[defen]

> we've even hit upon things like exponents and logarithms (fishes and babies do the trick).

Can you explain this part? A quick google search didn't reveal any relevant games/apps, so the only thing I can think of is that a school of fish can grow exponentially, and that a baby is the logarithm of an adult :-)

[wjnc]

Yeah exactly that, offline. We always play with paper and pencil. Fishes having babies is the analogy for drawing the first few steps of 2^x. And then reasoning about that. That went in easier than divisions. Although candy and cookies really make math more simple to reason about. I've introduced division and sets by putting candy in bags (again paper and pencil) and the empty set is trivial for kids. They see 'no cookies' everywhere now. The world is filled with empty sets.