11/18 Connecting all the dots

Interestingly the teacher I share the room with mentioned that it was a hard day for her and I also had more trouble than I like getting everyone to listen today. Multiple times I had to wait for the room to quiet and often that was while one of the students was talking.  (This isn’t crippling by any stretch but my goal is to build a stronger culture for the circle)   Long term I’m going to do another talk about listening respectfully to each other and probably will start randomizing the seating. We’re going to do a MOEMS sessions next week anyway which will work well with randomization.

Which One Doesn’t Belong

We  continued the routine I started two weeks ago and started with another which one doesn’t belong image?  One change I did this time was to draft one boy to tally how many ideas we came up with (20) . I plan to do this more just to add an extra element of fun and to strategically use some of the students as adjuncts.  Overall, this again worked really well. I had one previously quiet participant speak in front of the group for the first time and everyone was enthusiastic.

AMC 8 Feedback

I had all the kids say what they thought of the contest this year. The general impression was that it was harder than expected from almost all of the newcomers i.e. sixth graders. I don’t think many of them have seen a high caliber above level test before. So I did stress that this is a normal reaction, most kids don’t finish all the questions and that we’re focusing on **getting a baseline so we can see personal growth **in the next year.

Now that the problems have been released I can also discuss them a bit. Overall, I thought this year was fairly standard with no geometry standouts. My favorite problem was actually near the beginning and not a hard one:

Order: 15/11, 19/15 and 17/13

I started to cross multiply the fractions to do the comparisons and stopped to estimate the relative order first. After putting them into mixed form I suddenly thought aha.  They become  1 4/11 1 4/15 and  1 4/13.  4/n > 4/n+1 for all n so it doesn’t require any multiplying to rank the fractions which was oddly satisfying. 

For the main part of the session I refocused on a graph theory problem we tried a few weeks ago and didn’t finish:

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I was motivated this time by a  new Numberphile videos which I showed in pieces:

To start  I presented the Water Gas Electricity Problem on the whiteboard and had everyone break off and give it a whirl for  a few minutes.  We then discussed as a group and came up with a consensus that it seemed impossible.

I used another short video for a quick formal explanation:

Then once we had passed the point where it was mentioned that a graph is not planar embeddable if it contains K3,3, or K5 I asked if this reminded anyone of a previous task we had done. After a moment one student mentioned the “My Favorite Problem” from above.

So this time I had us a group add the numbers taking a volunteer for each one as we counted up towards 24.  Once we didn’t think that was possible I said based on the video a K3,3 or K5 was hiding in the graph we made and broke everyone up to go hunting for it. 

Success!  One of the groups found 2,3,6  12,18,24.

P.O.T.W:

I went with one from MathCounts this week to start exposing everyone to their style of problem:

https://www.mathcounts.org/sites/default/files/images/potw/pdf/PoTW111819.pdf