How fast?

A decent day, coming back from Thanksgiving. Opened each IMP3 class with this:

Thanksgiving Dinner.
Marcie's family went to her aunt's house for Thanksgiving, 120 mile away. They left home at 1:30 pm, arriving at 3:30 pm. After dinner, they drove back home, leaving at 9:00 pm and arriving home at 10:30 pm. Compare their speed each way. Which direction was faster, and why might that be?


Predictably, I got a lot of "coming back was faster, an hour and a half versus two hours going there" stuff. The thing that made it sing (in 2nd and 7th period, at least) was me taking notes on the board: Going there Coming back. 2 hours. 1 and a half hours. Then, I made a big production of it: "How is 1 and a half hours FASTER than 2 hours? Shouldn't the bigger number be faster?"

A good platform for re-teaching the idea of rate. Launched from there into mechanics of calculating rates, and then into the Big Idea: it's all about answering the question, "How fast?" Then into questions that start as "how fast does..."


I feel like I'm getting better at showmanship, which is good: if it's not interesting, they won't be interested. My passion for the subject needs to be a draw, to attract interest (think of busking your own show...) Interesting, how I started from the idea that I want to make it as little about myself as possible, and have gradually scaled back from that (also interesting, if dark, to consider how much of that is driven by this recognition: "Yeah, well, it's not like I'm actually succeeding at making it about THEM...")


Potentially good tape from today's Calculus lesson: put the limit-based defn of derivative on the board, said, "Sort out what it means. Explain it." I was worried, when one kid jumped straight to, "It's the slope formula", and relieved a few seconds later when he said, "oh, man, now I'm confusing myself..." From confusion, they can build their own clarity. It's when one kid gets it cold, and everyone else is lost, that I worry... Too easy for everyone else to just throw in the towel at that point...