The Great Wheel of China
This coming Wednesday is my first formal assessment. Sure, I’m a little nervous when it comes to being watched, filmed, evaluated, and judged on my ability to teach, but on the other hand, I’m stoked to show my supervisor the problem I’m going to be presenting. We’re beginning trigonometry this week – introducing the students to radians, circles, and exploring sine and cosine graphs. The essential question for my lesson is “how can we model cyclical movements.” In order to help the students explore this, I plan on introducing the ferris wheel problem (along with a ferris wheel model). The goal of the problem is to graph the hight of a ferris wheel from the ground as it rotates.
Here’s the back story (for non-link clickers):
The Great Wheel of China located in Beijing is the largest ferris wheel in the world. It stands at 682 feet high. When my sister was traveling in China, she bragged to me about getting to ride the ferris wheel. After thinking about it for a while, I realized that it’s really not that unique, as you are only 682 feet off the ground for a few moments.
Imagine you are sitting on a ferris wheel at the peak (point A). Your task is to graph your height relative to the ground as you rotate around the wheel.
The students will be working in pairs. I don’t expect all of them to answer all the questions on the back in the time allotted, but I do hope that all of them get through graphing the ferris wheel’s movement by the end of the period. I would love any feedback on the problem before I introduce it on Wednesday. I am still a little bit hesitant about the best way to debrief the problem at the end of the period.
This is beautiful, is it OK if I steal some of it for my intro to trig functions a month from now?
A few comments however: the weak point is the time. Why 12, and 12 what? Maybe instead ask students to estimate how long one revolution would take, and go from there? Or have them estimate and then give them the real data, obtained from the Ferris Wheel website?
The problem can be made slightly more complex if you add the stand of the Ferris wheel. I mean, it’s probably some 10 feet up above the ground or so. That’ll add to the principal axis but will also of course demand a fuller discussion at the end of the activity. You already have a question about what happens if it’s higher above the ground, so why not go with that from the start? Are you worried about it getting too complex?
An extension could be given as homework: to come up with other periodic phenomena and sketch the graph for these based on their period, principal axis, and amplitude.
Finally, I think the questions could benefit (further, they’re already awesome!) from a more explicit link between main concepts and the constraints of the problem. You already have that in questions 3 and 4, but throughout the questions the connection could be a little more explicit.
On the other hand, I’m toying with the idea of making questions much more open-ended – such as: “Write down what you notice and explain how the graph would change if the wheel was the London Eye instead”.
Since the worksheet is the students’ first introductions to sine curves, one big goal of this assignment is to make it as straightforward as possible. That being said, I came up with a ton of extensions when creating the work sheet such as raising the height, giving units for how tall the wheel was and asking students to come up with proportional measurements, and various other possibilities. On the time thing, I initially didn’t want to include units because I felt that either I would run into another proportionality problem or not give a realistic time for a revolution. Then I did some research and learned the Great Wheel of China takes 1/2 an hour to spin once, so I think I’ll take your advice and use 1 minute increments.
I actually planned making part of the homework assignment to come up with other sine curves, but I really like your idea of using what they learned about measurements to properly graph other real world periodic functions. When I write up the homework I will post it too.
Oh, and anyone is free to steal any of this.
Oh and by the way, regarding the assessment: how could it go other than spectacular? I’m so impressed by the things you share here on this blog, your students are very lucky to have you as their teacher and I’m sure that’ll become thoroughly apparent in the assessment.
(I’m also very impressed that you even have formal assessments. My own teacher training had none of that. Just an advisor (more experienced teacher) who would watch most of my classes and chat with me occasionally about what I could do better. I had a very good advisor, but still I really wish things had been more formal.)