# Ferris Wheel Fun — Intro to Sine Graphs

I watched Dan Meyer’s TED talk again (here it is you’ve somehow not watched it).

And I was inspired (again) to make better lesson plans.  I really was fascinated how he mentioned that “this is what I do during my 5 hours of lesson planning during the week”.  So I sat down and looked at the book’s introduction to sine waves in Precalculus and decided to create a more fun intro to that.  Here’s what I came up with:

First, I showed them this neat Youtube clip:

My students really appreciated it because it has sounds from (I think) transformers in the background.  Then I asked them “so what’s the largest ferris wheel?”  After blank stares, I showed them pictures from the Wikipedia of the Singapore Flyer and showed them this video.  (We talked briefly why there’s a floating field in one of the pictures… space issues in Asia are always fascinating to students who live in the middle of no-where New Mexico.)

So next, I told them that a small child walked up to them and asked “How far above the ground are we?” (I was going to ask “How high are we?” but I thought that would induce too much giggling.)  I didn’t give them any other information (inspired by Dan to “be less helpful”).  Eventually I had to lead them on and say “okay, suppose it is 20 minutes into the ride”.  They asked for the height of the wheel, which I gave them (165 meters) and they asked how long it took to go all the way around (30 minutes, according to Wikipedia).    They also asked for other things, such as “what’s the diameter?” (some students said  165m, “duh!”) or the speed or acceleration of the “barrels”, which I didn’t give.  (Perhaps I should have given that info to them and let them sort out what was important?  Oh well, they actually had enough info to figure it out, even though it was irrelevant information).

I didn’t realized this beforehand, but requesting that “20 minutes have passed” (out of 30 minutes) actually gives you a 30-60-90 triangle, which we had just learned about, so I was excited for them to use that knowledge.  I was impressed by how quickly some of my seniors figured it out and were happy for them to present their findings to the rest of the class.

Overall, though, I was somewhat disappointed by how slowly my 1st period went (the Seniors), but as disappointed as I was by 18 seniors, I was even more excited by the 4 juniors (yes, half the class was gone for various school functions) who got as far as the seniors did in 10 minutes, AND were able to come up with a generic formula for the situation!  Here’s what they discovered:

$h = \sin(360 - (90 + (\frac{t}{30})*360))*82.5 + 82.5$

Where t is time and h is height above the ground.

They discovered this before knowing anything about sine graphs.  They have no idea what amplitude, period, phase shift, or the sinusoidal axis means!!  Isn’t that awesome!?!

So yeah, I was pumped, and when the bell rang, even my good math students stated “woah, that was a short class!”.

Take it, use it, let me know what you did differently.  One thing I would have done differently, especially for my seniors, would be to have the students make guesses beforehand.  That would make students, as Dan states, “buy in” to the problem.  It would also help significantly with their intuition once they arrive at an answer.

Next, I’m going to be making a Geogebra file which shows how the height changes over time.  I’ll share that when it’s done.