Injecting a little engineering in the math

I have received this lesson fifth hand and seen multiple variations with colorful additions, but it boils down to this:

Here’s a stack of 6 plastic cups. The company you work for is needs to know what size of box to use to ship the cups in stacks of 50. How tall will the box be?

I have done it this way and it made a straightforward lesson with an intuitive linear relationship.

Last summer when doing this lesson with 9th graders, it came out (by accident) this way:

Here’s a stack of 6 plastic cups. Design a box to hold 50 of these cups.

A wildly different lesson ensued. Some students assumed one stack of 50, some students used two stacks of 25, some students made 10 stacks of 5, and some came up with even more exotic ideas including non-rectangular boxes and uneven stacks.

10 Responses

  1. Scroll over to Dan Meyer’s blog,, for yet another take on this problem. I tried it this year, as described in Meyer’s blog, with great success! I love these types of problems and wish I could replicate the learning involved all year long…Dan Meyer’s blog is a pretty good start on making it happen!

  2. I was thinking about Dan’s “stacking cups” problem also! I do this with my 7th graders & also have them write an equation to predict how tall a stack of 50 cups will be and to find out how many cups you need to make a 24″ stack (or whatever number).

    However, I would like to change up the project & make it more personalized, such as “what is the BEST way to make a box for them, and how do you know?” (get them thinking about materials use, surface area, volume, etc.) and “how many cups would it take to make a stack as tall as you are?”.

    I’m currently re-writing it & trying to come up w/ a grading rubric . . . thanks for the inspiration 🙂

  3. This is fantastic. Yeah, Dan’s thing came to mind too, but this is something more that can plug in directly to what he did with the problem and make it even more interesting.

    Everyone should steal this and use it. Even better, distill what just happened there and turn it into a design question you can ask yourself whenever you’re creating a “real-world problem” activity.

    • I have done this sort of thing intentionally before, but I’m not ready to make a Grand Theory yet.

      Basically I take some lesson which involves a building portion with preset directions and I throw out the directions.

  4. This is a great problem. It sounds like a great way to incorporate surface area and volume of prisms. I agree with Jenni, you can ask quesions about the BEST way to box them. You can go as far as you want with this one, saying the box has to be at least X wide and X tall, or ask them to find the box with the least amount of material and so on. I haven’t heard this one yet, so thanks. I will definitely use it next year!

  5. I really like this problem. I was going to get my Y7 to design a gift box later on this term, but I’ll be getting them to try this instead – thanks for sharing the idea.

  6. Three cheers for serendipity, and three more for rolling with it. Having had some small successes with my 6th graders this year and cups, I look forward to sharing your more wide-open problem with a group of kids come fall.
    And once they design boxes, they’re totally going to build them!

  7. […] all my lessons that have worked beautifully, an equal number have failed. Fine, so you tried something creative and it didn’t work: get […]

  8. […] more here and here. Hat […]

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