Yesterday, apropos of nothing, J. announced that 9 is not the only square number. 4 is, too. Even 1, he added. It turns out he didn't hear the phrase “square number” anywhere. He's just been playing with blocks.
Today I got out some extra blocks and showed him that 16 is a square number, too. He wondered, apparently at random, if 100 was a square number. So we counted out one hundred blocks and as it happens, it is.
He's been watching some math videos. We borrow one from the library each week. Last week's video, on division, explained that any number divided by 1 is itself. I doubt J. has any real conception of what division is and where it applies, but he liked that rule.
Properties of the integers, man. Before you know it he'll be telling me that 7 and 13 can't make any rectangles, except for long skinny ones...