Last week the math club at my older son’s school got started. The first day the kids received a handout with a few hundred practice problems and we’ve been working through them slowly – usually 5 problems per day.

One of the problems today gave my son a tremendous amount of difficulty. I was surprised – not by the fact that it was difficult for him – but rather the extent of the difficulty. Reading through the questions ahead of time, I’d thought all 5 problems were roughly the same level. It turned out that 4 were about the same level and this one was essentially 4 times as hard.

Even when we went to talk about it on camera I thought it would take 5 minutes – it took 20. I present that conversation below without much comment. Maybe not my best work helping him out either, by the way, but the 20 minute conversation below is what learning math sometimes looks like. Not a straight line, but zig-zaggy struggle.

Here’s the introduction to the problem and the first steps toward the solution, as well as a discussion about a few things that confused him the first time through the problem:

At the end of the last video my son was close to writing down some equations that would help solve the problem. Here he does write down those equations, but, unluckily, with one little error that we’ll straighten out in a bit.

At the end of the last video my son noticed that there must be a mistake in his equations – here we search for that mistake. Part of the difficulty in finding the mistake comes from translating the ideas from the problem into math.

In this last part we get to the solution of the problem – and the best thing is that after our long talk here things do seem to start making sense to him. That was nice to see.