Full 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 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.
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
