Last week, the main theme of both my Kindergarten and my second grade math classes was geometry. We did a number of activities that explored various shapes and their properties, but the biggest hit in both classes was Which one doesn’t belong: A shapes book by Christopher Danielson.
Each page of the book consists of four shapes and a repeating question: which one does not belong? The answer is also always the same: all of them, but for different reasons. Doesn’t sound very interesting? That’s because the real answers are the reasons and observations that the kids come up with, and these are truly wonderful and creative.
Here are some highlights from the discussions around two of the pages from both age groups.
On this page, the Kindergartners right away noticed the big square and pointed it out as different, whereas with the second graders this was the last shape that they found a reason for. In both classes someone pointed to the rectangle and said that it has two short sides and two long sides. In the second grade group, one kid also pointed out that the rectangle is the only non-square.
It was interesting that it took both groups some time to notice that one shape was a different color (perhaps because they weren’t thinking about color as a “geometric” reason?). In K, someone even pointed to it and said “the blue one is different because…” and then they couldn’t articulate a reason. After a pause I couldn’t help myself and suggested, “maybe because it’s blue?” The kid got very excited and agreed. When one of the 2nd graders pointed out that the shape was blue another one said, “Color doesn’t count.” I had to gently point out that every reason counts and all observations are welcome. When the kid kept insisting that he won’t count that, I told him that he was welcome to come up with a different reason as well.
The bottom left figure didn’t belong because it was a diamond (same formulation in both age groups). I asked the kids what makes it a diamond and the reply was, “it’s standing on it’s corner.” (Here the kid that didn’t want to count color as a difference said that this shape was just another square that was turned around, so he wasn’t going to count that either. I told him that he was making interesting observations but that he has to be respectful of other people’s reasons.)
This one was a little more complicated for the Kindergartners, but they were truly fascinated by the shapes. I also loved one kid’s observation that the top two are essentially the same shape but the heart is more curvy. The other reasons they came up with were: the bottom left is different because it has lots of pointy ends and the bottom right is different because it has circles.
The second graders had a ton of fun with this one. Some of their reasons:
- The bottom left is the only one without something pointing in (what better way to introduce convexity?).
- It also looks like a cupcake.
- The bottom right is the only one with 4 identical sides.
- It is also the only one with circles for its corners.
- The top right is the only one with all straight lines.
- The top two are the only ones that have very pointy corners.
- The bottom left is the only one not with 4 sides.
There was a fun discussion about how many sides the heart and the cupcake have. Someone argued that they both have 4 (one kid said, “I know it’s not a straight line, but it’s like a side”). Others said that the heart had none. Still others thought that you couldn’t tell.
When we work on problems with the second graders, the most common question I hear from them is “Is this right?” One of the many things that I loved about this activity was that I did not hear this question a single time.