Inspired by Math Teacher Mambo's post about relating graphs of f and f', I couldn't wait to test this out with my students. I was amazed- a concept with which they were likely to struggle was suddenly accessible and they were having great conversations with their partners.
I really tried this as an experiment and spent less time that I wish I had actually manipulating the pasta, so I may re-write this to give them more practice with the "approaching" idea.
Side Note: One of the reasons I love teaching so much with pasta is my now infamous "pasta speech." I did an activity with pasta my first year of teach about something (triangle inequalities maybe?) and haven't had to buy a new box of pasta yet. In that time, I've moved classrooms and moved schools and, quite frankly, not been concerned about the food safety of said pasta. I always give a very impassioned speech- a pasta-biography of sorts. It's humble beginnings on a grocery store shelf....it's long summer in a hot storage unit while I slowly moved trunk-fulls of stuff to my new city in my '92 Subaru....it's residency on the bottom shelf of my bookcase, close to the not so cleanly environment that is a high school classroom floor. All of this to lead to the moral of the story- don't you DARE put that pasta in your mouth! I even had a student buy me a box of pasta for Christmas and leave it on my desk with a note that says "Thought you could use an upgrade." Never gets old.
To get kids thinking about average vs. instantaneous velocity, I started with this question....
As a group, answer the following question & justify on your whiteboards numerically, graphically, algebraically, or verbally:
Alex and Erika both live next door to each other, 13 miles from school. Alex leaves home at 6:30 am and arrives at 6:45 am. Erika leaves home at 6:50 am and arrives at 7:00 am. Who passes the gas station halfway to school in a shorter amount of time?
The next activity was inspired from a University of Washington activity, but I modified it heavily so my kids could really build the knowledge themselves (without quite so much jargon).
We did get to some practice with the limit definition and I'm going to use this Derivatives Match Up as a warm up activity in class on Monday to give them some more partner practice. Derivasaurus Rex is very excited about all these rates of change (more on him later)!