What kids learning math can look like -> studying the geometric mean

Earlier in the week my younger son was struggling with a problem about the geometric mean of two numbers. I thought looking at the difference between how my older son saw the problem and how my younger son saw the problem would be interesting.

I asked each kid to go through the problem on his own. My older son had not seen the problem ahead of the project and my younger son had gone through the problem with me two days ago.

Here’s what my older son had to say:

Here’s the first part of what my younger son had to say. You’ll see that the he’s still a little unsure about the problem even though we had talked through it previously:

Finally, I wrapped up with my younger son by talking through the way he was intending to solve the problem originally. This approach is really nice, too – it uses the Pythagorean theorem and a little algebra:

This was a nice reminder to me of what a kid struggling with a math idea can look like.

Sorry for the brief post – needed to get this one out the door before running out for work.