Here is the continuation of the account of my lesson with Katie and Varya on Wednesday. This part was after the girls had their two minutes of going crazy, so it was a lot calmer. I brought out one of Katie’s magnetic ‘dress up’ dolls with three different color skirts and two tops (the doll actually has many more, but I wanted to start small). The doll was no ordinary doll, but a princess, and she wanted to wear different outfits for as many consecutive days as possible. The girls had to help her figure out how many different outfits she could make.
Katie and Varya took turns coming up with new outfits and I recorded them on a piece of paper so that they were sure not to repeat. Incidentally, one of the colors for the skirts and tops coincided, and this outfit gave the girls trouble for some reason. After they came up with the other 5 outfits, neither one of them could find this last one. And so they decided that 5 must be the total number of possible different outfits. I did not try to dissuade them or show them the sixth one.
We then moved on to counting outfits for the prince. He had three shirts and two pairs of pants, and again there was one color that overlapped. Once more, the girls took turns making outfits, and both carefully avoided the mono-colored outfit. Finally, they again had 5 outfits and it was Katie’s turn to make a new one or decide that there were no more. Katie chose the correct shirt (which was yellow) and spent some time staring at the two pairs of pants. She then started reaching for the red pants and I pointed out to her that we already had that outfit. When I asked her whether there was another pair of pants, she exclaimed to my great surprise, “but that’s not allowed!” Naturally, I asked her why not, and the answer was “because we didn’t allow the same colored outfit for the girl!” Aha, so they were deliberately avoiding that one! I had to point out that I never made such a rule. “But we didn’t count it,” she insisted. It was then unanimously decided that same-colored outfits were just as legal as all the other ones and Varya went ahead and made the last outfit for the princess while Katie dressed the prince.
In a future lesson I would like to guide them in counting such things systematically and tying this to multiplication, but first I wanted them to play around with it on their own and get some feel for it. Later on in the lesson we did some actual multiplication by placing colorful chips into equal rows and counting the total. We also played a few games. Overall, I was very happy with this first lesson and look forward to (hopefully) many more!