Teaching off topic 2

I go off topic all the time; it’s how I teach. But I was miles away twice last week, and both may make interesting stories. I wrote about the first earlier. Here’s the second:

I’ve been doing math stuff in the Bronx for years. I taught, eventually gave a few talks, did a Saturday enrichment thing for a while, picked up the college gig, got involved with pre-service Teaching Fellows for a few years…

There was a pause. I might have been in trouble. They were thinking.

Sometimes things come together. I encouraged a neighbor, Numbers Guy, to become a math teacher. Huge personality, a natural. And last fall he was accepted to the Teaching Fellows. One of my math campers from a few years ago, Early Riser, rises from his school’s Siberia, the trailers, and step by step, out of teaching: he is now an AP. Numbers Guy was looking for a job. It took a little convincing, since Early Riser does middle school and Guy wanted high school, but it has worked, exceptionally well, as a matter of fact.

So Numbers Guy picks up math team. And invites me to come. And Early Riser thinks it’s a great idea. Plus, their school sends my school a few kids every year. And last week I did middle school math team. What to do? Numbers Guy was open to anything. This was going to be fun.

1. For a warm up, an old standby:

If I said to open your books, and this is an extra activity, not class, I’m not asking you to really open your books, besides, I don’t know if you actually have books, and if I asked you to open your books, but not really, right? and if I asked you to open to page 75, and look, I’m not really asking you that, and I don’t even know if your books have 75 pages or if you have them in this room, but it doesn’t matter since you don’t actually have to open them, but if you had books here and they had more than 75 pages and I asked you to open to page 75, which I’m not doing, and I said to do some exercises, but this is an afterschool activity, I’m not really asking you to do exercises, but if I asked you to open to page 75 and do exercises 32 through 37, how many exercises would that be?

(in a very soft voice, and very fast… imagine an auctioneer whispering)

There was a pause. I might have been in trouble. They were thinking. I hear “6.” Oh no! Then a fraction of a second later “5,” then mostly 6s. Didn’t matter. We had our 5. I put up a fist, and counted “32, 33, 34, 35, 36” I swiveled my head, looking for the last finger, maybe I dropped it. Giggles. Brief discussion. Then I asked “if you walked from 32nd Street to 37th Street, how many blocks would that be?” Quick answers “6!” Brief discussion. I drew the silly fence, and discussed rail problems versus post problems, mentioned places later in the curriculum where the same or a related concept matters (endpoints) nad moved on. I had them.

2. Number guessing games. I told them that for a guessing game to be good, it had to impress and  seem mysterious, and it had to work.

A. Pick a natural number. Multiply by 10. Subtract 1. What do you have? And as the first few kids answered, I gave them their original numbers. Numbers Guy offered to guess one. And then I asked a kid to guess one. And we agreed that everyone in the room could quickly figure out the numbers. This was too easy; it failed to impress.

B. Write your birthday as a month (1 – 12) and a day (1 -31). Add one to the day, multiply by 20, add the month. And I correctly guessed 2 or 3 birthdays. And then a kid tried, and got one. And another. But some still were a bit puzzled. I had them help me symbolize it, and they all got each other’s birthdays. This is the sort of thing, I told them, that I get from friends, forwarding me e-mails. They want the explanation. For many people this would be a good guessing game, impressive and mysterious, but not for you anymore…

C. Take a number. Square it. Take the last digit. Square that. Take the last digit. Multiply by your original number. OK, now this was interesting. I agree that there is a weakness (there was a 10 and a 20, and I needed two guesses), but they are impressed. And I deny explanation. Try it with a bunch of numbers, 1 up until… by the time you get to 50 you will certainly know that multiple tricks that are in play. And then, to give myself a chance to recover (all high energy, middle school kids) I spoke briefly about Pierre Fermat. Turned out, the kiddies knew lots of pythagorean triples, and I sat back and let them recite a few.

3. The big puzzle. I was thinking Ghost the Bunny, but one kid said he knew a bunny problem (and lo and behold, it was just a simple explanation of the Fibonnaciness of bunny multiplication), and I was also thinking the Logical Pirates, so I put it to a vote, Bunnies or Pirates, and having rigged the question, I knew we were going for the pirates. (this means, of course, that I must post the Pirates problem, soon). I ran a good session. I let them make mistakes. Slowly correct themselves. I asked annoying questions (that seems possible. Are you sure that it shouldn’t be one more? how do you know that that’s enough?). The Numbers Guy helped with the questions (even as he did not know the answer). And the Early Riser came in and out and watched a bit. He solved the Pirates with me years ago.

And we had a solution. Then a refinement. Then an extension, which we noticed changed the nature of the problem. And then I turned to the Numbers Guy and said I really wasn’t ready to go on. Perfect, he answered. I was confused for a moment, then saw the clock. I’d been there for an hour and a half.

Loads of fun. But exhausting.