I started by reminding the students that I was moving toward “flipping the classroom” – they read and think on their own time between classes; in class we solve problems (even homework problems) in small groups and collectively at the board.

Started on units (Chapter 2), with the MPG illusion. You own a sedan (25 miles/gal) and an SUV (15 miles/gal) and drive each 10K miles/year. You can trade in the SUV for a second sedan, or the sedan for a hybrid that gets 45 miles/gal. Which is the better choice?

Before thinking it through, most guess sedan->hybrid. When you figure out first how many gallons each vehicle consumes in a year you see that the savings are greater if you trade in the SUV – even if the hybrid got 50 miles/gallon.

We worked the problem at the board using unit calculations. The important observation is that you need gallons/mile to make the units cancel.

Several students started out thinking about the size of the gas tank. I’m not sure they understood that changed the number of times you visited the gas station, not the total gas consumed.

More important: several students don’t drive, and have no intuition about what gallons, miles and miles per gallon mean. That’s a reminder (which I made explicit) that in this course all the problems are real, and you may need background information before you can even begin. You’ll have that for the areas that matter to you, which are the ones you’ll have to deal with in life. In this course, try to imagine that you’re interested, even when you’re not. You might even learn something.

Started on the cost of doing business with pennies: does 2 seconds extra fussing per transaction come out to 4 hours per person per year? Does that in turn amount to $15 billion when charged at $15 per hour?

 

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