# Play And Proportional Reasoning

Today we played in class — a lot! Yesterday, my student teacher, Ashley, introduced the class to our Tornado Challenge. Students learned about their countries and materials, and today they started planning. This morning, we looked closely at our Math Success Criteria, and tweaked it for this current challenge. Students also worked in groups to turn the Science expectations into Success Criteria to help guide their learning throughout the building process. After a couple of mini-lessons on detailed design plans and various ways to determine fractional amounts, students got to work.

Yes, the students had to create a plan (a labelled diagram) before they got to build. They also had to figure out 2/3 of the building materials (one of the project requirements) before building, but then the building began. And the building was a lot of “play” and “problem solving.”

• Some students struggled with their building materials. They couldn’t attach the wood together using the string. One problem to work through and solve.
• Some students struggled with their lack of fasteners. They didn’t have enough tape, elastics, or string for the amount of materials that they had. A second problem to work through and solve.
• Some students struggled with using all of their materials. They were given a large amount, and they had to use at least 2/3 of that amount. How could they do this? A third problem to work through and solve.
• Some students struggled with not thinking ahead. They gave away their extra materials, and then needed more and didn’t have enough to use. A fourth problem to work through and solve.
• Some students struggled with bad trades. They traded their items for materials that they really didn’t need, and then had to figure out a way to use them or trade again. A final problem to work through and solve.

And it was through the trading that the students really began to understand proportional reasoning. In the assignment outline, my student teacher and I set-up a store that allowed for these deals:

As students started to trade items for masking tape, I realized that I had a ton of additional items. Then students realized that masking tape wouldn’t hold many of these items together. They wanted duct tape. They wanted elastics. They even wanted hockey tape. I had no prices for these additional items though. What should I do? I let the students use the established prices to figure out what the other items should cost — enter proportional reasoning.

• Students decided that hockey tape and duct tape were stickier than masking tape, so they got 1/2 the amount of this tape for the same amount of materials.
• Students realized that the branches of wood were of varying degrees of thickness, so they negotiated additional tape based on how their wood pieces compared to an average stick.
• Students realized that they didn’t want to necessarily trade these amounts of materials, so they proportionally varied the amounts of tape by the amounts of materials traded. For example, if they only wanted to trade 1/2 the amount of materials, then they would only get 1/2 the amount of tape.
• Students determined a set number of elastics to trade for one of the materials, and then they varied this elastic amount based on the type of materials that they traded. They used the set tape amounts as their proportional guide for elastic amounts.

What was amazing to watch is how naturally this math was happening. Students wanted these materials. They needed these materials. So the trades needed to happen, and the students needed to figure out what was fair — be it when trading with me in the store or with their peers. It was great to hear the thinking and see how the students were working out their calculations all while creating and playing together.

Play is engaging. Play is fun. But play is also learning … and this can be true for students (and adults) of all ages. How do you develop math skills through play? What are the benefits and/or drawbacks in doing so? I’d love to hear your thoughts on this!

Aviva