Developing proportional reasoning means to think about relationships between numbers as multiplicative and relative rather than additive and absolute. It’s a different way to see things mathematically and the foundation of rates, functions and Algebra I.

Developing proportional reasoning is also fun. To introduce the topic in 6th grade, we had the chance to play with poker chips and food coloring.

We began our work by pulling out 5 separate blind samples of poker chips from a box of 50 reds and blues in order to predict the total number of blue and red chips in the box. The discussion after each trial revealed more and more accurate guesses and an increasing level of reasoning. The goal in the end was to make a guess that was supported by sound mathematical reasoning.

We then dropped 2 drops of blue dye and 5 drops of yellow dye into 500 milliliters of water. While always maintaining this ratio and concentration of dye, which produced a gorgeous St. Patrick’s Day green, the students had to determine different amounts of drops and water based on changing numbers.

The tables that the students had to complete are included in the photo gallery. All-in-all, level of engagement was high, interest was certainly piqued, and the pump appropriately primed for our work in this unit.

Tim Loescher
Middle School Math Teacher