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I have to explain to kids that $2^n$ can yield high values. Not with math and numbers but with a story rather.

There was a story about a pharaoh and wheat..

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  • $\begingroup$ I'd rather add a [story] tag, but i cant. Are there alternatives? $\endgroup$ – Barry Staes Jun 3 '14 at 14:41
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    $\begingroup$ Another common story is to count how many times you would have to fold a single sheet on the daily newspapers for it to become thick enough to reach to the Moon. $\endgroup$ – Jyrki Lahtonen Jun 3 '14 at 14:44
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    $\begingroup$ There is the story, "would you rather have one dollar per day, or one cent on the first day and twice as much money each subsequent day?" Put it in terms of something that they might care about. $\endgroup$ – DanielV Jun 3 '14 at 14:58
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    $\begingroup$ My favorite story of $2^n$ : youtube.com/watch?v=ESpRFkXon7g $\endgroup$ – DanielV Jun 3 '14 at 15:09
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A nice way for him to realise by himself is to let him start with one and multiply it by two.

Ok, that was easy. Multiply again by two.
Ok, still too easy, so multiply by two again and again.

When he finds it difficult because numbers are too large, ask him how many multiplications he did and let him compare with $2n$ so that he can realise how big he got in comparison.

Another similar way with money. Whatever your currency, start with one (hopefully it shouldn't be too much). Does he have this amount of money? Probably yes.
Multiply this amount by two over and over again. Pretty soon he certainly won't have enough money!

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While asking my question, i remembered.

The Farao's architect.

When asked what he wanted paid, the architect said: "A chess board is 8 by 8 squares. Give me one grain (seed) on the first square, and for each square double the amount. So two on the second square, and four on the third square. And so on for the remaining squares."

"Very well", said the Farao, and his country soon went bankrupt.

Why?

A chessboard with grains on it

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  • $\begingroup$ Also found a nice description on en.wikipedia.org/wiki/Wheat_and_chessboard_problem $\endgroup$ – Barry Staes Jun 3 '14 at 14:41
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    $\begingroup$ When I told my kid this story, she suggested that we should try it. So we did try it, with rice grains, and I think that made the point much more strongly than just the story alone would have. $\endgroup$ – MJD Jun 3 '14 at 15:15
  • $\begingroup$ check out $2^{65536}$ on google's ownbrand calculator. Not that that's good education $\endgroup$ – chris scambler Jun 4 '14 at 12:24
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An interesting interactive one could be breaking a rock or stick in half a bunch of times and showing how quickly there are a lot of pieces. I personally would find it awesome if a someone lectured me on how $2^n$ was big by hitting a rock repeatedly.

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    $\begingroup$ This is a cool and perhaps counter-intuitive suggestion. I would do this in conjunction with the Rice & Chessboard problem. $\endgroup$ – Newb Jun 4 '14 at 12:45

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