Modeling Trig Functions — The Ripple Effect

I wanted to imitate “bringing alive a lesson” like so many other bloggers have done and been doing, so I’ve got this lesson idea that we’re going to do tomorrow for Precalculus, but I really need to get it set in my mind what we’re going to do, so what better way to do that than blog about it?  (Okay, yes, I could write a lesson plan, but I’ll do that after I have a better idea what I’m going to do…)  That’s one great thing that writing and (even more) following blogs has done to my teaching: I’m now actively looking for connections to phenomena in the real world and tying it to what I’m teaching in class.

I had some students help me create the following video by shaking an extension cord up and down (using the super-nice high-speed camera that my principal got our Physics class!).  We get a nice transversal (why does spell-check not like the way I spell that word?!) wave out of the following video, and we’ll warm-up by freezing it at some point and finding a function to match the image.  I’ll probably try to use Geogebra to show the students the results of their hard work to obtain an equation.  I’m going to try to stick to Dan Meyer’s advice: “Be less helpful”.

So I have several videos I created trying to get “the perfect wave” from water.  First I tried a small “tank” and then finally got brave enough to pull out the big fish-tank that’s been empty for what seems like ages.  Still couldn’t get a very pretty wave, and I’m a bit worried about having to explain transversal vs. standing waves to the students because this is Precalculus, not my Physics class, but regardless, I can still pause the video and have students work on a specific wave. I’ll use one part of one of the following videos:

The goal is to move the students to modeling what happens when you throw a rock into pond.  I’m hoping students will want to test different things like rock size, shape, strength of the throw, etc.  I’ll probably also convince the students that it is very important to tie a string to their rock so that they can retrieve it easily (hehe).  If I can get a video of how goofy they look, perhaps I’ll post that in a followup.

Then, if we still have time, I’m hoping to wrap it up with sound waves, leading to the technology behind sound cancellation.  The sound waves alone will take a long time just to explain, so maybe that’s next week’s lab.  Wow, we are way behind where we were last year in Precalculus, but the students have gotten so many more authentic experiences, and I really think they understand the material better at this point in the year.

Oh, and I called this post the “Ripple Effect” not only because we’ll be observing ripples, but also because I am hopeing to be a contributing part of the “ripple” of teaching who are blogging and teaching/learning from each other.  I have definitely  benefited from other teachers’ blogs, so thank you!