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## It's All Relative

### Key Ideas and Common Misconceptions About Ratio and Proportion, Grades 6-7

#### Anne Collins and Linda Dacey

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.

#### Product Details

• Author: Anne Collins and Linda Dacey
• ISBN: 978-157110-982-8
• Year: 2014
• Media: 98 pp/flipchart
• Item No: WEB-0982

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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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
Appendix

Anne Collins
Anne Collins has thirty years of teaching experience having taught all grade levels K-12 including undergraduate and graduate level courses. >more

Linda Dacey
Linda Dacey, professor of mathematics and education at Lesley University, began her career teaching at the elementary level and early in her career, received an NSF grant to develop a model program for preparing middle school teachers. >more

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