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.