I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. A couple of possibilities
    1) show them a video of a ferris wheel and ask “any questions?” a la 101qs.

    2) choose some metric, like “you want to wave to your friends, how often will they come over the top so you can wave to them?”

    or some other question that calls for using some tools, that the students ask for themselves, rather than this sort of paint by numbers context.

  2. I did a similar activity with teachers… or an intro at least, where they had a k’nex ferris wheel, took measurements, and graphed their data points. Many of them are going to borrow the ferris wheels and try similar lessons and extensions in their classrooms this year. I am excited to see what they come up with for their students.

    I am also working on a STEM lesson with a science colleague using the k’nex Ferris Wheels… so I am looking forward to some great ideas from your makeover!

  3. SanchezTemple

    August 1, 2013 - 7:01 pm -

    Perhaps ask students if it matters at what point they get on the Ferris wheel? Does everyone get the same amount of time on the ride? If not when is it best to get on?

    Take it from there…

  4. This ​probably isn’t much better, but it’s a thought.

    Maybe find a video like this… (I’m sure there are millions out there) of a hamster that can’t stop spinning his wheel.


    This one shows the ending in slow motion, and conveniently has a digital clock counting in the background. Count the rotations in a certain period of time​ (before he falls off)​. It does 1​0​ ​revolutions in x seconds, how long does it take to do one revolution?

    Tell them the hamster falls off at y seconds. ​A​sk​ what height the hamster is going to fall from.​ Is it going to crash from the top of the wheel, or closer to the ground?

    It’s at least a more entertaining context than a ferris wheel.

  5. The Ferris Wheel is a fantastic analogy for what’s going on with the unit circle, so I wouldn’t want to change that.

    General idea for activity flow:
    1. Initial graph sketching — if you went on the Ferris Wheel, sketch your height vs. time (naked graph, no specific numbers).
    2. Calculations to test sketch and make more precise.
    3. Generalization to sine function or whatever else you’re going for.

    The tricky part is motivating the curiosity / need for the height graph and the following calculations. Maybe a quick comparison (warm up) with other familiar height vs. time graphs would get them thinking and wondering in this direction.

  6. Nicole and Karl, I love your ideas. I may borrow them for my Pre-Calculus class next year. The K’nex ferris wheel and hamster video are great visuals for the more visually-inclined students.

    I thought you could do some interesting problems with a combination lock. You could give them a combination and have them find the degrees of rotation (both clockwise and counterclockwise). You could also have students calculate the arc length of each rotation.

    Maybe introduce a rate of rotation, say 2 numbers per second, and have student calculate the number of seconds it would take to get from one number to the next. Also, how many seconds would it take to complete the entire combination?

  7. Real-life example (as in: I experienced it): If the Ferris wheel is on a square in a city where the surrounding buildings are 35 ft high, how many seconds will we actually see a view of the city instead of just the square? (35 ft probably isn’t that high, I went with the example Ferris wheel)

  8. The Price is Right! Or Wheel of Fortune, or really any sort of spinner where you can win a prize. If we make brakes that will stop the wheel, how long do we wait to hit the brakes to win? How is this different from what happens on the show? What sort of things are we assuming and what happens when we change characteristics of the wheel (make it accelerate, change its radius, etc.)