(March 24, 2016) The kids got right to the business at hand, no introductions necessary: NIM. They chose teams. The experimented with strategies. They changed their teams (multiple times). After about six games,
(March 24, 2016) The kids got right to the business at hand, no introductions necessary: NIM. They chose teams. The experimented with strategies. They changed their teams (multiple times). After about six games, some strategy emerged. “We should have taken two,” said S at one point.
I gave each student 4 paper cups: three upside-down and one right-side up. “Can you get them all in the same direction by flipping exactly two cups at once?” The kids got to work.
“It’s impossible,” said S pretty early on. (Earlier in the class, before this activity, one of the students had posited the conjecture that “nothing in math is impossible.”)
“It is possible,” said L. M and B were not sure. L demonstrated various ways he thought it was possible. M, B, and S questioned each of his methods. With each question, the math got deeper, to the point where the kids’ questions were really about exploring equivalency:
- Is doing a “180” flip with 2 cups the same as a “360” with one cup? (Everyone agreed that this is the case.)
- If 2 cups are touching each other as they flip can they count as one?
- What is a 360 plus a 180 the same as?
- Is the answer still valid if you change the starting configuration?
- What if you change the rules for the motion?
- Is the result from flipping 4 cups at once always the same as from flipping 2 cups at once?
- And so on
They could have spent a lot more time on this, but with eight-year-olds sometimes things fall apart suddenly and unexpectedly, so I decided to quit while I was ahead. (We’ll return to this activity on another day.) I was so excited to see such deep thinking coming from the kids. I said almost nothing during this game other than facilitating the kids taking turns for their demonstations. I read a post recently on a math education listserv that seemed to imply that there isn’t much deep mathematical thinking going on with this age group, but I so beg to differ!
“Have you ever played Rock, Paper, Scissors?” I asked the students, who had decided to move class outside at this point.
“Are you kidding?” replied one of the kids, incensed at my ignorance of the group’s sophistication.
I quickly covered for myself by saying, “Yes, but how about Math Rock Paper Scissors?” This got their interest. “Do you know what multiplication is?” One knew this term, but the rest didn’t. Once I explained it in terms of “sets of” they knew what I meant.
“Times tables!” said M and S. I asked M to help me demonstrate this game, even though she had no idea what the game was.
“So after saying ready set shoot, you hold out fingers – 1, 2, 3, 4, or 5. We multiply your number of fingers by my number, and if the product is even you win, and if it’s odd I win.” I played a round of this with each child. They had fun, but were getting antsy because of the beautiful spring day, and no one could focus on any strategy. I decided to move the group inside