Today in precalculus we worked on a "real life" application of the sine curve. Sure I could have done this without a worksheet, and put the data on the overhead, but I like the sheet because it's a different way of differentiating instruction. Everyone can work at their own pace, and I'm free to wander around helping and hinting instead of being trapped up front talking at the class.
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...)