Matt Enlow and Suzanne von Oy’s geometry problem

Saw a tweet from Matt Enlow today that led to a fun discussion and also a fun project tonight with the kids:

The last tweet in the conversation was a new Desmos activity from Suzanne von Oy showing how the problem worked:

I couldn’t wait to try out this problem with the boys tonight. We aren’t (obviously!) going to go into a lot of depth – this isn’t really a problem for 5th graders! But, I thought the boys would have some fun talking about it.

Since the problem is a pretty challenging one for kids to even understand, I started the project by trying to explain the problem carefully.

Next we tried to pick some points at random and then draw some triangles. If there are infinitely many equilateral triangles passing through these 3 points, it ought to be easy to draw one of them, right?

My older son went first. The cool thing for me in both this and the next video was seeing kids experience the problem and struggle with both trying to understand it and trying to solve it. There really is a lot of great geometry for kids here:

Next my younger son gave it a try. His approach was absolutely terrific to watch – I never would have approached the problem the way he did.

Next we went to play with Suzanne von Oy’s Desmos program. We got interrupted by the new puppy in the house across the street between leaving the living room and heading upstairs to play with the program, so I took the first minute of this video to review the problem again.

My older son went first again. He quickly found a picture that didn’t satisfy the conditions of the problem and that threw him for a little loop. Once we got past that, though, he seemed to have a much better understanding of the problem.

My younger son went next and eventually found an arrangement of the points that didn’t work at all. That was actually a really cool surprise ( we’ll deal with that surprise in the next video).

So, we got a wonderful surprise in the last video when we stumbled on an arrangement of the three points that didn’t seem to have any equilateral triangles passing through them.

Talking about what went wrong was a fantastic little surprise and it really made this project for me.

This was a super fun project. Thanks so much to Matt Enlow and Suzanne von Oy for sharing both the problem and the Desmos activity. Math twitter is amazing!