio and rate reasoning to solve real-world and mathematical problems, real-world and mathematical problems, real-world and mathematical problems, mathematical problems, including ratio, including ratio, unit rate percent and unit including ratio, unit rate, percent and including ratio, unit rate, percent and unit rate, percent and unit conversion conversion problems. unit conversion problems. unit conversion problems. problems. Uses and connects a variety of representations and strategies to solve these problems. Finds missing values in tables and plots values on the coordinate plane. Uses a variety of representations and strategies to solve these problems. Uses a limited variety of representations and strategies to solve these problems. Uses a limited variety of representations and strategies to solve these problems. Finds missing values in tables and plots values on the coordinate plane. Finds missing values in tables and plots values on the coordinate plane. Finds missing values in tables and plots values on the coordinate plane. PARCC Abbreviation Key: PBA: Performance-Based Assessment EOY: End of Year Assessment M/S/A: Indicates whether this standard is considered Major content, Supporting Content, or Additional Content MP: Standards for Mathematical Practice * Indicates a modeling standard PARCC Sub-Claims: Sub-Claim A: Information on how PARCC will assess major content Sub-Claim B: Information on how PARCC will assess additional and supporting content Sub-Claim C: Information on how PARCC will assess reasoning Sub-Claim D: Information on how PARCC will assess modeling