2+2 != Maths

February 23, 2012

To the moon

Filed under: classroom,teaching — Numbat @ 20:06
Tags: , ,


what to do in Maths class period 6 on a hot day when 1/3 of the class are off on excursion? I decided it was time to try something different.

The question is “how many times would I have to fold a piece of paper for it to reach the moon?”. Obviously, you have to assume it’s a pretty big piece of paper to begin with. I started with asking the students to estimate how thick a piece of paper was, or as one student corrected me, how “thin” was the piece of paper.

I then asked them to estimate the distance between the goal posts on the playing field outside the classroom (for the non Aussie’s amongst the readers – there is no standard length of an Aussie rules field).

I then asked them to estimate how many times they’d have to fold a piece of paper to fill the playing field. Then I let them loose. Most of them figured out you have to at least measure the playing field, and at least half the groups came up with a measurement that was reasonably accurate.

Only one group managed to make an estimate which was reasonably close – they calculated 10 times. The comment by the student was that it was a “surprisingly small” number. The actual number was closer to 17, but the lowest estimate by the students was 120. I will concede that 10 is surprisingly small against 120.

However, as a group they did not manage to convert that to the moon question. They all knew the rough distance to the moon (we’d used that number in a class a few weeks ago so they had a good idea), but they all still thought of a number in the thousands range.

Although I was disappointed in the quality of the estimates (even after the preparatory work) what I took away from this is that all the students engaged in the activity, and the discussions I overheard were very encouraging. “what’s the formula for ….”, “how do you work out ….”, “what should we do here…”

When I exposed the answer, a number of the students asked “how can that be”, and a couple of students attempted to explain it to them. I even heard one use the term “exponential”. I will count that part of the exercise as a success.

I was a bit rushed in this exercise as I wasn’t sure how long it would take and how long the students would need to measure the oval and make their calculations. I think I could prepare them a little better next time round. They were in no state after the exercise to debrief and that was a little disappointing. Next time I’d like to challenge the non-believers to prove me wrong.

Overall, however, I am very pleased with the outcome and I think many of the students saw a different side to Math than sitting in a classroom answering questions from a book. I’m hoping I can do many more of these sessions this year.




  1. I wonder, what would happen if they did a paper folding activity themselves (perhaps first)? Maybe they would develop more of an intuition as to how quickly things grow exponentially? Most people’s number sense is too weak to really see this by just doing calculations.

    Comment by dwees — February 24, 2012 @ 02:52 | Reply

  2. I’m not sure I get the initial question “how many times would I have to fold a piece of paper for it to reach the moon?” Are you really saying “How many times would we have to double the length of a piece of paper to reach the moon?” Maybe it is an Aussie English to U.S. English translation issue.

    Regardless, I like the idea of kids up, and out of their seats doing math not just mimicking math. I like the estimation piece, and I’m also not surprised (nor concerned) that they were far off. The dissonance could lead to learning.

    Comment by Jeremy — February 24, 2012 @ 03:29 | Reply

  3. @dwees – great suggestion. I will try that next time.

    @Jeremy – What I meant was that as I fold the paper it’s thickness doubles each time, how many times would I have to fold it so that it was thick enough to reach the moon.

    Comment by Numbat — February 24, 2012 @ 07:25 | Reply

  4. Great story, mate / fellow Aussie educator!

    I love the learning that you can generate with a comparatively simple activity like this. In fact, sometimes it seems that if your plans are thrown awry and you have to be creative at short notice, you come up with something that engages students better.
    I remember my dad asking a related question: “How many times could you fold a piece of paper in half?” I was surprised that the limit is around 6 or 7, again because of exponential changes. I think this is a really powerful, important piece of learning for all of us – think of saving for retirement, investing in an asset with steady growth, inflation predictions, etc.

    Comment by Peter Price — February 27, 2012 @ 08:32 | Reply

    • Mythbusters has a great video on paper folding using a gigantic piece of paper and a forklift. The kids will love it.

      Comment by Kirk Newman (@Root_4_Math) — February 28, 2012 @ 04:19 | Reply

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