It's All Relative

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.

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Description

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 achievi...read more

Anne M. Collins

Anne Collins has thirty years of teaching experience, having taught all grade levels K-12, as well as undergraduate- and graduate-level courses. She has been providing mathematics content professional development institutes and courses for teachers for the past fourteen years.

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.

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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