I hit a brick wall with my son lately.
Me: Hey! Let's do Maths!
Amazing Maths Boy: Uh, okay.
Me: Want to do indices?
[AMB runs away and has to be recaptured.]
Me: remember when we did numbers squared?
Me: [writes out 2x2, 3x3, 4x4, 5x5] Can you do these?
Me: [writes out 2², 3², 4²] so that's two squared, three squared, four squared. Remember?
So we boxed it up and drew a smiley on it, and then I hit him with: 'What's two times two times two?' - fully expecting him to say six. Actually he hit it first time, with 'eight'.
Then we carried on and did 3³ 4³ and 5³ - that's three cubed, four cubed and five cubed. The trick here is to get them to do this:
3x3x3 (=27), 4x4x4 (=64) and 5x5x5 (=125)
or break it up so:
4x4=16 x 4=64
We were feeling pretty good after this. Another problem solved. AMB's mental maths stands the test and lives to fight on.
So then, because I'm evil, I asked him to tell me what two numbers multiplied together give 81. This time I almost didn't manage to recapture AMB, he ran away so far and so fast. And I thought, why?
It took me a while, but then I figured it out. To me, it's easy. I've seen 9x9 = 81 a million times. He freaked out because he was trying to figure it out from scratch - using mental maths - and it's impossible. You have to know the answer already, and then what seems impossible becomes easy. Once I pointed it out to him, he came down off the ceiling.