The video (which hopefully you can click to in the above link) includes a Fawn Nguyen-like counting exercise that I thought would be fun to try with the boys. For many similar exercises, check out Fawn’s amazing site: http://www.visualpatterns.org/

We started off just talking through the problem. In retrospect I should have set up the shapes first, but these are the things you don’t think about at 6:30 in the morning! It was interesting to hear both of the kids try to explain the pattern in words.

I’d intended to proceed as Boaler does in her video, but my older son happened to notice hat the number of blocks in each step was a perfect square. My younger son also picked up on that fact quickly, so we jumped into talking about the squares right away:

Talking about the squares led to a slight diversion to see if there was a different geometric way to see that 1 + 3 + 5 + 7 + . . . (odd integers) always adds up to be a perfect square. This is something that we’d talked about previously, but talking through that point one more time felt pretty natural here:

Finally, we returned to the original problem and looked for new ways to think about the patterns we saw there. I thought that the last videos sort of got the kids anchored to thinking about the pattern in rows, so I switched to having the shapes all have the same color blocks. Probably should have been doing that from the beginning. Sorry for the slight goof up at the end of this video, but at least we caught the mistake!

All in all, a fun problem. We’ve done many similar little project before, so this type of problem isn’t completely new for the kids – see here for just one example: