Layer 1 — Photo of Ferris wheel
Layer 2 — Video of going around
Layer 3 — Timer
Layer 4 — Unit Circle
Layer 5 — Trig. Graph

After we discussed and slowly added layers it was pretty amazing; in the end I didn’t need to say anything but show the video and student’s minds were abuzz with making connections. Light bulbs were going off left and right. This is definitely something I will try in the future. Thanks for all your thoughts Dan they have really helped me grow professionally.

http://eduflection.blog.com/2014/01/20/ferris-wheel-problem-teaching-in-layers/

I hodge, I couldn’t get your link to work, but it could be my lame work computer’s fault. The plugins and other software are out of date.

I might show a video of this: http://www.youtube.com/watch?v=g8d63aFposU (Big Seattle Ferris Wheel starting at 0:55), and this http://www.youtube.com/watch?v=0FjddxnLMmY (Small Human Powered Ferris Wheel).

Or use a geogebra applet: http://www.geogebratube.org/student/m45663 to model the ferris wheels.

Possible questions:
1) Which ride looks like more fun? What are some similarities and differences? Which ride do you think is faster?
2) Suppose each ride only lasted two loops. Which ride could handle more people in an hour?
3) Sadly, you and your friend were not able to get on the same car for the big ride. Will you ever be at the same height? If so, where? And when?
4) Suppose each ride lasted the same amount of time. How many loops would you get on the smaller ride compared to the the larger ride? How much distance would you have covered on the smaller ride compared to the larger ride?
5) How many miles per hour would you be travelling on each ride?
6) Sketch the height of the first car as a function of time for each ride.

I don’t understand the rational for giving them a form of an equation (y = asin(bx — c) + d) they do not understand and asking them to play around with parameters to make it fit. Doesn’t that encourage superficial thinking — sort of like “b” is the y-intercept and “m” is the slope because…, well because that is the way it works? What if a student asks why that kind of equation makes that kind of graph? That is a three or four day explanation. I love Desmos, but what does it give us that the sketch did not?

So I think I’d like to use the activity as Dan laid out but conceal the name of the function. I’m not sure how to do that on Desmos, but you could do it on GeoGebra. Just don’t let them see that it’s sin (x).

After Act 3, I’d like to ask them how high the red dot would be at some random time that’s not a multiple of 1/4 rotation. That way they’d have to draw a triangle and actually use the sine or cosine to find the height after rotating, say 3000 degrees. For this purpose, it would be better if the ferris wheel rotated in the other direction, because that mimics positive rotation on the unit circle.

I wanted to get to this this summer, but here’s what stumped me. How can I get kids perplexed and wanting to know where the dot on the rotating circle would be after 10 seconds? My thought was to do something that’s a take-off of the OK Go Chevy Sonic music video. Like they have to do a music video, and at the grand finale (which according to the song will happen at a given value of time), they have to shoot a laser at a target on a rotating drum. So they have to aim the laser correctly, so they have to know the precise position to which the target will have rotated at that time. Then they have some anticipation about “will it work or won’t it?”.

But I haven’t gotten around to it. If anybody has any suggestions or ideas, that’s be great.

If you want it a little realistic you could say the wheel turns as it loads up, then goes for 60 seconds, holds for 10 seconds, turns for 60, holds for another 10, then runs for 60 and unloads.

I can think of a few applications for this. One, given the rate the wheel turns – is this a fair stop interval? Or do the same people end up on top both times? Two, if you know this and want to maximize your time on the wheel (regardless of placement – maybe your date will smooch anywhere and/or this gets you away from your pesky little brother for the remainder of the ride) is there a better time to get on the wheel – sooner or later?

For time maximization, is first on likely to be first off or last off? Does it matter? This will let you get into some more group discussion/argument about the time involved in loading people on and off.

P.S., Dan, thanks for the Twitter shout-out!