My younger son and I also happen to be studying a bit of geometry right now in our Prealgebra book. In fact, just this morning we turned to the section on area. I thought it would be interesting to see how a kid who is seeing area for the first time would approach this problem.

Well . . . it was tough for him, but we were able to have a great conversation nonetheless. I definitely learned a lot about how kids see geometry from listening to him.

His first instinct is that the shape is a square with a side length of 4. His reasoning is below:

At the end of the last video he’s calculated that the area of the shape is 17. One difficulty, though, is that he’s assuming the shape is a square, but a proof of that fact is just a tiny bit out of reach (though he nearly walks into it, and looking back at the video now I wish I would have done a better job encouraging his ideas there.)

Eventually we end up looking at the larger square and subtracting off the areas of the four right triangles, just as my older son did last night:

So, as I said yesterday, I really like this problem. For my older son it turned out to be a nice review problem and a great chance to talk through several ideas in geoemetry. For my younger son it was also a great conversation, but rather than review it the conversation with him had lots of ideas that were brand new to him.

I love that this problem is able to lead to great math conversations with kids who are new to geometry and kids who have been studying geometry for a while. Really nice problem.