# Widgets and Squares and Lines, Oh My! (9/4/14)

Today was everything I had hoped for in geometry. I completely stole Lisa’s idea (and most of her process) involving having the students write their own definitions for terms based on examples and counterexamples. Just like she did I started with the Widgets example from Discovering Geometry and had students write a definition of what a widget is. Then I showed them the pic of “Not Widgets” and had them revise their definitions. Finally, they had to decide which figures were widgets and which were not. We discussed the importance of writing accurate, but succinct definitions in geometry, and how it’s important to use the correct terminology accurately.

Then I asked them, “What is a square?” They again wrote definitions and then read them to their group as they tried to find counterexamples of each others definitions. When we came back to discuss it as a class, I asked what information we absolutely NEEDED to have in our definitions of a square. One said 4 equal sides (the class agreed), one said 4 right angles (the class agreed), then, the thing you always hope for during a discussion, one said that we needed to include the fact that the sides had to be straight lines…the class erupted. OK so maybe they didn’t “erupt” but it immediately sparked disagreement. We had a majority of the class arguing that the four right angles guaranteed that the sides would be straight, while a small but passionate group began trying to draw a counterexample. It resulted in a great debate about whether a “line” can be curved and whether the figures they came up with worked as counterexamples.

They were so engaged that when I told them we had to stop because the bell was about to ring, a collective “ahhhhh” rang out in disappointment. This was my class before lunch and my class after lunch told me that several of the students continued the debate during lunch. Now that’s what I call a great day in math class!