The first SF Math Teacher Circle was held yesterday, December 10th, at Proof School. It was nice to see some familiar faces that had attended the Oakland PCMI professional development a few weeks ago. We joked how our spouses were asking if there is a math event every weekend. Nope, but just recently.
Paul Zeitz, who organizes the Proof School, organized the event. It was a rainy day and I took BART to avoid any parking issues, and they were very generous with coffee, pastries, and bagels provided as well as some Chinese food for lunch.
They started with a pledge to not give answers out to spoil it for the rest of the group. We also were seated randomly with cards.
We started off with a group activity from the awesome Get it Together book. It was an activity I hadn't done before, which was about a sequence. As you can see below, the clues were: a person had 10 acres of land after the first year of the big drought, in the summer of 1914 she had 410 acres of land, after every fall harvest she bought all the fields that shared a fence, and finally each field was a 10 acre square, that shared a fence with 4 neighbors.
We worked separately then shared ideas. I used a diagram as you can see below, and kept track of the acres with a table. We had a nice discussion about how she had 410 in the summer, so it was BEFORE she had bought more in the fall. So, at the END of 1914, she had 610 acres. From there I just labeled the years going backwards, seeing that the starting point in 1908 was 0,0 when the drought happened.
Then Avery Pickford presented on some voting topics. I like how he started with a table of values and asked us to notice and wonder. We realized each column had the numbers 1 through 5 in different orders. He then added the labels to the table to see how the columns were different sized groups of people and the rows were the food preferences ranked on a scale of 1 to 5, 1 being their favorite.
The big question was, how could you satisfy the most people? It was interesting, because different methods produced different winners. John in our group did a golf score method where he multiplied the rank by the number of people in the group, then summed those results for each type of food, and burritos had the lowest score. Another method is taking the average of each score, which ends up not being too fair. There were also some other methods we discussed.
We then looked at how voters would vote based on what type of candidate there was in a 2 party system and a 3 party system.
Finally, Paul presented on some math games. It reminded a bunch of us of the 21 flags survivor game from PCMI. Game 2 was Basic Takeaway. Start with 16 pennies and remove 1, 2, 3, or 4 pennies. Our strategy was to go first and take 1, leaving your opponent with a multiple of 5 to choose from. The person who grabs the last penny/pennies is the winner.
Game 3 was Don't be Greedy. Basically you start off with pennies, but you can take any amount that is not all the pennies. Your opponent can then take that amount, or less.
We also investigated a Cat and Mouse Maze that seemed to be never ending, unless the Mouse got to to the top left corner and was trapped.
The last one we talked about was breaking the bar. If you have a 8 by 6 chocolate bar like a Hersheys, whoever makes the last "legal move" or break is the winner. Basically, every time you break a piece, you are left with 1 more piece. So, the game has 48 moves, so I BELIEVE you'd want your opponent to go first on this one.
Once it was lunch time, I took off because I had to pick up my 6 month old from my parents who were watching her, but it was a fun day. It reminded me that I've got to prepare some Get it Together card sets for my support classes as well as my 8th grade classes.