## Thursday, February 8, 2018

### 2/6 Olympiad #3 and AMC 10

I almost cancelled this week's math club due to feeling ill the night before. But in the end I was well enough and the activities were straightforward so I went ahead with the meeting. We started with the candy I had forgotten to bring last week. My wife picked up some red vines for me, the reception of which I was curious to see.  They were all eaten by the end so there may be more licorice in the future.

Participation in the problem of the week was lighter that I would like but I had enough kids to still demo solutions. In particular with this problem: http://www.cemc.uwaterloo.ca/resources/potw/2017-18/English/POTWD-17-NA-16-S.pdf the key is to count the total number of pips in the set
of dominos.

The students demonstrated two different methods which was good. Most approaches end up with a triangular table since when you calculate the combinations you often end up with  n pips | m pips and m pips | n pips which are the same domino.  I'm trying to elicit more questions from the other kids. This time it worked well when I asked "Does anyone have any questions about X's diagram and how X did ...."  I also spent some time modelling asking questions about their strategies and why they had created the triangles to draw this out.

Once done we participated in the third MOEMS olympiad. My feeling is this was the most unbalanced of the set so far. The starter questions were all fairly easy and they gave a hint that unwound most of the complexity of one of them and then it ended with a really interesting
Diophantine fraction equation that was quite a bit more difficult to do.  One followup question I have for myself: is even in cases that simplify is it enough to consider just the factors of the denominator of a sum i.e. if   K1 / A + K2 / B = K3/K4 where all the cases are constant.

Finally I chose another AMC based question for the Problem of the Week:

Overall everything ran well but it was not my most inventive day which was probably just as well since I felt very low energy at points.

The next day,  one of the teachers at Lakeside graciously let me send a few students over to take AMC10. I couldn't justify the cost to do this on site for so few students. In the future, I'm hoping with more eight graders this might change. At any rate, this was fun for me. I had the three kids take a practice test first to make sure this was a reasonable move. My goal was for everyone to get at least 6-10 answers correct.  What I don't want to happen is for kids to go and get so few questions correct that the entire experience is discouraging.  I've also been feeding more sample questions from AMC10 as problems of the week. Generally, given enough time they often make really good exercises.  The kids reported this year's test was a bit harder than the practice versions so I'm cautiously awaiting the official results.

Looking forward: next week is going to be real fun. One of the professors from UW, Jayadev Athreya is coming to give a guest talk to the kids on Farey sequences (which by coincidence we didn't quite get to on: http://mymathclub.blogspot.com/2017/11/1128-egyptian-fractions.html.

#### Resource Investigations

I just learned about the MoMath Rosenthal prize winners https://momath.org/rosenthal-prize/ I'm going to look through the sample lessons to see if there is anything that is usable in our context. By that I mean far enough off the beaten curriculum track.

I also really like this investigation from the Math Teacher's Circle Network:   https://www.mathteacherscircle.org/news/mtc-magazine/s2018/touching-infinity/  on countable infinite sets. I have to spend some time thinking about it but it looks quite promising.