Its gratifying when you plan a Math Club session where your time estimates work out and you achieve really good engagement. I had a few goals for this time since we're starting up.
1. Redo introductions and talk about club principles for the new kid.
2. To celebrate the new year with some work on factoring.
3. Try out a cool puzzle I'd seen online.
Having worked out a sequence in my mind, I started to worry that I'd need a little more filler activities. I have a new game from Math4Love: Tiny polka dots that I brought with me just in case. But in the end my instincts were correct. This worked to out to a good hour long session.
First, I had everyone assemble on the carpet. I'm trying to use that more often since being closer seems to sharpen focus for everyone. We went around and everyone introduced themselves, named their homeroom teacher and their favorite activity from last quarter or why they joined this time. As usual candy for Problem of the Week celebrations was often mentioned. I chuckled when someone asked if they could use Pi day from last year. This seemed like a good time to promise we'd have pie again this year.
I also had the kids debrief about the last Math Competition. Overall, everyone seemed to be fairly upbeat about it.
With that out of the way I went over my core principles for this quarter.
1. Respect the room and leave it as we found it.
2. Listen to me and each other.
3. Work on perseverance or "What to do when you're stuck" . For this one I asked several kids for real examples of their thinking during the last MOEMS test and gave a bit of talk about how real math problems aren't always solved in a few seconds. The one strategy I talked up the most was moving on and coming back to something you couldn't get. My example was some geometry problems I've worked on. For the kids, I mentioned that they should try this out with a problem of the week.
This was a natural bridge to talk about one of the problems from last contest which was given 2016 = 2^a * 3^b * 7^c find a,b, and c. First I asked about the exponential notation and we quickly went over what it means. (This is a subgoal of mine for the quarter, work a bit on exponents) Then I asked what kind of problem was this? After a few false starts one of the girls came up with the idea it was factoring.
Next I asked for ideas from the room on how to factor. Most kids know about factor trees but have a weak idea of the entire process. For example, there was a lot of "start by dividing 2". When I asked what if you can't see any obvious factors there was a long pause. So I decided to switch things up and ask everyone how can we factor 2017? (which is prime and doesn't have any easy factors.)
Eventually I started them off with the statement "I can try dividing 2017 by every integer between 2 and 2017 and I'll find the factors but gosh that will take a while, are there any ideas you can come up with to speed this up?"
From there there were a lot of suggestions about individual divisibility tests for various numbers. I was able to tease out what made the numbers interesting was that they were prime after several rounds of questions and observations from the class. So finally, I was able to get to the key question do I have to try all the primes less than 2017? This was a bit less satisfying. One kid finally volunteered we need only go to the square root but didn't have a reason why. So for the final part, I gave an informal discussion of why this is true on the whiteboard. If I repeat this again I might have the kids try out a sample and look for patterns first. I was then easily able to get some estimates from the room that the square root of 2017 lay between 40 and 50. I finally had everyone go back to there tables and try the process out on 2017. My main suggestion was to be orderly and assign the different primes to different table members to avoid repeated work.
While everyone was computing I went around the whiteboards and put up some more 2017 number trivia I'd been collecting off various sites. Sara VanDerWerf has a great summary here: https://saravanderwerf.com/2017/01/02/geekin-out-on-2017/. After all 4 tables had confirmed 2017 was prime I pointed each one out. I didn't stress these much but left them up for inspiration for the rest of the afternoon.
Finally from there we transitioned to an awesome geometry puzzle I found from Sarah Carter:
The Zukei puzzles involve finding a given shape on a coordinate plane from among a set of potential vertices. These were highly engaging and kept the entire room's focus for the rest of the day. Interestingly, I was able to work a bit on geometry definitions along the way as questions about what is an isosceles triangle or rhombus came up. I love that this flowed naturally from the problems rather than just being a giant exercise in taxonomy.
Finally I chose another one of the "favourite problem" posters for the P.O.T.W:
Bonus: I'm trying my hand at T-shirt design for the club. Here's my version for this year.