Abrahamson, D., & Cigan, C. (2003). A design for ratio and proportion.

Mathematics Teaching in the Middle School, 8(9), 493-501.

This article describes a method for teaching ratio and proportion in a fifth grade classroom. Our unit design creates and follows a learning path that begins with revisiting multiplication as repeated addition. It then explores patterns in the multiplication table and moves to the concept of rate as a single column out of the multiplication table. Next, students discuss ratio as two linked rate columns, or a ratio table, then look at two rows out of a ration table, or a proportion quartet. As a fifth grade introduction to ratio and proportion, this unit focuses on integer cases, that is, situations in which the question mark in a:b = c:? is an integer. This emphasis fosters multiplicative reasoning in a developmentally appropriate numerical environment.