Units, Ratios, and Rates

Books:

Lamon, S.J. (2010). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers, 2^nd ed. New York: Routledge.

• Chapter 15 (pages 181-201) explains ratios and rates separately and then discusses how to compare ratios and rates.  A rationale is provided for the various notations used to represent ratios.  The process of comparing ratios and determining equivalence is detailed in a step-by-step process followed by examples of how to perform arithmetic with ratios.  Instructional activities and discussion questions are given for teachers to try in the classroom.
•  Chapter 16 (pages 202-211) provides a more in depth look at the distance-time-rate relationship and introduces the concept of speed.  Common student misconceptions are discussed and sample activities are given for teachers to use in the classroom.
• You can find this book on Amazon by clicking here if you're interested in purchasing it or would like more information.

 
Van De Walle, J.A., Karp, K., & Bay-Williams, J.M. (2010). Elementary and Middle School Mathematics: Teaching developmentally, 7th ed. Boston: Pearson.

• Chapter 18 (pages 348-368) defines proportional reasoning and explains how it relates to multiplicative reasoning.  Types of ratios and various notations are shown.  Activities and assessment items that can be used in classroom instruction are provided along with discussion questions.
• You can find this book on Amazon by clicking here if you're interested in purchasing it or would like more information.

Links to Lessons and Teaching Activities:

Learning Ratio and Proportion Through Tangrams

A series of lessons are presented where students use 2 sets of tangrams that are different sizes to explore ideas of proportional reasoning including finding and defining "like" shapes from each tangram set and figuring out if "like" shapes also share "like" areas.

http://www.pasadenaisd.org/Curr_Instr/math/images/7th%20Grade/2nd%20Six%20Weeks/Proportions/Proportions%20with%20Tangrams.pdf

What is Proportional Reasoning?
This link has some great examples of student work and student thinking related to proportional reasoning.  Many of the content and activities  are those used in the Lamon and Van De Walle books.

http://sunburst.usd.edu/~kreins/learningModules/Proportional%20Reasoning.pdf