Math Salons and Base Eight

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

Math As Story

Once upon a time, math came packaged in textbooks, and most people had never (ever) even seen a math story. Unless you count things like: "The westbound train leaves at 1pm going 50 miles per hour and the eastbound train leaves at 2pm going 60 miles per hour. If they're 300 miles apart, when will they crash?" (Except the textbook would have said 'meet', leaving out the tiny bit of drama I couldn't help adding.)

I love stories, and I love how much they can add to the appeal of math. History is one storytelling genre that adds a lot of drama to math. Why do we need calculus? Seems to me every calc course should start with enough history for students to see the story unfolding. Where did that crazy number i come from? What's up with geometry proofs? (I still don't know enough to tell these stories properly. It's one of the things I'm doing during my sabbatical year.) Biographies of mathematicians are also a great way to ground all the headiness of math in the details of a life. (My review of The Man Who Knew Infinity, about Ramanujan, is here.)

If you follow this blog, you've seen some of my storytelling attempts (Eight Fingers, Crash and Count). They pale in comparison to some of the literary delights below. Today was a blockbuster day for storytime in the math blogosphere.

Glenn is posting an ongoing adventure story about a place called Verdania, at his blog, Off the Hypotenuse. Each chapter ends with a math puzzle. In the current chapter (Chapter 10), the main characters, who were shipwrecked, are leaving the children's village, and heading to the adults' village. At the end, we're asked to figure out the lengths of 3 paths the characters could travel to get from Sentry Point 1 to Adult Village. If you want to start at the beginning, he's made a new blog with just this story.

But don't leave Off the Hypotenuse behind; there's lots of other great posts there. I am delighted over and over as I try to catch up on all his older posts. The strange thing is, I can't figure out who to thank for pointing me there. I just could not retrace my steps successfully the day I found it.

Glenn linked today to another new delight: Number Gossip, hosted by Tanya Khovanova. It's not exactly stories, but it's in the same spirit, and fun.

Then Jason Dyer, at Number Warrior, pointed to a gory delight over at Emily Short's blog. Word problems with a decidedly 'unfortunate events' twist.

Then there's the pirate story, over at The Math Factor.

Dave Richeson, at Division by Zero, pointed to a great series starting up in the NY Times, written by Steven Strogatz, on:

... the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.

It starts with a story about penguins in a hotel, ordering fish, fish, fish ... fish. Check it out!

It made me chuckle to see Richeson mentioning Strogatz. I just finished reading Steven Strogatz's lovely new book, The Calculus of Friendship, after hearing him give a talk about it at the Joint Mathematics Meeting a few weeks ago, and I've just started reading Dave Richeson's exciting new book, Euler's Gem.

One last link, not quite a story: Mike Croucher, at Walking Randomly, posted this great piece on the Math Carnivals. (Sorry I neglected to link to the last Math Teachers at Play, over at Math Hombre. It's lovely, and I'm still working on getting through all the links.)

The math blogosphere is exploding with stories today. Yeay!