Today’s lesson started with a game of catch. The goal was for the girls to figure out who would have the ball after some number of throws. (Actually, throwing turned out to be a terrible idea because their coordination isn’t good enough yet and they were constantly running for the ball. After a few throws we switched to rolling the ball.) Varya had the ball first and we in turn figured out who would have the ball after 0, 1, 2, 3, etc. throws. We recorded these on a piece of paper that was divided into two halves, labeled with the girls’ names.

We then moved on to a seemingly unrelated activity using the Montessori beads. I took out all the rods with 2 beads on them and asked the girls to figure out which numbers can result from putting together just these rods. We were underlining the possibilities as we were getting them. They were all on the same side!

The final activity involved figuring out which numbers of (singleton) beads can be divided evenly among the two girls. At this point Katie started to get upset that her side had the ‘boring’ odd numbers. Since I wasn’t too successful at convincing her otherwise, I decided to have them roll the ball back and forth again, but this time starting with Katie. Instead of successively going through all the natural numbers again, I wanted to see if they could figure out (without counting) the answer for some random numbers. The first few they answered correctly, even though I saw that they were counting in their heads. Then I asked them to tell me, without counting, who would have the ball after three throws. Each girl named herself. When I asked Katie to explain her answer she said, “3 was on my side before so I should have 3 again now.” When I pointed out to her that we were starting with a different person and showed her by counting that Varya would have the ball, she got upset again (perhaps she became attached to those ODD numbers after all). It was time to end the lesson.

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## About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.