In the meantime check out my collected problems which are almost at 30 in total: http://mymathclub.blogspot.com/p/collected-problems-2.html

## Wednesday, February 21, 2018

### Aloha

In the meantime check out my collected problems which are almost at 30 in total: http://mymathclub.blogspot.com/p/collected-problems-2.html

## Friday, February 16, 2018

### 2/13 Farey Sequences

Today was a special occasion for Math Club. Instead of just me or a vicarious video, we once again had a guest lecture from the UW Applied Math department.

This time, Professor Jayadev Athreya came out to the middle school to give a talk on Farey Sequences. That was fairly propitious, since I had meant to get to this subject during this session: http://mymathclub.blogspot.com/2017/11/1128-egyptian-fractions.html but quickly realized I didn't have enough time to cover even Egyptian Fractions. So there was a good thematic fit with some of the other things we've done.

My favorite moment of the day came early on when Jayadev had each of the kids talk about why they came to math club. (I usually do this on the first session too) There were a smattering of "I like competitive math" responses but then we reached a girl who roughly said "I don't know why I came originally but I like it so I keep coming." That's victory in my book!

What's also interesting here is a chance to more closely observe all the kids and another person's teaching style. Jayadev's basic structure was fairly similar to what I might have done.

- Closely investigate the numerators of the fractions (in suitable common denominator form) when comparing them to notice a trend: they always differed by one.

- Build up the definition of the mediant: https://en.wikipedia.org/wiki/Mediant_(mathematics) and see how it relates to the fractions already found.

- Do a formula proof that the mediant is always 1 apart from its generators if they are 1 apart.

A lot of this was structured as group work at the tables with discussions after a few minutes where things were consolidated. I always find these transitions a bit tricky to time so it was useful watching someone else. I would also probably have done a few of these parts as group work on the whiteboard itself and then gallery walked for the discussions but there was good work done at everyone's seats.

Like last time, I also noticed some unexpected hesitancy with operating on fractions. It took a bit more time to draw out the kids and have them explain how to compare fractions with different denominators. Although create common denominators was mentioned as well as variety of numeracy instincts ("for unit fractions, the fraction become smaller as the denominator increases" or "you can also create common numerators to do informal comparisons"). Again, I felt like this was a useful practice/review for some. Alternate hypothesis: the kids were more reluctant to volunteer at points which was more social rather than indicating any gaps. If this is the case, I'd like to work on activities to bring out more questions. One idea I have toyed with in the past is, is selecting one student to be "the skeptic" during any demo and come up with at least one question about the logic. If I do go this way, I'll probably start with having them do this with something I discuss and depending on how it goes try it also during all whiteboard discussions.

Overall I was really pleased. We now have an invitation to visit the Applied Math Center on the UW campus. I have to investigate whether the logistics are workable.

## 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:

https://drive.google.com/open?id=1N4HaNYRjwhhSSYq9UqMZNyBvqaL2w65UFIjV83z3G6Y

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.

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.

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:

https://drive.google.com/open?id=1N4HaNYRjwhhSSYq9UqMZNyBvqaL2w65UFIjV83z3G6Y

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.

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