I've been doing monthly math salons at my home since the fall, where parents, kids and other adults play with math. At the last session I had decided to play with base eight, and had told participants we'd be doing 'alien math'. I waited until the last minute to look for good activities, and couldn't find anything I really liked. I did find two good activities related to binary, though, and prepared those.

The night before the salon, I laid in bed thinking up a children's story about my eight-fingered aliens. I got up early and wrote it, and then printed it in booklet form. On the first page I asked the readers to illustrate it for me. The kids really liked doing that.

In the story I claimed because their system is based on 2x2x2, these aliens are really into doubling. I also claimed that the kids figured out a code for counting up to eight using just the 3 fingers from one hand. I figured binary would come pretty easily to the aliens, and mentioning this would be the tie-in with the binary activities we'd do at the salon.

Here's the story:

Eight Fingers, by Sue VanHattum & Friends

[Dear friends, I wrote this story, but I wasn’t sure how the people looked, except for their fingers. Can you help me illustrate it with pictures? Thanks! Yours, Sue]

Once upon a time, on the planet __________, there lived people who looked very much like we do, except for one thing. On each of their two hands, they had a thumb and only three fingers.

Longer ago than anyone there remembers, they used to use stones to keep track of things. But then, just like us, they began to use their fingers to count.

Eventually, though, they starting writing down the numbers they were counting on their fingers. Just like us, they had a symbol for each number from zero up to seven. Their 0 and 1 looked like ours, an empty circle of nothing, and a tally mark for one. But the others were a little different…

But then they wrote this 1 0 to mean all eight fingers. Or to mean eight horses, or eight flowers, or eight yummy strawberries.

Do you know how they wrote nine? _____

Now, eight is a very special number, even here on Earth, and they discovered long, long ago how special it was. They liked doubling even more than we do.

If you started with one finger, and doubled once, you could hold up your two fingers in a circle. Then if you doubled again, you had all the fingers of one hand up. The next time you doubled you had all your fingers up. If you did it again, all your fingers and toes were up. Again, and you had to have a friend put all their fingers and toes up with yours. Most kids started giggling so much when they did that, it made them fall on the ground laughing.

Now all that doubling helped them discover a very neat pattern. Kids liked to tell each other the secret code that used just three fingers, and showed all the numbers from zero up to seven. Their fingers were a little more flexible than ours, and they had great fun flashing the codes for each number to each other. I wonder if you can make a code like theirs …

There’s much more to their story, of course, but I just haven’t written it yet…

There is no end

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I love this story! Alternate base math is a great topic for a math circle. I like that you start by having them illustrate. Very non-threatening.

ReplyDeleteThanks, Kate! Another friend asked permission to use it. Anyone who wants to is welcome to use it, and I'd love to know what kids think of it.

ReplyDeleteI like your story problem, but I'm a little confused. It's all in base 2 right? Why is eight represented by 10, then? Shouldn't it be 1000?

ReplyDeleteWell, I meant for it all to be in base eight, since they have eight fingers, but it isn't very clear in the text...

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