Monday, October 27, 2008

Where's the Math?

Anyone familiar with recent children’s literature knows that some picture books have mathematical themes. I have written a few -- How Much Is a Million?, If You Hopped Like a Frog , G Is for Googol, for example -- and there are myriad titles by other authors that have come to comprise a sub-genre of children’s literature that some call “math-lit.” But many non-fiction (and even some fiction) books that no one would call "math books" have hidden math connections nonetheless. Teachers and parents can use these books to introduce children to important math concepts and to encourage children to solve mathematical problems. I will provide a few examples from books of my own, and I invite blog readers to post their suggestions for books with subtle mathematical messages.

Super Grandpa tells the true story of a Swedish grandfather who, in 1951 at age 66, rode his bicycle about 1,000 miles in the Sverige Loppet (Tour of Sweden), despite having been barred from entering the race on account of his age. As an unofficial entrant, he finished the course in six days and became a national hero, remembered to this day. End of story. Or is it? The story has many numbers that can generate math problems. To take a simple example, Gustaf, our hardy grandpa, rides his bicycle 600 miles to the starting line because he has no other way to get there. Then he begins the 1,000 mile race. Obvious question to ask a reader: how many miles all together did he ride? Less obvious questions: was the race itself twice as long as the distance he rode to get there? More than twice? Less than twice? By how much? More difficult question: The book says he rode the 1,000 miles in six days. On average, how many miles per day did he ride? Research question: if a 1,000 mile race started in our city, where might it end? Get out the map. Use the scale. Find several points that are 1,000 miles away. Note the distance between as-the-crow-flies miles and actual road miles. How about a circuit that starts and ends here. What are some of the cities it could pass through? Christina Nugent, mentor teacher and math supervisor for Dubuque Public Schools in Iowa, has written two mathematical lesson plans for Super Grandpa (for primary and intermediate grades), which can be downloaded at the publisher’s website, Here’s a caveat: don’t forget to let the story be a story. Read it and enjoy it. Then mine its math.

Ladybug, along with eleven other titles in the “Life Cycles” series, are nature books, not math books. Right? Not exactly. I’d agree that Ladybug is a nature book but, as in so many nature books, you can find plenty of mathematical learning opportunities. One of the photographs shows about 20 bright orange ladybugs on a bed of vegetation. Their spots can be seen and counted, and the number of spots per beetle ranges from zero to a dozen or so.

Along comes Patty Brown, an elementary school math coach from Freso, CA. Patty gives first graders orange cardboard cut-outs resembling the backs of ladybugs, each divided into two “wings” (actually elytra, a beetle’s hardened wing cases).  The first graders also get ten yellow cardboard circles representing spots. They are asked to arrange the ten spots on the backs of their ladybugs. Every child in the class arrives at the same solution: five spots on each side. “Can we arrange them any other way?” Patty asks. No one budges. “Is five and five the only way to make ten?” The children resist admitting to any other possibilities. “How about this?” Patty picks up a lady bug back and puts six spots on one side, four on the other. The kids get it but they’re not happy about it. The symmetry, which they see as “fairness,” of five and five has a very strong pull on them, but eventually they come to discover and accept all the other combinations of numbers whose sum is ten. Patty writes each combination as an equation. Everyone is happy and an important first grade math concept has been learned.

In the Forest is one of 24 titles in my “Look Once, Look Again” series. In these books, readers look at a close-up photo of an animal and they read text hinting at its identity. Turning the page reveals the full animal and more information about it. One section shows a close up view of one antenna of a cecropia moth. The text that accompanies the “reveal” photo of the whole moth explains that its two antennae are its nose – a nose sensitive enough to allow a male moth to smell females three miles away. The second graders of Judy Baker in Vacaville, CA, found this interesting and a class discussion showed their teacher that they had no idea of the distance defined by a mile. And so began an extensive classroom project Judy called “How Much is a Mile?” in which 15 students taped together the paper yardsticks they had made earlier in the year to create a long strip of paper which they dubbed “Longie.”
At first they thought Longie would be a mile but they figured out it was only 45 feet long, and a little research told them that a mile was 5,280 feet. This led them to wonder aloud, “How many Longies make a mile?” They sought the answer by repeatedly adding 45 + 45, etc., but Ms. Baker saw a teachable moment and used the project as an opportunity to teach hows and whys of multiplication by ten. Excitement grew as they approached the ultimate answer. “It was time for lunch,” Judy wrote in an email to me, “but they had such momentum, they didn’t want to go to lunch!”

Building on Judy’s classroom experiences and adding some new technology, another 2nd grade teacher, Laura Bush, in Andover, CT, went online to pull up a high-resolution map of the local area on an interactive whiteboard. Placing the school in the middle of the map, she aske
d her students to imagine a male moth at the school, and to plot several points three miles from the school in order to see how far the moth could smell. Referring to the scale of miles, they entered points on the map; as more and more points appeared on the screen, a magical thing emerged: a circle. What an opportunity to teach the vocabulary of circles: radius, diameter, circumference, area, and so forth, and to make it relevant and meaningful.

To think that all that math started with a nature book.

1 comment:

Rebecca Haden said...

I love the way you've given these examples. I nearly always include math in my lit lesson plans (they live over at, but your suggestions are so clear and specific that someone who never uses picture books for math could not only follow them, but feel inspired to make it a habit.