Don’t Forget Answers, Iteration

With the question, “how high will the club soda go?” we have taken WCYDWT media into calculus, which is fun.

It’s important with these media-based math questions that you have on hand a) answer media (like this, showing how high the club soda went) that students can contrast against their own work, and b) iterative practice problems that scale in difficulty.

Maybe you start with i) the cylinder tumbler, building towards ii) angled, linear sides, moving through iii) the parabolic bowl, and culminating with iv) the piecewise monstrosity that is the margarita glass, which, it turns out, holds exactly 12 oz. of club soda. I only know that to make WCYDWT media worth your while, you must iterate them.

[Click each for high quality.]

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I'm Dan and this is my blog. I'm a former high school teacher, former graduate student, and current head of teaching at Desmos. More here.

5 Comments

  1. Lee Trampleasure

    July 24, 2009 - 9:30 am

    Glad to see you’re measuring in the metric system (says the physics teacher) ….

  2. Steven Peters

    July 24, 2009 - 4:12 pm

    At first, I thought you were saying how high would the foam go. That’s complicated. The volume analysis is cool though. It’s a nice way to make the concepts connect.

    I wonder if there’s something similar about surface area. It’s hard to control thicknesses I guess.

  3. Dan Meyer

    July 25, 2009 - 10:16 am

    @Lee, we’ll often convert answers to feet or miles but the base 12 system has been killing me for the last few years.

    Student: “You mean 5.4 isn’t 5 foot 4 inches?”
    Teacher: Agh.

  4. Mr. K.

    July 27, 2009 - 9:26 am

    My first thought with that was the refraction problem, where the glass looks like it holds more than it actually does, and the outside measure isn’t representative of the internal volume at all.

  5. Phil

    April 21, 2011 - 7:12 am

    Hey. Its an old post, but did you video these? Seems like they would also make good graphing stories for depth against time, where the line will be curved. I’d video some myself but I don’t have such a wide array of glasses!