This week my younger son and I have started a new section in our Prealgebra about basic geometry. Today we talked about parallel lines and angles for the first time. The book had a pretty typical example problem of a someone (well, a chicken) changing direction while walking across the street and I thought it would be fun to see how my son would think about this problem having just started learning about lines and angles.

He’s obviously still an absolutely beginner when it comes to geometry, and some of the ideas that we’d normally take for granted – 180 degrees in a straight line, 360 degrees in a circle, for example – still trip him up a bit. But, he’s got a great way of thinking about math, and his 15 minute walk through this problem was fascinating to me.

In the first part of the discussion, he has some interesting ideas, but he applies one of the ideas about angles and parallel lines incorrectly and we don’t quite get to the correct solution:

In the second video we take a slightly deeper dive into angles and parallel lines to help him see the mistake in the prior video. He sees pretty quickly where he went wrong, and actually gives a great explanation of why the assumption he made wasn’t correct.

The last step was going back to the problem and looking for a new idea. Although we haven’t studied it, he’s heard that the angles in a triangle add up to 180 degrees, and the solution he finds to the problem uses that idea. I’m fine with that for now – we’ll cover triangles in more detail eventually.

I love watching kids learn and talk about math. It is so hard to put yourself back in their shoes and imagine what it is like seeing an idea for the very first time. I’m really happy with my son’s though process here. Especially since, once again we show that learning math isn’t always a nice, straight line.