Cultural Connections

• Ratio, Proportion, and percent are core elements in math programs in countries throughout the world.

• Low performance has been documented on items involving proportional thinking

A Glance at Where We’ve Been

• Ratios: comparing two or more numbers– Different forms and applications

• Money, measurements, consumer purchases, scale drawings, and blue prints

• Proportions: relationship between two or more ratios.

• “Together, ratios and proportions provide an opportunity to practice many computational skills, as well as strengthen problem-solving skills.”

• Proportions provide ways to find answers to problems where the numbers are relational– Additive (absolute)

• Multiplicative thinking- quantities

– multiplicative (relative)

• Double number line- engaging in proportional reasoning.

• Facilitates algebraic thinking• Provide natural ways of studying percent

– Concrete models in instruction• Benchmarks of 100%, 50%, 90%, 10%, 1%

Books Supporting these Concepts

• Bair, S. Rock, Brock, and Savings Shock, Morton Grove, IL: Albert Whitman & Co. 2006.– Gramps teaches his twin grandsons the value of saving

money when he pays each a dollar a week to help with summer chores, then matches each dollar each boy saves.

• McCallum, A. Beanstalk: The Measure of a Giant. Watertown, MA: Charlesbridge Publishing Co., 2006.– A story about Jack, who climbs a giant beanstalk and meets

a lonely giant boy. Using ratios and proportions, he makes toys that both can use.

Chapter 13, pg. 299