Thursday, November 02, 2006

Want a Challenge?

Here's a challenge for you and your kids (don't give any clues to your kids--just let them answer as they think!):

Question: How thick will a folded piece of paper be if you fold it in half 50 times?

Take a piece of paper. Fold it in half.
Continue folding it in half, keeping track of how many times you are folding.

What did you discover while doing this? How close was your estimation?

I'll provide more information in a few days! :D Feel free to share your results and observations in the Comments.

ADDED Nov. 5:
As indicated by someone in the comments, a piece of paper can actually only be folded 8 times--although sometimes you can only reasonably manage 7. Don't tell your kids this! My kids had a great time trying to see just how much they could fold the paper and if the size of paper made a difference. Once they saw how thick 7 or 8 times were, I asked them to think about how thick it would be if, theoretically, you could fold it in half 50 times. (The answer is that it would go past the sun!) You can have older kids work this out by thinking of having sheets of paper and doubling the layers each time. Those who are into exponents can do the 2^50. They can chart how many layers there are at 1 (2^0), then doubled, then doubled again, etc. If they aren't yet at those math skills, you can tell them that doubled 9 times (2^9) is 512, a little more than a pack of copy paper. 10 times is twice that. And so on. We worked out that you would need over 2 quadrillion packs of paper if you were to double the layers each time until you had doubled 50 times. That's over 200 trillion boxes of 10-packs of copypaper. The results thoroughly impressed the kids. And they loved discussing the math involved!

1 comment:

Kunoichi said...

A piece of paper cannot be folded more than 8 times.