Mathologer put out a fantastic video last week:

I had the boys watch the full video and come up with two things that they thought were interesting. Here they explained their choices and gave a few thoughts about the video:

My younger thought the approximation of a circle by 1×1 boxes was interesting. Here we talked about that idea and sort of hand waved why the approximation gets good:

My older son thought that the concepts of the “good” and “bad” numbers was interesting. I let my younger son do a lot of the talking when we were talking about sums of squares. It was also interesting talk about why the proof that none of the integers of the form 4n + 3 can be written as the sum of two squares was easy, but the proof that all integers of the form 4n + 1 can be is hard.

I hope to return to the more complex questions the boys found interesting in a different project. Maybe next week!