I’ve been working on What in the Wild? Secrets of Nature Concealed . . . and Revealed (a sequel to Where in the Wild? and the soon-to-be-released Where Else in the Wild?). One of nature’s secrets to be discussed is the nest holes of kingfishers, those handsome, crested birds of watery places who burrow into the riverbanks to make their nests. How deep? It turns out there is no clear answer to this question, as I discovered in my research, which led to some ruminations that will be the subject of this post.

The authors of Wildlife and Plants, 3rd edition (Marshall Cavendish Reference) write that the nest tunnels are “3-7 feet long.” In Water Birds of California, author Howard L. Cogswell says “3 to 6 feet (even 10),” while World Book Encyclopedia reports “4-15 feet.” So which is it?

Those who read non-fiction often seem to have the impression that facts are facts. Period. The writer of non-fiction must merely learn them and report them, and that’s that. I’ve gotten this attitude often from children, egged on by the adults in their lives. “You wrote X, but we read Y in another book. Who is right and who is wrong?” Cheers for the author of truth. Jeers for the liars. But in reality, the depth of kingfisher tunnels (and many other facts) are unknowable. It might be instructive to consider how the figures above have come to light.

Over 200 or so years of American ornithological research, what percentage of kingfisher nests have been measured? [Read more…]

The opinions and questions of children often fascinate and delight me. 

As an author of non-fiction children’s books, I receive many letters from young readers. One that stands out came from a nine-year old girl named Lisa who wondered about the accuracy of various statements in my first book, How Much Is a Million? I was thrilled to receive her letter, for I am always happy to learn that my books are being read critically.

Lisa wondered about the truth of my book’s claim that counting from one to one billion (saying each number individually) would take 95 years. After questioning a few other statements in my book, she closed her letter:

“I had mixed up feelings about your book. That’s where the magic comes from the world of books. The magic of books is not knowing whether the facts are true or not.”

In my presentations at schools, I often tell children, “Wondering is wonderful.” [Read more…]

This month I am still traveling in Southeast Asia visiting international schools and speaking at an education conference in exotically named Kota Kinabalu (in the Malaysian part of the island of Borneo), and I have asked my friend Nancy Raines Day — an environmental educator, bookseller and author of both fiction and non-fiction for children — to write a guest post for me. I will be back in April.
— David Schwartz

 

 

Thanks, David. I feel lucky to be in touch with this community! After spending the last couple of years working on California’s new environmental curriculum, I’ve been ruminating on how best to hook kids into nature right from the start, and how books might help do that.

 

 

Many of you know the book, The Last Child in the Woods: Saving Our Children from Nature-Deficit Disorder. In it,Richard Louv makes the point that children and nature are and must be connected for the health of our children and our planet.

 

 

It worries me that American children probably spend less time in touch with nature today than ever before. Especially city kids may have trouble relating to living things in environments they have no personal connection to. Of course, the more outdoor experiences—walks in the park, camping trips, or days at the beach—they can get, the better.

 

 

In between such opportunities, putting the right books in their hands can be a great way to connect kids with nature. As Louv wrote, “People who care about nature often mention nature books as important childhood influences.”

 

 

Many fine nature books are out there for school-age children. Nature books at the earliest (0 to 4-year-old) level can help build a base for later understanding. Rachel Carson has said, “It is not half so important to know as to feel when introducing a young child to the natural world.” Below, I’ve rounded up some books that help the youngest audience feel their connection to the natural world.

 

 

My favorite “young” books new for spring are In My Nest and In My Pond,written by Sara Gillingham and illustrated by Lorena Siminovitch (Chronicle Books, 2009). These tiny books are a tactile delight, allowing little fingers to delve through layers of thick pages while wiggling a baby bird–or fish–in the midst of its family. In My Nest shows the twigs, leaves, and feathers that go into building the nest. When a child later sees a real bird carrying a twig in its mouth, he or she will feel such satisfaction knowing why!

 

Also perfect for spring is Kevin Henkes’ Birds, a large book with appealing illustrations by Laura Dronzek (Greenwillow, 2009). Kids everywhere see birds in their daily life, so feathered friends are the perfect wildlife ambassador. The imaginative text engages all the senses. You have to see the illustrations to get a sense of the utter joy conveyed in this passage: If there are lots of birds in one tree and they all fly away at the same time, it looks like the tree yelled. . .

S U R P R I S E !

 

 

Another great intro to birds and other animals for toddlers is the whimsical, geometrical art in Charley Harper ABC’sand Charley Harper 123’s (Ammo Books, 2008). He captures each creature’s essence with warmth and humor. Harper said of his bird art, “I have never counted the feathers….I just count the wings.”

 

 

To introduce very young readers to environments they may not know firsthand, try Over in the Ocean in a Coral Reef by Marianne Berkes, illustrated by JeanetteCanyon, (Dawn Publications, 2004). Based on the traditional rhyme, “Over in the Meadow,” the bouncing, joyous text and colorful clay art will delight young listeners and lookers with the wonders of life on a coral reef. Likewise, Over in the Jungle (2007) enfolds young readers in the splendor of the rain forest. Both luckily come in board book editions.

 

 

 

I’d love to hear about your experiences with these or other books that strengthen young children’s nature connection!

If you’re of a certain age, you will remember the one-word career advice given
to an ambitionless Benjamin (Dustin Hoffman) in the opening scene of the immortal 1967 film, The Graduate: “Plastics!” If an aspiring author of children’s non-fiction picture books asked for two words of advice, I might say “Guessing Games!”

Children love to guess. The opportunity to figure out something or to find objects hidden in illustrations, combined with a chance to show off what they have already learned, gets kids jumping (sometimes literally) with knowledge and joy. If an author can present good factual material in an enjoyable format that allows to children to take guesses, the author might have a popular book on his or her hands. It’s happened to me 25 times, with number 26 on its way.

