Talking through David Wees’s square problem

Yesterday David Wees posted this problem on twitter:

Since my younger son was on a little trip today I didn’t mind using this slightly more advanced geometry problem for our Family Math project. I hoped that the solution would be accessible to my older son, and we did indeed end up having a really great conversation about the problem.

We started by looking at the original question and seeing what he noticed. His first thought was to look at two simple cases:

After studying two of the easier cases we moved on to the general case. He struggled quite a bit to see what to do in this next step. This struggle was great and exactly what I was hoping for when I chose to go through this problem. Although we don’t make a lot of progress in the 4 minutes of this video, this part shows what learning and thinking about math often looks like – no straight line to the solution, and a lot of ideas that are good, but don’t quite work:

After about 4 minutes of struggle in the last video we turned the camera on and off after he asked “what else can we do?” The next couple of ideas after that question don’t lead anywhere, but then there’s an “aha” moment around 1:30 – “well . . . I see something now.” That “something” turns out to be a really nice congruent triangle argument.

So, a great problem from David Wees led to a really nice struggle + solution for my son. Hopefully a nice example of what a kid learning and thinking math can look like.