It’s been too long since I updated the blog with math circle news…quite a lot has happened:

Binary arithmetic
We did two days on binary numbers.  Five students sat at the front of the room, each holding a card with dots. From the right, moving left, the first card had one dot, the second two dots, the third four dots, and so on.
I asked the students how to make the number Ten by selecting cards.  I told them that the new way to say the number Ten was to name the students who were holding up cards. To make things clear, we said the names from left to right, and if a card was being left out, we said “blank” instead of the name.
We named a bunch of numbers in English, and translated them to “math circle-ese”.  This was great.
We then took turns adding one to different numbers, which was also great.  Then we ran out of time.
The next week, a few students showed up who hadn’t been there the week before, so we reviewed the activity, then we moved on to adding two different binary numbers.  The big trick here is carrying, but quite a few students got it. Unfortunately, I think we went too fast for some, and I wasn’t able to take the time to bring them back into the fold.
The next week I brought two dice for each student, and sheets of paper with number grids from 1-6 and 2-12.  We all rolled first one die, then two dice, filling in a square each time a number (or sum) was rolled.  I was amazed at the distributions.  Finally we all reported our 2-12 sums to the front of the room and added those up. 8 won by a landslide, but 7 & 6 came in 2nd and 3rd.  Interesting!  Everybody enjoyed the activity, but I think the summing felt “forced”, so the learning wasn’t as effective.  This could have easily been spread out over two or three sessions with lots of discussion and less dice-rolling.
The next week we made paper snowflakes, and discussed the math of the activity.  We talked about reflection, as well as “how many diamonds will my snowflake have if I fold my paper X many times and cut one diamond?”  Some of the students delighted in the fact that this pattern brought back our binary numbers (woohoo!).  If we had more time, and enthusiasm, it would have been good to bring everybody along for this, but the energy in the room was very scattered.
Finally, yesterday I brought in a code (with key) for the students to decode.  This was wonderful. The energy was subdued but interested. (Interestingly, a number of the students proposed they read instead of do math circle.  I said that’s fine, please do it at a table behind the others.  Very quickly that whole table was engrossed in decoding the message. Neat!)  Once the students finished this, I suggested they encode messages, and a number of them wrote long messages and handed them to me to decode.  I showed them a quick way of decoding using a tree (left is “.”, right is “-“). None of them thought it was faster (hmmmm.)  I was flattered by the messages they sent me. Thanks! 🙂  I finally told them this was Morse code, but not before Madi called it “binary code”.  Cool.
What’s next?
I’m going to ask the parents to send me frank evaluations of what went well, and what didn’t (both from their perspective and to ask the students).  I’m planning on doing something in the Winter or at least by Spring, but it won’t be exactly the same. I’d like to have fewer students per group, but figure out how to do multiple groups. So my work moving forward will probably be more volunteer coordination than direct student interaction. This is both sad and happy for me (less directly fun, but more impact).

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