What learning math sometimes looks like: a 30-60-90 triangle struggle

By chance I’m going through some similar topics with my older and younger son right now. My older son is learning about 3d shapes for the first time and my younger son is learning about 2d shapes. Both are having a few struggles. Nothing super surprising, but I’m finding it really interesting to watch.

The topic with my younger son today was “special triangles” which was mainly a discussion about 45-45-90, and 30-60-90 triangles. We encountered the problem in the videos below in the exercises at the end of the section. Quite a challenging problem on the first day you see 30-60-90 triangles, but the good news is that he had lots of ideas. Though he needs a little help keeping track of all them, what is cool is that by the end of this video these ideas have led to a picture that solves the problem in a way that I was not expecting at all.

Now that he has the right picture, finding the lengths that he’s looking for just comes down to the Pythagorean theorem. The tilted picture gives him a bit of trouble initially, but we eventually get things oriented the right way and compute the side lengths:

Having walked to the end of this problem, I thought it would be worthwhile to go back and have him put all of the ideas together from the start. Hopefully that gave him a chance to reinforce some of the connections he made.

At the end of his solution I showed him an alternate way to compute the lengths using a different 30-60-90 triangle.

So, a good struggle and hopefully a productive one. As I always say in this “learning math” posts – learning math is definitely not a walk in a straight line!