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Sidebar: Edible Equations

Crazy for Calculating! Making Math Fun
By Sue Smith-Heavenrich
Issue 112, May/June 2002

I was never a math wizard. In fact, if you had asked me way back in third grade what my least favorite subject was, I'd have said math. Or maybe it was fifth grade, when we began learning long division. For some reason, numbers and I just never connected. "I never failed math," I tell my small group of fifth graders, "but I came this close." I stretch my hand out to them, index finger a mere half-inch from the thumb. The students find this amusing. Perhaps it's because I'm their math coach, and we are getting ready for the county "Mathalon" competition. To them, I am the Puzzle Lady. I lead weekly math enrichment workshops full of algebraic thinking games and challenge them to find solutions to word puzzles. At the end of our always too short sessions, I have to force them to go back to their classrooms.

Ages ago, when my husband and I made the decision to homeschool our children, I knew that I'd have to come to grips with my math phobia. That's when I resolved not to say, "I could never do math," or "It's okay if you don't understand math; you'll never use this stuff in real life anyway." Instead, I determined that we would have fun with math. Surely there must be a way of learning without resorting to workbooks and flash cards.

It would be an adventure!

As we set off on our journey, I began to record our discoveries in a homeschooling journal, entries from which I share with you here.

June 16, 1992
Today, after I measured Coulter's height against the paper ruler taped to his bedroom door, he dashed off to his desk and began scribbling furiously. About ten minutes later he came to show me his project. He'd developed a ruler of sorts--a quarter sheet of paper marked with the numbers 1, 2, 3, 4, 5 spaced at various uneven intervals up one side, and 6, 7, 8, 9 written down the other side. He's been comparing the sizes of Lego blocks, tin cans, and my old slipper.

September 7, 1992
Last month I introduced addition by talking about "one more," as in, "Here's a cookie. Would you like one more? Now how many do you have?" This week our homeschooling friends from New Orleans are visiting. Their daughter has introduced my children to the idea of drawing tally marks to figure out problems. You can write 7 + 7 as /////// and ///////, then count up all the marks, she says. Earlier we discussed the idea of using "sets" to talk about things: a six-pack of juice is a set, two cookies for dessert is a set. Coulter wants to know if he can serve cookies and milk for a snack. Cookies in sets of three, he points out. That's two plus one more.

Young children can learn a tremendous amount of math from their everyday experiences. Setting the table, sorting clean silverware into the kitchen drawer, or matching up socks as they come out of the dryer are all practical applications of math skills we take for granted. You don't need to purchase workbooks or expensive manipulatives to begin learning. Manipulatives are simply concrete objects, like beans or coins or clothespins, that your child can move around as he counts or explores math ideas.

Children who are invited to help bake brownies learn a lot about teaspoons and measuring cups. The holiday season, when you need to bake double batches of gingerbread men, is a good time to let them help you figure out how much 1 2/3 cups doubled is. As our children experience life, they develop ideas about numbers, shapes, patterns of time and space. What math concepts they learn come through their direct observation and play, as well as the language we use to help them talk about what they're doing. Our job is to challenge them to explore their ideas and to explain their thinking to us.

April 4, 1994
"How heavy is my bike?" Toby wonders. This is an interesting problem, since all we have is a bathroom scale and the small pan balance the kids have been using to weigh pennies and toy cars. I'm wondering how a four year old approaches problems, as we carry the scale out to the garage.

"Can you weigh yourself?" I ask. He shows me that he can read the scale and know how much he weighs. But the bicycle is too big for the scale.

"What if you hold it and stand on the scale?" he asks. "That would work," I say. "But then what are you measuring?"

"You plus the bike." He thinks for a moment. "Then we could take away your weight and have the bike's weight."

April 11, 1994
We're playing around with pattern blocks this week. I was planning to make designs, but Coulter and Toby have decided to build towers with the hexagons. When they run out of hexagons, they use other shapes to make hexagons. Two red trapezoids will work, or six green triangles.

This segues into a game we call "The Stock Market." (I think they've been listening to too much National Public Radio.) You can trade in any shape for equivalent chips, but the person you're trading with cannot give you the same thing you offer. I give Coulter a yellow hexagon and receive a red trapezoid and three triangles in exchange. After some wild bargaining, we decide to build a dragon with green spikes down its back and huge wings. (We leave the design on the art table, and every day a new dragon shows up.)

Beyond keeping score, there is a lot of math in the games we play. We love to roll dice and move pieces around a board, plot battleship strategies, play cribbage, chess, and mancala. Saturday nights after dinner are good times for card games: UNO, war games, crazy eights, rummy, old maid, poker, 21. The car is a fine place for working on mazes and crossword puzzles, scribbling secret coded messages to one another, playing tick-tack-toe, hang-man, and I-spy, and keeping track of how many blue and red and green cars we can see in five minutes.

