Here is a teaser for upcoming posts:
This week in my calculus classes we are going to start our discussion of finding volumes. I've already picked up a supersized box of Play-Doh and dental floss so that we can easily explore area by cross-sections. I'll make my famous mathematical paperweight out of a sine curve and semicircles and we'll try to estimate the volume.
After the Play-Doh, I'm modifying Dan Myer's WCYDWT volumes of rotation with glasses project. I have some glasses to bring in and we'll test out our ideas. I'm thinking a good follow-up would be to have students create their own Coke bottle that holds 20 oz of fluid. They will make their own curve and give me the integral. I wonder if there is a good software program or applet out there where students can easily enter their own curve and have the program rotate the area for them? My mind is quickly filling with ideas about this project. I can't wait to see the student results!
And one other big thing- I'm doing my first live, in person conference presentation this Friday at the ATOMIM spring conference in Bangor. It's not too late to register online! If you're there and reading this now, you probably don't need to be attending my presentation about Edublogging, but stop by and introduce yourself!
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You can definitely use WinPlot to revolve curves around any axis (or any line!). It's free. Some more stuff it does: http://samjshah.com/2009/02/05/what-is-true-love-winplot/
ReplyDeleteOnce you do your project, I'd love for you to blog about what exactly you did, and if you can throw out any resources, that'd be awesome too.
Revolutions are my favorite thing to teach in calculus, I think.
Sam
Oh, don't worry Sam, I'll definitely be sharing this stuff! Thanks for the idea about WinPlot too. The teachers have Macs but the students have Windows in the labs, so I never think of using WinPlot.
ReplyDeleteI totally agree that this is my favorite part of teaching calculus. It's funny because volumes of rotation had been what I was most afraid of teaching when I started. Now I love it.
The same happened in BC calculus. My favorite part of teaching that course is by far the units on series which I had no idea about my first year of teaching the course.