Today I had a lesson with double my usual number of pupils; Katie was joined by her friend Varya. Officially the lesson was a whole hour, but part of it consisted of the girls playing games or just jumping around like crazy. The actual math content took up about half of the time, which I was quite happy with since after the first few minutes I wasn’t sure I’d be able to get them to sit down at all. What it took was me saying that they can do whatever they want for two minutes (I set a timer in the form of a two-minute hourglass) but then they have to calm down and start listening to me.
Now on to the actual content of the lesson. We did three activities, one introducing the concept of measurement and two relating to multiplication (although one in disguise). The measurement activity got a little fumbled since it was the first one and most of it happened while they were going crazy. But here is what we did manage to do.
I started out with putting five objects in front of them, all of different lengths, although some of them pretty similar. We spent some time comparing them against each other, determining which one was the longest and which one the shortest. After we decided that one could always determine relative lengths by putting one object next to another (carefully!) I asked them which was longer, their arm or their leg. Varya confidently said that her leg was longer, but when I asked her how she knew that she couldn’t come up with a satisfactory answer. Then the girls spent some time trying to put their arms against their legs, succeeding much better than I expected them to but still not quite perfectly.
Then I took out a big roll of string. This made the girls very excited. They started chattering right away about how the string could be used, but they couldn’t quite get the mechanics right. At some point Katie cut off a long piece of string and I had to point out to her that she hadn’t actually measured it against anything. Finally, with a fair amount of guidance from me, we successfully cut off a piece of string that was the length of Varya’s arm and placed it against her leg. The leg turned out to be longer after all!