As our children grew, our games became more sophisticated. Early on we played UNO by matching color only, or number only; we found a children's Yahtzee game and drew board games on the backs of cereal boxes. As their abilities to keep score and follow rules increased, the boys developed a passion for making their own games and fell in love with the ancient set of polyhedral dice from my "Dungeons and Dragons" game. Instead of Parcheesi, they now choose role-playing games in which moves depend on calculated probabilities. According to them, this is not math.

December 17, 1995
I don't remember when we first started doing math puzzles for breakfast, but it's great fun. Some mornings I'll put the tangram sets on the table with a puzzle for each child to solve. Other mornings it's a word problem: if a dragon lays four eggs and half of the dragonlings survive and breed, how large will the population be in five years?

This week I forgot the puzzles. No matter. The boys made up a new tradition: math challenge. The rules are simple. You can challenge another person to do any kind of problem, within the limits of what's reasonable for him to know. So asking Toby, who's five and a half, to add or subtract is reasonable, as is asking Coulter, now nine, to solve multiplication problems.

I asked Toby what 47 minus 26 was, and before I could pour the milk he had an answer. "How did you figure that out so fast?" I asked.

"Easy, Mom-40 minus 20 is 20, 7 minus 6 is 1, and 20 plus 1 is"

"Twenty-one!" we all said.

"Okay, I've got a harder one. Five times 12."

It turns out Toby's method works for multiplication, too: 5 times 12 is the same as working out 5 times 10 and 5 times 2, my children inform me. While I'm counting on my fingers, they're developing a rule for mental math. I have them explain it to me, and we discuss whether their rule will work for any number. Basically their rule is this: x (a + b) = xa + xb, where (a + b) is written as the sum.

The math challenge did not stay at the breakfast table. It hopped into the car with us when we drove to soccer practice or to the orthodontist.

"Count by fives," Coulter challenged Toby. "Up to 50." Then it would be Toby's turn.

"Count by 13s up to" He looked at me and shrugged, then turned to his brother. "Up to as far as you can go but as close to 100 as you can get."

Our best math lessons grew from questions raised by the children. The International Study of the Color Distribution in Populations of M&Ms was a direct result of one of them saying, "It's no fair! He always gets more green ones than I do."

When I snapped, "Prove it!" they did. They sorted and counted green, blue, red, yellow, and orange emmies and made a graph to show me the disparity between their packages. "Hmmm," I said. "I think maybe we should go down to John's store and get more packages to study." We spent nearly a year sampling M&Ms from various towns and received data from homeschoolers in Australia, Canada, and from across the US. My children transferred data to charts, drew graphs, and calculated the probability of getting a green M&M in your first handful. The results, published in Growing Without Schooling 112 (Sept/Oct 1996), prove beyond all doubt that some packages of M&Ms are more equal than others!

One field trip took us to Ben and Jerry's so we could figure out how many double-dip combinations were possible, given the flavors available at the shop. According to our calculations, at our regular rate of one town visit per month, my kids will be buying their own children ice cream cones before exhausting all the possibilities.

Heavy lobbying for shoes with Velcro closures brought us to the mall. My children hated tying their shoelaces. It ought to be easier, they said.

"Let's go find out what kind of shoes folks wear for walking," I offered. Armed with small clipboards and papers divided into two columns ("shoelaces" and "no shoelaces"), my children began looking at feet. After 140 feet had passed our bench, Coulter spoke up, saying, "We really should have a column for men and women."

"Children, too," added Toby, giving me a meaningful glance. "They probably don't wear shoelaces as much!"

After a quick redesign of their data sheets, they were ready to count shoes again. This time they had three columns: men, women, and children. Each column had a side labeled "shoelaces" and a side labeled "no shoelaces."

Three hundred sixty-four shoes later, we gathered at the center court to munch pizza slices and tally our observations. Of all the feet seen in the mall that afternoon, two-thirds were wearing shoes with laces. We looked at our own feet under the table: four double-knotted laced-up sneakers and two sandals with Velcro tabs. (Guess who was wearing the sandals?!)

My children love math. They like the challenge of ripping into a complex algebra problem and playing around with logic puzzles. And although we talk about math problems at the dinner table, I still need a calculator to balance my checkbook.

Sue Smith-Heavenrich lives on a rocky hilltop in Candor, New York, where she designs puzzles and word problems for elementary schoolchildren. She is currently at work on a book of math games for preschoolers and their moms.