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It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7

For years, students have been taught to cross multiply when presented with proportion problems. Few understood what they were doing or why they were doing it. Rarely were students invited to think about various representations to determine the relationship between the two ratios being compared. The ideas and activities in this guide will help you provide students with the conceptual understanding of ratios and proportional thinking that is essential for solving real-world problems and achieving success in higher-level mathematics.
It’s All Relative includes thirty modules, which are aligned to specific Common Core State Standards. Each module in this accessible, spiral-bound flipchart addresses specific mathematical practices and common misconceptions; features timely classroom examples; includes proven, ready-to-use activities; and provides ideas for adapting activities to meet the needs of individual learners. The authors particularly emphasize how to use visual models—tables, tape diagrams, graphs, and double number lines—to represent ratios and proportional thinking. These visual models, which may be new to many teachers, enhance students’ conceptual understanding and improve their ability to solve a wide range of proportional reasoning problems.

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It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7

For years, students have been taught to cross multiply when presented with proportion problems. Few understood what they were doing or why they were doing it. Rarely were students invited to think about various representations to determine the relationship between the two ratios being compared. The ideas and activities in this guide will help you provide students with the conceptual understanding of ratios and proportional thinking that is essential for solving real-world problems and achieving success in higher-level mathematics.
It’s All Relative includes thirty modules, which are aligned to specific Common Core State Standards. Each module in this accessible, spiral-bound flipchart addresses specific mathematical practices and common misconceptions; features timely classroom examples; includes proven, ready-to-use activities; and provides ideas for adapting activities to meet the needs of individual learners. The authors particularly emphasize how to use visual models—tables, tape diagrams, graphs, and double number lines—to represent ratios and proportional thinking. These visual models, which may be new to many teachers, enhance students’ conceptual understanding and improve their ability to solve a wide range of proportional reasoning problems.

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It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7

It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7

It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7
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It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7

It's All Relative: Key Ideas and Common Misconceptions about Ratio and Proportion, Grades 6-7

Overview

For years, students have been taught to cross multiply when presented with proportion problems. Few understood what they were doing or why they were doing it. Rarely were students invited to think about various representations to determine the relationship between the two ratios being compared. The ideas and activities in this guide will help you provide students with the conceptual understanding of ratios and proportional thinking that is essential for solving real-world problems and achieving success in higher-level mathematics.
It’s All Relative includes thirty modules, which are aligned to specific Common Core State Standards. Each module in this accessible, spiral-bound flipchart addresses specific mathematical practices and common misconceptions; features timely classroom examples; includes proven, ready-to-use activities; and provides ideas for adapting activities to meet the needs of individual learners. The authors particularly emphasize how to use visual models—tables, tape diagrams, graphs, and double number lines—to represent ratios and proportional thinking. These visual models, which may be new to many teachers, enhance students’ conceptual understanding and improve their ability to solve a wide range of proportional reasoning problems.

Product Details

ISBN-13: 9781040289259
Publisher: Taylor & Francis
Publication date: 11/01/2024
Sold by: Barnes & Noble
Format: eBook
Pages: 98

About the Author

Anne Collins is the director of the mathematics program at Lesley University. She has been providing mathematics content professional development institutes and courses for teachers for the past fifteen years and recently served on the NCTM Board of Directors (2010–2013). Linda Dacey, professor of mathematics and education at Lesley University, works with preservice and in-service teachers, helping them to develop both their content knowledge and their practice. Her research focuses on problem solving, number sense, and strategies for differentiation.

Table of Contents

Introduction; Representing Ratios; Squatters; Ratio Drama; Equal Values; Tape Diagrams; Double Number Lines; Comparing Ratios; Graphical Representations; Ratios and Decimals; A Round and a Round the Pie; Choose It! Unit and Scale Factors: What Is a Unit Rate? Different Unit Rates; Proportionality and Unit Rates; Area and Unit Rates; Scaling and Proportional Figures; Solving Problems on a Double Number Line; Animal Rates; How Big Are These Chairs? Proportional or Not? Why Cross Multiply? Summer Travels; Posing Problems; Percents: Converting Ratios to Percents; Finding Percents; Given a Part, Find the Whole; Taxes, Tips, and Commissions; Percent of Increase; Percent of Decrease; Math in the News; Working with Ratios and Percents
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