Teaching off topic (yet again)

The occasional lesson, free-coverage, or spot fill-in, allows a lot of freedom. Since there is not really an “on-topic” unless we count the ubiquitous test-prep, everything is off-topic, which is how I like it.

This week I was the guest at an after-school hour-and-a-half 7th grade math team session. I love this stuff. I could have done some model American Math Competition problems (we just gave the AMC this week), and thought about it, and maybe one day I will come and do some, but this week I did not.

We started with counting vs not-counting endpoints. Good buy-in, and tested if they could algebraically represent the result. They could. Good sign.

I ran some silly “guess the numbers” – in the first they added one to their number and told me the result. They did play, which was nice of them, although they laughed at how ridiculous it was. Then we did a “pick a number, multiply by 10, add your age” which they also, for the most part, considered lame, although not all of them immediately got the decoding. But then we did “A Little Math Magic” and after two rounds I gave them a chart to fill in, and I gave them enough time to play, and to look for patterns, and they did, magnificently.

In the wind-down from the Math Magic I introduced Fermat, although I only hinted at the content of Fermat’s Little Theorem. We instead just verified our base 10 modular arithmetic. But then we spoke about Fermat’s Last Theorem (ohsobriefly), and then Pythagorean triples, and they proposed some, and I checked some (on theme) by checking their last digits – nice point that we can reject if the last digits don’t add correctly, but we can’t accept on that basis only. And then I told them that there were no triples with all odd numbers, and asked why.  OK, these are little kids, but bright. I was not sure what to expect. Two of them hit explanations based on parity. And one explained the approach nicely. I was quite pleased.

I wound up with a prisoners/hats problem, and a promise to return. This was FUN for me, (with capital letters, as you can see for yourself). It was also fun for them, with lots of questions about exactly when I would come back.

An hour and a half is a long time. An hour is a long time. In my regular classes I often digress or allow the kids to bring us off topic for a moment. Can make a nice break. With these little kids? I like digressions. And so I did wander off-topic. Two meanders were linguistic:

in the first i was discussing the difference between “problem” and “exercise” and used the word “algorithm” in my explanation, and went off to discuss “al-” words from Arabic in English, and then “al-” words into Spanish, then into English without “al-” (algodón/cotton, arroz/rice) but I think rice had a different path, and I lost them there anyway because despite being in an overwhelmingly Hispanic neighborhood, where much Spanish is spoken, not one of these kids (all Asian or African) knew “arroz” or “algodón.”

in the second I was introducing the prisoner/hat problem and I heard breaths when I used the word “warden” and sure enough, it was not a familiar word to most of them, and in explaining it I pointed out the correspondence between “gu+/v/” and “w+/v/” (warden/guardian, warrior/guerrilla, and so on) and this time a few got very excited, and one asked about “wily” and “guile.”