What Can You Do With This: Glassware

[Updated here with my response.]

Click through to view embedded content.

Two things:

  1. It isn’t “what question can you ask?” but “what can the students do with it?” What is your lesson plan here?
  2. If Jason Dyer doesn’t come around to tell me I’m doing this wrong, I’ll be very surprised.

[high quality: photo, video]

[BTW: I updated the original image because josh g. is exactly right.]

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. Slight aside, but I think the first photo would be more compelling if you don’t immediately see the hand and ruler first. Maybe one shot with just the glasses, and another shot from the same position with the ruler in it that you can switch to once you need the numbers? (Unless you’re showing the video first, in which case it may not be as big a deal?)

    Ideas are still percolating for the actual WCYDWT question so I’ll go back to lurking on that for now.

  2. Slight aside, but I think the first photo would be more compelling if you don’t immediately see the hand and ruler first.

    Yeah, that’s exactly right. Gotta delay the application of mathematical structures until the problem asks for it. Thanks for the reminder.

  3. Not sure about the exact lesson plan at this point, but I am sure that I would want them to end up being able to predict the path of the glass if they know the radii of top and bottom as well as the height of the glass. GeoGebra makes this pretty nice to check. Rather than start with the lesson plan, I started with the applet. Check my work on this, it was late when I made it: http://tinyurl.com/r89q8e.

    If you want the original .ggb file go to: http://tinyurl.com/rx4qnc. The name of the file is “Glass Path.”

  4. Hey, someone’s gotta keep you in line.

    You mean, given you’re filiming in your classroom and you obviously have the glasses, why aren’t you having them use the glasses?

    I’d say this is a good opportunity to have them work from the media and then whip out the glasses at the very end so they can find out if they’re right.

  5. Heck, Jason, why wait until the *end* of the lesson? I mean, I understand the extrapolated usefulness of this kind of media in some situations: after all, one must think beyond one’s boundaries, and there are too many underprivileged societies out there whose citizens have never seen or owned a glass. The UN really needs to step up on that. But the US of A is not one of them. And never will be, thank god.

  6. Yeah, I don’t think that the applet is sophisticated enough to deal with degenerate cases. If the radii are equal, it fails because the glass would roll straight (which I was happy about). Other than that, I think it works. You planning on giving the kids degenerate glassware to roll around?

  7. no nuking intended. My judgement of the silliness of this particular video (re: would you just give them the glasses already?!) is merely heightened by the fact that Dan has used video in the past to so very, very much greater added-value effect.

  8. If the kids had the glasses in hand from the start, what would be the motivation to use geometry to work out how the glass will roll? They could just, you know, roll it.

  9. (Whether that’s an argument for using the video clip or for tweaking the lesson, I don’t know.)

  10. Jason’s standard-issue argument applies here more than ever but the media isn’t as useless as Dina suggests. Two reasons why:

    1. Online learning.
    2. A digital cupboard is useful for storing dozens of cups of different shapes and sizes.

    Real cups are essential components of this investigation but they won’t be the only component and the other components won’t be exclusively non-digital.

    I could probably illustrate that better if someone would kick off the lesson plan, though. The framing of these objects into something that every learner can access is tricky.

  11. Josh, if I was running the lesson probably first I would hand out plastic cups that students could experiment where yes, they could just see how they roll, but they have the assignment of *why* they roll the way they roll … then they get the purely digital cups, and have to figure out based on their experiments what the answers should be.

    Essentially I’d do it as a science experiment, where one gathers data, forms hypotheses, then tests those hypotheses to a new situation. If the hypotheses fail, then I’d have the students go back to the original glasses to try again and then go back at them with Digital Glass #2, etc.