Although the Common Core State Standards for Mathematics (CCSSM) and other mathematics curricula do not formally introduce proportional reasoning until grade 6, building fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author includes examples and questions that help teachers see the larger purpose in teaching early concepts, such as unitizing, in ways that lay the groundwork for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year by year, and the questions provided are intended to be both interesting for students and useful in supplying teachers with diagnostic information. Chapters are organized by grade level around CCSSM.

Designed for use by teachers and coaches and in preservice instruction, the book provides the following:

• Connections between proportional reasoning and the NCTM strands
• Background information on the mathematics of the standard related to proportionality
• Suggestions for appropriate multiple representations, including manipulatives, for specific mathematical ideas
• Guidance for explaining ideas to students
• Alerts to frequent misconceptions or situations to avoid