How Many: Folds

(note: this post was previously under: Two problems, but it seemed better to split the two problems into separate posts. The other problem is found here.)

If you could, how many folds of a sheet of paper would it take for the thickness of the paper to reach the moon?

Asked for them to write their guesses down first.  They are so damned hesitant in math that this takes numerous trips around the room to get them all to record an independent guess.  This is a class of kids who have failed often in math, so the fear is evident in their eyes.  Next I write their guesses on the board, most of the guesses are in the hundred’s of thousands to millions range.

I asked “What information do you need?”.

  • They asked for the distance to the moon; wolframalpha’ed (yes, I just verbed it) it and gave it to them in meters.
  • They asked for the thickness of paper, so I gave a couple students a sheet of paper and a caliper. They tried to find the thickness, and then rolled their eyes at me, so I asked what do you want?  They said more paper, so I gave them a ream of paper (500 sheets), and they found the thickness.
  • To keep everyone on the train, I gave them a skeleton setup for how to find the result (e.g. How many layers of paper with one fold, two folds, three folds, etc).
  • (semi-furious calculations commence.  Many of them are finding out that the calculator on their smartphone is not so smart, so they ask to use each other’s calculators.  Maybe 4 kids actually end up bringing their calculator to class, sigh.)
  • Answer found is the same as in the video that spawned this investigation: found here.

My first favorite part about this calculation is that I was able to show them how quickly a spreadsheet calculates the same result after they’ve filled a sheet of paper with numbers.  They had use of the laptops if they wanted, maybe this will help buy them into the usefulness of spreadsheets.  Maybe not.

Me second favorite part about this calculation is that they’ve all tried to fold a sheet of paper as many as times possible, and many of them have seen the mythbusters episode with the folding paper.  It’s a problem whose result shocks them, and I like that.

The second class of students that I gave this to, had 3 kids who had already seen the video with the answer, and the magic was significantly reduced for the whole class because they knew that someone else already had the answer.  Much less driven to find the answer.  Lesson for me: Verification isn’t anywhere near as exciting as Mystery.

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