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Unit 1: Ratios Sequenced Units for the Common Core State Standards in Mathematics Grade 6 Suggested number of days: 20 This unit introduces students to the concept of a ratio and engages them in using ratio and rate reasoning to solve problems. It builds upon students’ work in earlier grades with whole number multiplication and division. The multiplicative reasoning required for working with proportional relationships cuts across 1 most Grade 6 mathematical content domains and is therefore a crucial starting point for the course. Common Core State Standards for Mathematical Content Comments SBA Claim 2: Problem Solving Students can solve a range of well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Ratios and Proportional Relationships — 6.RP A. Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 6.RP.A.3a Students plot pairs of values representing ratios in unit 5. The content standards for this unit require that students make sense of real--‐life and mathematical problems (MP.1) by modeling relationships with ratios (MP.4) using a variety of tools strategically (e.g. equivalent ratios, tape diagrams, double number line diagrams, or equations) (MP.5). 3. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Common Core State Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. Suggested Instructional Resources 4. Model with mathematics. Kems Level F Student Lessons Lesson 1-3: SOLVE 5. Use appropriate tools strategically. Kems Level F Student Lessons Lesson 18 Warm-up Page: Word Wall Set-up Kems Grade 6 Student Lessons Ancillary Lesson 4: Ratios and Unit Rates pg.S31 Kems Grade 6 Student Lessons Ancillary Lesson 5: Ratios and Tables pg.S 41 Kems Level F Student Lessons Lesson 21: Units of Measurement pg.S195 Kems Grade 6 Student Lessons Ancillary Lesson 8: Converting Measurements with Ratios pg.S1 1 Integrated Resources Math Skill and Problem Solving Activities Interactive Science: Section 6 pg. 57-67 Performance Task: Piano Keys Task Pre-Assessment: SBA Interim on Ratios and Proportions For additional information about the role of ratios and proportional relationship across the middle grades, see the Ratios and Proportional Relationships progressions document. NGA Center/CCSSO are the sole owners and developers of the Common Core State Standards. © Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Charles A. Dana Center at The University of Texas at Austin January 14, 2013 1