I wanted to get my students to model periodic behaviour using Trigonometry. This lesson did that, but it got us to talk about something much more mathematically important: What information is needed, but also what information is attainable? For example, my students wanted to google the “Central Axis of the Ferris wheel at Chicago Navy Pier”. This information is necessary to solve our problem, but unattainable in these words… I included a video with this discussion, and had some really great conversations with students about what information we can actually expect to find out there, and what math we can use in order to manipulate the information we find, into what we need.
Act 1: I started with just this clip of the Navy Pier Ferris Wheel from Chicago and asked the students what questions they had:
Not the most effective Act 1 I’ve ever had, but it got them to think about things like:
- How long are you on the ride?
- How tall is it?
- How high off the ground do you get on?
But the question that got my attention, and that drove the rest of the class was: How far can you see from up there? So we made up the question “You can see US Cellular Field from a height of 100m. How long do you have to take pictures of it?”
Act 2: We brainstormed for a long time the information needed. I’ve included a video of the discussion here, but I think the coolest thing that came out of it is that we learned to translate math language into Lehman’s terms. For example, my students wanted the “central axis of the Ferris Wheel” and I asked them if we could google it. They all agreed with a “no” and told me I was ridiculous. I agreed, so we tried to find what it was that we could google about the wheel.
Also, towards the end, a student asked if we could google the answer to “You can see US Cellular Field from a height of 100m. How long do you have to take pictures of it?”, and I really appreciated that comment. Lots of good discussion came from it.
I finally gave them very little information that I could scrounge up, and it was this little slide:
Students moaned and groaned a bit, because in the video you may have noticed that they wanted things like: Radius, diameter, min heights, vertical shift etc… and none of that is given… they had to use math to interpret all of this information to make it usable.
Act 3: Use your model, and interpret whether it makes sense or not.
So that was it from me, the rest was on them. They actually came up with very innovative ways to determine the second time when you’d reach a height of 100ft. Here’s some of the work they produced:
I actually tried to interrupt them a few times…but to no avail…they wanted to figure it out themselves. They make me want to keep teaching…