What Can You Do With What Can You Do With This?

I’ve been on a Dan Meyer “What Can You Do With This?” kick for the past week in my 6th grade classes.  They had so much fun doing the Apple Countdown (some of them stayed up to see if they could get it – one kid claims that he watched and waited for hours, got bored, started watching videos on YouTube, and then missed it by mere minutes), that I thought I’d see what else we could do with What Can You Do With This?  Here’s what we did (and what I learned while doing it).

On Monday, we watched the Boat In The River video.  I particularly like this video because, like the Apple Countdown, it poses a question that is really compelling.  Everyone (I hope it’s not just me) has wondered, at one point in their life, how hard it would be to walk up the down escalator.  It’s a somewhat subversive thought – you aren’t supposed to go up the down escalator.  But here’s a video of Dan doing just that, giving you the chance to answer that burning question!  It’s also one of those top-notch What Can You Do With This? videos that contains all of the information you need to answer your question.  No external research or measurements necessary.  (Though requiring research has its pluses, as I learned later)

We watched it twice before I took suggestions for questions.  I got three different questions:

  1. How long with it take him to climb the down escalator?
  2. What song is he listening to?
  3. How did he make the movie, with himself in it four times?

Now, I really wanted the kids to answer the first question.  I tried to steer them towards it.  And we watched the video several more times, gathering information and using it in various ways to figure out the answer to our question – as a class.  Pretty productive, no?

But it didn’t feel great.  If you’re a teacher, you know the feeling in a class when things really are great.  And this wasn’t it.  Things were good – but not totally awesome.

For homework, I gave them a sheet with the picture of the gumball machine with a kid standing next to it.  I didn’t give them the one with the measurements – just the kid and the machine.  I asked them to come up with an interesting mathematical question to ask about the picture, and to make a list of the other questions they’d need to answer, formulas they’d need to research, and measurements they’d need to take to answer their question.

We were going to return to the assignment on Wednesday, because Tuesdays in our class are Skills Challenge/Free-Choice days (basically, a quiz and math activity free-for-all).  But, to my surprise, two of the students were so excited about their gumball machine questions that they wanted to share them with me and work on them during free-choice time.  And the things they shared with me really changed my perspective on this activity.

The first student had posed the “intended” question: how many gumballs are in the machine?  Not surprising.  What was surprising was that he had already answered the question – without me giving him the diameter of the gumball or container!  He did this by measuring the teeny, tiny gumballs in the photograph, Googling the size of an average gumball, finding the ratio of the two sizes, and using that to scale-up the radius of the container that he measured from the picture.  He then looked up the formula for the surface area of a sphere (an unfortunate but understandable mistake, because we hadn’t talked about volume yet in class at all) and calculated… I think it was something along the lines of the number of gumballs needed to wall-paper the container.  But he’d done all of this by himself!  I gave him a bit of re-direction during class (distinguishing between volume and surface area), but this was an example of student-powered investigation at its best.

From this student, I learned that I really didn’t need to – and probably shouldn’t – give the students much guidance in measurements or methods.  This student didn’t just learn about volume and scaling – he also learned how to do research, use the tools you’re given resourcefully, plan an investigation, and troubleshoot during an investigation.  In the grand scheme of things, what do I care more that my students learn?  Volume, or those other things?  I think the latter win.

The second student didn’t pose the “intended” question.  She asked: how tall is the kid?  My first reaction when she shared this question with me was, “Ok, great.  But is there anything else you want to know?”  I had intended for this to be a finding-volumes-of-spheres activity.  But there wasn’t anything else she wanted to know.  And when she started showing me the work she’d done, I saw how genuinely excited she was about her question and how much great thinking she was doing to answer it.

From this student, I learned that if I was going to ask them what they wanted to do with a situation, I had to let them do what they wanted to do.  One of my goals was for them to develop as mathematical question-posers.  I wanted them to use this activity to exercise their curiosity, and I wanted them to know that I valued their ideas.  Again, what was more important to me that they learn?  Volume, or curiosity?  Curiosity takes the cake any day.

Armed with this knowledge, here’s what we did in class on Wednesday.  I said, Kids!  Your choice!  You can work on your gumball question (whatever it is), work on your escalator question (whatever it is, so long as it’s mathematical), or pose a question about these pictures of Russian stacking dolls (here and here).  Rulers, calculators, the internet, your classmates, your teachers – all are tools at your disposal.  Go for it!

And they sure did go for it!  The questions in the room ranged from the classics – how many gumballs, and what’s the size of the next-smallest doll? – to the very personal – such as, how many of my favorite kind of frog will fit in the gumball machine?  And, how many average-sized Russian stacking dolls would fit in my friend?  Because some of them were watching the escalator video on computers (we have a class set of Chromebooks), they started browsing Dan’s blog for more pictures and videos, and got more and more inspired.

This made for a rather hectic class for me.  Everyone wanted to share what they were doing with me, and every time someone needed my help, I had to learn about their unique question.  But the classroom was bursting with energy, creativity, whimsy, resourcefulness, curiosity, and excitement.  It genuinely felt great.

My question for you, readers, is where do you think I should go from here?  How do I build on this momentum?


Author: Anna Weltman

Anna is a PhD student in math education at University of California, Berkeley.

2 thoughts on “What Can You Do With What Can You Do With This?”

  1. This sounds so cool. I love that the student thought to ask the question of how tall is the kid in the gumball photo. One possible next step I can think of is having the students present their findings in some way to the rest of the class. Maybe there’s some very cool presentation method (not a prezi) I can’t think of this late at night that lets one see all the investigations that can be developed from just one bit of media.

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