Tuesday, June 5, 2012

Average Rate of Change: Burgers

Summer classes started this week, which means I've started my two calculus classes (wohoo!).  One is essentially a survey course and the other is Calc I.  I'm enjoying it a lot, but I've also been continually up to my eyeballs in lesson plans, homework, and tests.

And it's only the first week.

In any case, as I was preparing for these classes last month, I came across this wonderful introduction to rates of change using (wait for it) a burger-eating competition.

So the first day of Calc I, I asked the class, "What do you think of when I say, 'How fast'?"

I got some good answers, like speed and rate.  I also got a suspicious answer:  average rate of change...way to steal my thunder.

We talked a bit about the importance of units when it comes to speed and then I asked them to consider speed in another setting--the speed of a person consuming an exorbitant amount of burgers:

And now for the questions...
  • How many burgers were consumed in total?
  • What does that mean that this man/woman's average speed was (in burgers per hour and burgers per minute)?
  • Is this speed constant?  How can you tell?
  • During what 10-minute interval was his/her speed the greatest?  How can you tell?
  • Find the average rate of change (or speed) in burgers/minute between 50 and 60 minutes.
  • Between 30 and 60 minutes.
So it's not revolutionary or anything, but it was a nice way to introduce calculus and ease everyone's nerves a little (including my own).

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