“The rules today are going to be different,” Katie said. “Girls are going to sit next to girls, and boys next to boys.” I pointed out to her that in this case the dolls are going to be in two separate groups, which wouldn’t be very social. “Well one boy can sit next to one girl,” she decided. But the symmetry lover in me did not like this arrangement.
So I suggested that we have everyone sit next to one boy and one girl. Katie liked this idea and immediately started rearranging the dolls. At the end, she had two boys, followed by two girls, then by two more boys, and finally by two more girls, all in a line (sorry, no picture). And again we had the same issue as the day before: the girl and the boy on the ends were each sitting next to only one person each. I asked Katie whether we could remedy this, expecting her to immediately put them in a circle. But to my great surprise, Katie started moving the dolls from one end to the other! Only after about a minute did she stop and said, “Ah, I know how to do this. It’s the same as yesterday!” And she drew an imaginary circle with her hand in the air.
Luckily for us, we had 8 dolls so everything worked out like planned, with everyone sitting next to a boy and a girl (actually, there were 9 at first, but one got tired and went to take a nap on the couch). I wanted to take away two of the dolls and have her see that the same thing wouldn’t work with 6, but she was tired and wanted to have the dolls dance. Plus, I think that trying to do too much at once can be counterproductive. We have many more balls, lessons, explorations, to look forward to!
Musings of a Mathematical Mom 