(May 20, 2014) Rachel Steinig co-led the session with me today, so I’ll let her tell the story of what happened:
Today at Math Circle we did a lot of math (no kidding). WE started out reading a puzzle from the book by Smiullyan. I had read the puzzle earlier, sort of guessed the answer, but I never was totally sure. As we worked it out in Math Circle, all of the kids were very enthusiastic and voiced their conjectures. The problem didn’t take that long to answer though, because our combined brain power made us amazing geniuses and we felt like we could solve anything. You should totally check out the problems that we’ve been doing, because they are really awesome and yet really hard. Earlier I was paging through the book of problems and most I had no idea how to solve. However, they are great for Math Circle because they require lots of inquisitive minds working together to solve.
Next, we looked at clumps of blocks. Each array or formation had 24 blocks in it, the rows were just set up differently (for example 2 rows of 12, or 4 rows of 6). We asked the kids which formation had the most blocks. Almost everyone picked a different formation and said it had the most, but G loudly exclaimed “They’re all equal!” After that, when looking at the blocks, N agreed. I asked how they knew this, and no one was totally sure. Everyone set about counting the blocks, when I realized that I had made a mistake in counting and one formation only had 20 blocks. Oops. Soon enough, we came to the consensus that each pile was equal.
After that, each kid got a pile of 18 blocks and was allowed to line the “ants” as we called them into formation. Most kids started doing that, and A said he needed more blocks to make his formation so he started making a 50 block formation. Soon, we came to a problem. F said “I want to make rows of 4, but I have 2 left over.” M faced the same problem. We discussed it a while, and no one was really sure why we couldn’t make rows of 4. M added blocks to hers so that she could have rows of 4 (heehee, nice idea) and now she had 20 blocks.
We were running out of time, and decided to return to the problem of the wolf, the goat, and the cabbage. A had worked on the problem at home and knew the solution. He gave the group a hint that first the goat needed to go across. He didn’t give away the solution to the problem, which was very impressive. I know I would have been jumping all around. We worked on it for a few minutes, but we had limited time. However, we were getting closer and closer to the solution. Next week I think that we can solve the puzzle.
Right when we ended I was thinking about the puzzle and I drew a diagram on the board. I finally solved it!!! Yay, I was so happy because earlier I thought it was impossible. I called A over and explained it to him to see if my solution was right, and he said it was. What was cool was that he had found a slightly different solution that also worked. I guess that there is more than one possible answer. This just goes to show that in math, anything is possible; you can look outside the box.
I had lots of fun leading math circle and hopefully I can again soon!
Rodi talking again:
Rachel is right that a LOT of math happened today. She realized it only once she began writing this report because during the session there was a lot of noise and movement. Rachel left me to describe this because I asked her to write up her report without using adjectivesJ
When she began the session with the Smullyan puzzle, Cleveland unexpected came into the classroom for a visit. Cleveland is a very friendly dog who put his head in everybody’s laps. He was visiting the grounds of the arboretum outside. We got him out, but this set a tone for the session of minimal boundaries between outside and inside. If you haven’t been to our location before, we’re in the middle of an arboretum, in a trailer, on spacious grounds. We keep the windows and door open for fresh air, but it’s easy for kids to bounce between the indoor and outdoor space and still maintain full attention to the math. This can be distracting.
Kids today were also very excited about the puzzle we were doing, and were talking over each other to posit their conjectures. It’s hard to find the balance between allowing freedom of movement and expression, and meeting everyone’s need for being heard.
I can’t believe I forgot to use my mindfulness tools. I have training and experience in using mindfulness activities as tools to help students focus and sharpen attention in math. Why was I not using these here? (Rhetorical question!) Well, at least we have one more week of class. Here comes my chance. I’ll be prepared next time.
A few miscellaneous notes about the math we did:
- Smullyan’s Inspector Craig puzzle # 76 – our first logic puzzle with 4 variables/suspects. The other puzzles had 3. The students quickly deduced that only 3 of the suspects could logically be under consideration, so they literally erased the fourth one’s name from the board. I mentioned that determining that’s something’s not really a variable, and removing it from consideration, is an important mathematical skill/strategy.
- Arrays of 18: the plan was to ask each child to put the “ants” (blocks) into formation, and then have the kids compare theirs with each others to see multiple factoring of 18. An unexpected surprise here was the concept of remainder (those 2 pesky extra blocks) coming up.
See you all next week for our final session!