I ended up deciding to give the students a choice of 3 projects to do for the remainder of our time in class:
1. a volume of cross section project using colored cut foam that I've done before
2. a volume of revolution project again with foam (never done and I'm doing it with the kids)
3. a video or power point (never done before, and thanks, Sam, for your tips which I've incorporated).
I'm happy that 7 students picked the video project, and 2 picked the power point project. From talking with the kids, they mostly had great ideas and are working hard. One student is resisting everything and being really derisive and dismissive and coming up with every argument in the book as to why he shouldn't be doing this. Or talking about doing something sarcastic and such (because, you know, math just isn't that exciting). I'm working on setting him straight using my teacher voice as I'm simultaneously resisting the urge to vigorously shake some manners/sense/attitude-adjustment into him.
I'm excited about the volumes of revolution project. There are 6 (?) of us doing it. I picked the same region for all of us (y = 4 - x^2 , y = 0 , x = 0) and we're each revolving it around different lines. That way we can put them all together and see what's what.
One video pair is working on a video about someone getting ready for a "math party" and they have to cut eggplant and for some reason need to know about the volume (details will emerge). They wanted to know how to get a function that looked like an eggplant. One girl was really excited and happy to learn something new when I showed her how to plot the shape on paper, pick some points on the "graph", put them in L1 and L2 on the calculator and then do a Quartic Regression. Cool. It DID look like an eggplant when she showed me.
hihi! (i tried posting this before but it didn't work...)
ReplyDeleteI CAN'T BELIEVE IT! We actually had the exact same idea for a calculus activity this year, but I decided to postpone it for next year.
I thought, when we were doing revolutions, that I could take various bottles (e.g. san pelligrino) and vases, and take pictures of them in front of graph paper. then we could read off points, do a regression of some sort, and do revolutions to find surface areas (for labels on the bottles) and volumes (how much can the bottle hold).
And if I got really crazy, I was thinking I could do something with the thickness of the vases/bottles, but I wasn't sure what yet.
But I have to say, your kids doing the eggplant thing with the math party (who doesn't love a good math party) is a much less lame version of what I was thinking of (who doesn't love a good eggplant deconstructed mathematically?).
Huzzah! Love it! Calculus teachers of the world unite!
It WAS kind of cool to see her "eggplant" on the graphing calculator after she had decided the shape.
ReplyDeleteShe then suggested that maybe I could let next year's kids come up with their own shape, and they could then do the same thing and then even cut them out of foam.
Ms. Cookie