1. 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

2. 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.”

3. • 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%

4. 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