[3ACTS] Ditch Diggers & Bubble Wrap

Here are two new tasks – Ditch Diggers and Bubble Wrap. They’re united by one common feature:

I saw something interesting and tried to turn it into something challenging.

This process is always harder than I think it wil be.

With Ditch Diggers, I was bobbing up and down on an inner tube in Kauai as a tour guide told us that two groups dug these irrigation tunnels by blasting and digging their way towards each other from opposite ends.

With Bubble Wrap, I was reading about an Italian performance artist who passed out sheets of bubble wrap of different sizes so people waiting for a train could calm themselves down.

Both of these things interested me, but the line from there to a classroom modeling task forces me to ask myself:

  1. What question would lead to that interesting knowledge?”
  2. Is there some way I can provoke that question visually?
  3. Could a student guess at that question?
  4. What information would a student need to answer that question?
  5. What mathematical tools would a student need to answer that question?
  6. Is there some way to confirm the answer visually?

So the next time you see something that’s simultaneously a) interesting to you and b) mathematical, try running through those questions above and see how they’d play out. In the meantime, you can check out my specific answers above.

BTW. Many thanks to Chris Hunter for helping me brainstorm Bubble Wrap.

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. Ginny Brackett

    February 6, 2013 - 6:42 am -

    I just looked at the ditch digger. Perfect exploration for linear functions. This is actually how the tunnel was dug under the English Channel. The French started at one end, the English at the other. This will make a great tie in to the importance of correct calculations.

  2. I certainly like the idea of Ditch Digging, but I think it would work better if it were under ground. As in, tunnels, not ditches. On the surface, you can see the other guy coming (if not immediately on Day 1, then towards the end) and aim for him…which brings up pursuit paths, perhaps, but it’s not really interesting from a “will they meet” standpoint.

    Underground though, you’ve got that blind aspect to it, as well as the 3rd dimension to deal with. Which is a lot more interesting, if you ask me…though maybe more from an engineering standpoint than pure mathematics.

  3. Just used “Bubble Wrap” to talk proportions and models with middle schoolers. And they really did cheer when the saw the Act 3 videos!

  4. The Bubble Wrap is rad! I look forward to using it with my kiddos. You know I’ve already thrown this one out there, but we can’t ignore the law of diminishing return. Popping bubble wrap is one of life’s simple pleasures for me, but I couldn’t see myself doing it for over 20 minutes. Furthermore, I’d think one’s rate would start to slow down as time progresses and the satisfaction level tapers off. Don’t get me wrong, I think the Italian performance artist presents a wonderful idea and stress-relief that I’d gladly pay him for. I’m curious to try this one out with students. I think I just might invest in the large bubble wrap roll I found at Home Depot and see what students get tired (or bored) the quickest and who has a joyful marathon experience.
    Regardless, I think there are some important conversations to have with students and this task. Could someone literally sit for 40 minutes and pop bubbles, ending with the same amount of satisfaction as they started with? At what point would it become more of a task to pop all those bubbles, possibly having an adverse affect on the stress-relief? Could more than one person share the same square of bubble wrap? Now we have a work problem. Last, but not least. One of my favorite ways of popping bubble wrap is to roll it up and twist it. I’d love to know if we could work that in somehow.

  5. Be still, my beating heart.
    Are those… non-integer coordinates on Ditch Digger?
    Mr. Meyer, you continue to impress. Consider that one stolen for my units on Parallel lines and Systems of Equations.