I thought it would be fun to share with the boys for our project today. Here are their initial thoughts on the problem. My younger son’s initial guess at the amount of area shaded was “a little bit bigger than 1/4” and my older son’s guess is was 1/3.

In the last video the boys decided to use coordinate geometry to solve the problem. Here’s that work:

Next I wanted to have them try to solve the problem by folding paper. Studying eometry through folding is an approach that I always want to do more of, but almost never do more of. This tweet from Patrick Honner last week reminded me to fold more:

Here’s how I introduced the idea of approaching this problem through folding to the kids:

The boys folded the patty paper off camera (and without me – I was publishing the previous videos). Here are the ideas that came from the time they spent folding. A bit of a surprise to me was one of the ideas really was a folding idea, and one was really a similar triangles idea that my younger son noticed when he was playing with the paper folding.

So, a fun project on a couple of different levels. The problem is definitely great, and it was also a really nice surprise to see ideas that at first glance seem like similar triangles emerge from playing around with paper folding.