You’ve been to Christopher Danielson’s awesome site Talking Math With Your Kids, right? Of course you have. And you’ve downloaded his awesome new shapes book, “Which one doesn’t belong?”, right? Of course you have. Well I have too, and over the past few weeks I’ve been using it with my 8th grade classes as a warm-up once a week. When I showed them the first set of shapes and asked them which one didn’t belong, there was obviously some disagreement and some outrage that there seemed to be a reason why any of them wouldn’t belong, but I was forcing them to choose ONE.
Now, 8th graders NEED resolutions to situations like this, so I had to give them an answer. Obviously, if I told them that any could “not belong” depending how you look at it, that would’ve been the end of it. So instead, on the spot, I just decided to pick the shape that the least amount of students thought didn’t belong. But here’s the best part: I didn’t tell them WHY. Instead, I told them that I’d show them 4 new shapes next week and they could use the information gathered from today to make their decision next week. This has happened for the last 4 weeks. Every week I tell them that there is a pattern to figuring out the shape that doesn’t belong, and a few have mentioned, in jest, that I just pick the shape with the least people.
But the shape I choose is clearly not the point. The point is the discussions. They are great discussions with students analyzing side lengths, angle measures, polygon properties, and polygon dissection. The discussions are rich with geometric reasoning and several students always change their minds during the course of discussion, when another students brings up a point they hadn’t thought of. I’m going to do this for at least one more week, and if they’re lucky, I just MIGHT tell them how I’ve been choosing the shapes. Maybe.