A child’s non-commutative model of multiplication
DECEMBER 3, 2013 AM31 11:52 AM
I was playing math with a niece and nephew a few weeks ago. Really, just playing games. And challenges.
We played who can get to 12 (by adding 1s or 2s). I wasn’t going for a rule, but my niece was close, so we (sister-in-law helped) got her to discover that 9 was a good number. And so was 3. And my nephew (younger) wasn’t going to discover it, but once his sister announced it, he kind of sort of followed.
We played puppies and kittens (game I learned from Sue Van Hattum. Adopt as many puppies as you like. Or as many kittens. Or an equal number of each. And – here’s a twist – whoever adopts the last furry animal loses). The two kids played with each other (I watched), and while the girl discovered some strategy, it was not a complete solution, and the two seemed to enjoy it.
I broke out some wonderful dice that my games mentor gifted me. Blue dice have the numbers 5 – 10 on the sides. Red dice have 0 – 5. 2cm, wood. I gave my niece one red, and I rolled one blue, and we saw who got higher. I won two or three rounds before she called me on it. Then I gave her two red dice, and him one blue one, and they rolled against each other, sum of the red against the blue. And then I gave her five red dice, and him 2 blue dice, and they both had some quick adding to do. They played for almost fifteen minutes, and needed to be stopped. Completely engaged. (And no, not a fair game. I didn’t calculate the probability, but the expected value favored the younger child. Intentionally, to help maintain interest).
I pulled out some graph paper (1/2 inch) and some crayons. Here I didn’t involve my nephew (I asked him to draw me something), but I drew a rectangle for my niece, 4×3, horizontally oriented. I counted the boxes (12) and the lines on the outside (14). I asked her if she could make another 12 box rectangle. She copied mine. I asked her if she could make a different 12 box rectangle. She drew a 2 unit high rectangle, and counted, and closed it at 6 wide. I asked her