This week’s school drama, actually our only school drama this week, was about place value. Meg took to addition and subtraction like a Bales to bubble solution, but then came place values. For some reason it isn’t magically intuitive to her that when a number is over here, it counts as a bigger number and you have to remember it and add it to the other number. Who came up with such a ridiculous system? Daddy should not be making me learn this! Shouting will make the problem go away!
I’m keenly, tragically familiar with “don’t understand math on the first try.” My side of the family approaches math emotionally, and warily, kind of like you’d approach an angry wildebeest. It might not gore you today. I remember avoiding algebra in high school by memorizing the Greek alphabet in the back of the text book (and Mom wondered why it took me so long). I’m trying to get over this. I want better things for our homeschool.
A morning or two later, Meg and I were looking through an ancient history book that had a chart of how the Babylonians wrote numbers 1-59. The Babylonians mostly had a “base-60” system, as opposed to our “base-10” system, which I already knew. But I was fascinated to see that they kind of had a base-10 like ours nestled into the base-60!
This is how it worked.
A one was an upright, kind of like a capital “I”. A ten was a left-pointing arrow, like a less-than sign. To write a 6, you’d write six of the ones; to write sixteen, you’d write a ten arrow next to the six ones. Ten + six = 16. To write 36, you’d write 3 tens and six ones.
Babylonians actually only had to learn to write two digits, instead of the zero through nine we use! (They made up for it with the gazillion of cuneiform words, and they didn’t really have a zero, so I’m not regretting it too much.)
Using a separate kind of number to symbolize tens is just different enough from our system that I thought it might help Meg figure out tens and ones in English. Meg loves decoding secret messages—g square = A, circle = B—that kind of thing. So I promptly wrote out a worksheet on our dry erase board and had her decode some Babylonian numbers. She managed them with aplomb. We did more numbers the next day. She counted the tens, counted the ones, added them together. Done.
Is this going to be my magic go-to strategy? Whenever we hit a wall in math, have her learn how the ancient Babylonians did it? Well… no. Though I probably could, because they managed some alarmingly advanced equations; the Wikipedia article on Babylonian math stomped right among way too many wildebeests for my taste. But among other things, we aren’t going to be in Babylon forever.
I think what I love about this is how we went around the back of her expectations and snuck past her mental blockade. When I related the assignment to history and turned it into a decoding game, it wasn’t painful at all. I think it probably helped that I was learning and excited about it at the same time she was.
I’m also beyond delighted at how nicely math and history dovetailed there. Unit studies sometimes have to work really hard to connect math to the rest of the unit, but that one just fell into place. I guess it helps if the civilization you’re studying was revered for its rockin’ math skills.
If you want a little more information on Babylonian numbers (written in English, not in Alarming Math Major), I like this page. It will even let you type in a number and show you how to write it in Babylonian, which amused me for quite a while.
Photo Credit: All photos by Carolyn Bales.