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| Home | This afternoon, my friend Mike was leafing
through a book called "After Math," a book of mathematical puzzles
and tricks. "Hey, come look at this," he said, sounding
excited. When I went over to him, he held the book open. The
heading at the top of the page was, "APPENDIX A: CASTING OUT
NINES."
"'Casting out nines' really exists," he told me, grinning. "I thought you might want to see this." Back when I was in sixth grade, I had a terrible math teacher. She was old. She was cranky. She didn't like kids. I'm not sure she liked math all that much. She smelled like soured milk. Her name was Mrs. Sawyer. I assumed that she was named that because she looked like I imagined Tom Sawyer would when he was old. No, let me be fair. I don't think she smelled like soured milk. But she sure looked as if she should. One day I had finished my math homework early and was reading a book I had brought, as I tended to do when I got bored in school. I was reading quite happily when a shadow fell over my desk. It was her. "What are you doing?" she asked. I looked at the book I had on my desk. I looked at her. "Reading," I told her. (I was a good kid. I never sassed my teachers.) "You're supposed to be finishing your homework," she said. "Uh, I've finished it already." "Let me see your work," she snapped. I could tell it might be a while before I got back to my book. I pulled my homework out of my math book and handed it to her. "Mmm," she growled. "Well." She frowned at me. "You just need to redo your homework." "Again?" I asked. "Yes," she said, taking my book and my homework. "And hand it in to me when you're done." I did it again. Like I said, I wasn't one to sass my teachers, and besides, the actual work was pretty easy. I must have finished it in ten or fifteen minutes. I took version 2.0 of my homework up to Mrs. Sawyer's desk, fully expecting to get my book back. Boy, was I in for a surprise. Instead of my book, I got a small lecture. "I've given your book to the principal. You can get it from him at the end of the school day." She leaned forward, dreadfully earnest, preparing to deliver a little life lesson. "You have to realize that what we're learning today is something useful that you'll use the rest of your life. And if you don't apply yourself now, you'll never be able to do math." What we were learning was a process called "casting out nines." It was a way of checking your addition or multiplication by getting rid of nines or digits which added up to nine in the numbers you were adding or multiplying, leaving you with a simpler addition or multiplication problem. To be honest, I never can remember the actual details; despite what Mrs. Sawyer said, I have never used "casting out nines" since that day in her class. It always seemed like a stupid way to check addition and multiplication, since it required you to make an extra calculation. Either you were good at addition and multiplication, in which case you could check your own work, or you were bad at it, and making you do more wasn't going to help. But Mrs. Sawyer was from the time before calculators, and probably had visions of little sixth graders stranded on desert islands with no way to check their math other than casting out nines. After school I went to the principal's office to get my book back. Looking back on my middle school years, I realize now that the principal, Mr. Forte, was a man promoted far beyond what he could handle. At the time I just knew that he made me uneasy, as if he were the pilot of a jet spiraling towards the sea. "Have a seat." He had a few small wooden chairs in front of his desk for when kids came to see him. I sat on one and gazed up at him. "Mrs. Sawyer told me what happened," Mr. Forte said gravely, hands folded together on his desk. "And I'm very disappointed in you." I sat there quietly. I didn't really want to be there, but I didn't feel very guilty. I had a habit of blissfully ignoring other people's opinions of me if I didn't like them much. "You see, we don't come to school to read." He held up my book and waved it in my general direction. "We come to school to learn." There was more to his impromptu lecture, but I didn't listen to any more of it. We don't come to school to read? I imagined myself solemnly telling my history teacher, Mrs. Ramsauer, "I'd like to read the assignment, but Mr. Forte told me that we don't come to school to read." He finally wound down after some minutes of lecturing. "Do you understand?" he asked me, giving me back my book. "Oh, yes, sir," I said. "Good." I got up and walked towards the door. "And don't let me hear of you reading in school again." I've told this story to a fair number of people, Mike among them. So he was extremely pleased when he found instructions for casting out nines in a book. I was merely surprised that anyone else knew about this wacky method for checking your calculations. "Now you can learn how to cast out nines again," Mike told me. Perhaps, but knowing that it existed, and that it was so unimportant that it was in the appendix of an obscure book of math puzzles, was enough for me. Well, that and the irony of finding it some fifteen years later, when I'm close to finishing a Ph.D. in physics. Ah, the things I learned in school. |
