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Friday, November 11, 2011

When the Problem Does the Teaching

This recent Geometry lesson is a good example of setting the kids in pursuit of a problem, where they have to learn the thing you want them to learn anyway in the process. (That wasn't that eloquent, sorry, I will illustrate.) On Tuesday, we developed the rule for the sum of the angles in a polygon by the chopping-into-triangles technique that many of you are probably familiar with. The next day I wanted them to be able to find the degree measure of one angle in any regular polygon, so I set them this task, which I stole from a PCMI problem set:

I did not include that first question when I did this in class, and many students stumbled over restricting their search to regular polygons. So I added it after the fact for next time I give this problem.

There are lots of these triplets to find, so all the kids met with some success pretty quickly. It is also a little like finding a pearl in an oyster, so they were rewarded and motivated to keep looking. Regular polygons are hard to draw, so with a little reminding and prodding, they started to find the degree measure of one angle in a regular pentagon, hexagon, octagon, etc (the whole, covert point of the activity, anyway! Yay!) I had them add their finds to a whiteboard everyone could see as they were discovered. They also wanted to verify by using the Smartboard to render regular polygons perfectly, and fit them together like puzzle pieces, which I was happy to allow them to do. This was actually a pretty great class - some kids conjecturing likely candidates, some kids armed with calculators cranking out angle measures, some kids organizing all their finds, some kids going up to the smartboard in groups of two or three for visual/spatial verification. And when I assessed them the next day, no one had any trouble understanding the question or coming up with correct angle measures. This problem is a keeper.