A few days ago Katie was at home sick, and after we had watched a number of cartoons and read many chapters she asked me whether we could do some math. As you might guess, I was happy to oblige. However, I didn’t want to do anything that would require too much mental effort or stress. As it turns out, earlier that day we had received a nice, long number line in the mail, and as with anything new, Katie was eager to play with it.
I thought that a fairly mindless (but not completely useless) thing to do would be to walk along the number line in some random fashion with the help of dice (where the walking would be done by game pieces and not by us). However, no matter how hard I searched, I could not find any dice in the house. The few games that we had with dice had been borrowed by friends. After some deliberation, I realized that a deck of cards would suit our purposes perhaps even better than dice would have.
The game was simple. We took turns flipping over cards and moving the number of steps determined by the card (Aces were 1 and face cards all 10); the color of the card determined whether we moved forwards or backwards. The number line went from -20 to 100, but luckily we never stepped off of it. In fact, we never went below -10 even though we went as high as 19 in the positive direction. At some point Katie asked me whether we would ever reach 100 and I told her that this wasn’t very likely. If she was a bit older, this would have probably led to a probability discussion.
At the end of the game, Katie was standing on 6 and I on -6. She observed this with some amusement and I explained to her that this happened because for every forward (white) card there was an equivalent backward (black) card. She was a bit confused by my explanation so I decided to simplify things a bit. I told her to imagine that only one of us was playing and at that point she understood my explanation for why that person would land back at zero after going through the whole deck.