Crisc, your son's amazing algebra example reminded me of something else:

DS6 just finished the second disk of Descartes' Cove with me. He told me he wanted to skip to the algebra disk after that. The first problem on the algebra disk was

Given that x+y=586, what is 2x+2y?

DS asked me what x and y were and I told him we don't know, but that they are two numbers that add up to 586. He thought for a minute and then said, so 2x+2y would be 2 times 586. Then he worked that out on paper by himself.

I was impressed!