This took about an hour. I basically said, "go" and let them struggle. They had various issues:
*amplitude, how do I find that? (I showed them something more familiar to them, and they then figured it out ... say a sine graph shifted up with max of 10 and min of 6).
* period? what? 360? (no ... think about how long the yearly cycle would be)
* vertical shift? now wait a minute lady (think .... look at old work we've done)
* horizontal shift? what the?!?!?!? how? (think .... )
They finally got through enough of the answers, so we talked it through, and then the final what?????? hey, it doesn't go through EVERY point! That bothers me! Make it stop! (calm down. real life is messy. It's a MODEL. We make assumptions...)
I call this activity Days of Our Lives. I'm curious why you chose the days you did.
ReplyDeleteSince this is physics, the points should go through each point exactly if the model is right. I'm very curious about what's wrong with this model, and what a better model would look like. (But have never yet pursued that question.)
Hi Sue,
ReplyDeleteThese were the days where data was recorded, so that's what we used. And since our model only used the facts of maximum and minimum temperature (after looking at the curve and observing the sinusoidal shape), I don't think it's true that the resulting model has to go through every data point.
And I guess it makes sense that it doesn't. Suppose there was some freak weather pattern one day (in general), then that would be a crazy temperature value that didn't fit a particular model. ....
Anyway, if I remember correctly, our model was:
y = 3.1 sin [(2pi/365)(x - 365/4)]
Are you thinking that there's a better model other than a sine curve? That would be interesting to explore.
It looked like the handout said daylight hours. If you were doing temperature, that's a totally different story. Kinda cool to think about how those two applications differ in relation to the model.
ReplyDeleteIf you'd like to see the project I use, email me at mathanthologyeditor on gmail. I'm not completely happy with it, and will revise in about a month, when my pre-calc class gets back to trig.
Ackh! You're right, Sue. I was thinking about the homework that was related to temperature. That was what my answer was based on.
ReplyDeleteI went back to the source, and he had a good argument as to why the daylight hours problem isn't exactly a sine curve. ... since the movement of the planets is more elliptical than circular, that accounts for it not being exactly a sine graph. ... but it caused a good discussion with my students about models and assumptions and clarity of your work and reasoning.
I'll e-mail you, and thanks for the offer.
This is a really interesting assignment. I do act prep for students, and have seen questions about the Sin curve on the test. When students ask me where this is used in math, I've been at a loss. Finally I have something to which I can refer them! Thanks.
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