In the late ‘90s, I wrote two dozen science books in the series “Look Once, Look Again.” They came out in two batches of 12 – the first oriented around habitats and the second around anatomical features of animals and plants. The publisher, Creative Teaching Press, predicted they would be in print for five or six years but it’s now been almost a dozen since the first series came out, and the “LOLA” books (as photographer Dwight Kuhn and I fondly call them) are still going strong.

There was nothing special about the idea, other than the interactive possibilities that come from children using both visual and textual clues to identify plants and animals. First they see a close-up photograph of an organism that gives a magnified view of part of its exterior (the plates of a turtle’s carapace, for example, or the kernels of an ear of corn). The text hints at the organism’s identity (“These are plates but you wouldn’t want to eat from them. What animal has hard plates on its back?” or “What has ears but cannot hear?”). And the child is on his or her way. Kids tear through these books and reach for more. With so many colorful covers, I long ago began to call them “book candy.” Unlike mouth candy, this kind of confection allows kids to think and have no-calorie fun at the same time, while expanding their knowledge of the natural world and, in a subtle way, encouraging them think like a naturalist — in terms of a creature’s characteristics.

As an author who visits schools, I have had the most fun when I’ve seen class projects derived from mybooks, including class-created books based on “Look Once, Look Again.” Typically, first or second graders have drawn close-ups of animal or plant parts and written clues about the identity, followed by drawings of the complete animal or plant and further explanation. In one school, the students went beyond modeling their work after the LOLA books. They invented fantastical animals that combined characteristics of various real creatures. It reminded me of one of my favoite Dr. Seuss books, On Beyond Zebra, which I first encountered on the shelf of one of my biology professors at Cornell.

Late last year, I published (with co-author Yael Schy, who is also my wife) a book of poems that hint about the identity of well-camouflaged animals found (if you can spot them) in the photographs (also by Dwight Kuhn). The challenge is to find the animal hidden in the picture and identify it from the poem. We adopted a unique design element in which the gate-fold pages open up to reveal another version of the same photo; the difference is that now the background is faded (thanks to the miracle of PhotoShop) to allow the hidden animal to stand out. Then come prose “naturalist notes,” identifying the animal and offering more info about its life history, its use of camouflage, and a few more photos.

Many readers, both young and older, have suggested that Where In the Wild? reminds them of I Spy and Where’s Waldo?. Our book hasn’t yet enjoyed quite the success of those (their illustrations are not limited by the true arrangements of objects in the world), but it has captured the attention of many readers and reviewers (and, I’m pleased to say, award committees–most recently the Animal Behavior Society, which just honored it with its 2008 Outstanding Children’s Book Award). Again, I think the hook is the guessing game format.

With great anticipation, I am waiting to see student projects based on Where In the Wild? Teachers and home schoolers: this is your chance to combine science with poetry. Please show me what you come up with by sending an email to (you know how to turn that into an email address). And all INK blog readers can post some of your favorite non-fiction books that use a guessing-game format. Why limit ourselves to science? How about history, geography, grammar, philosophy, math — there’s no limit! Aspiriing authors of non-fiction: it’s better than plastics.

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.

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 asked 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.

I am just back from San Antonio, where I spoke at NCTE (National Council of Teachers of English). An annual appearance at NCTM (National Council of Teachers of Mathematics) has been on my agenda since 1996 but this was my first NCTE. I started thinking about similarities and differences between the two organizations in how they encourage teachers to use literature, and I mostly came up with similarities. And then I remembered a book on my shelf at home that makes that point exactly, focusing on mathematical literature. Appropriately, the book is published jointly by NCTM and NCTE. If I could put just one resource in the hands of a teacher wanting to mine the many treasures of “math-lit” as a teaching tool for both mathematics and language arts, this would be the book.

New Visions for Linking Literature and Mathematics by David J. Whitin and Phyllis Whitin is more than a resource book about using math-related literature in the classroom. It does indeed illustrate a myriad ways that teachers can use a wide range of quality books to support both math and literacy. But note the word “quality.” In addition to providing examples (plenty!) and illustrating how teachers have used them (impressive!), it tells you how to judge mathematical literature. That’s where New Visions differs from any other resource book I’ve seen. “Many (math-related books) seem more like workbooks than stories,” write the Whitins and I agree wholeheartedly. “Some give detailed prescriptions for reading, much like a teaching manual for a basal reader, while others mask doses of ‘skills’ with comical illustrations or popular food products…” Bottom line: not all math lit is created equal, and New Visions shows you how to evaluate. It even shows why some books just don’t make the grade, and it does name names. Harsh! But someone had to do it.

The Whitins put forth four criteria as a guide for judging mathematical literature as worthy. They then select one book as exemplary, showing how it makes the grade in all four areas. More on that later. Here are their criteria with an example of a book that stands out in each category.

1. Mathematical integrity Stories and literature have enormous value when they inspire children to apply mathematical ideas to the world around them, but for that to happen, the math in a book should be not only accurate, but should be presented in a context that is believable, not forced; it should be presented in an accessible way; and it should “promote healthy mathematical attitudes and dispositions.”

The Whitins give several examples, including Ann Whitehead Nagda’s Tiger Math: Learning to Graph from a Baby Tiger, which provides both an exciting non-fiction narrative with photographs and statistical data from the true, suspenseful story of a motherless tiger cub being raised at the Denver Zoo. Data (such as weight gain over time) is expressed in a variety of useful graphs. It’s an engaging book that connects math to the real world in a way children find spellbinding — and educators find supportive of the standards they are trying to teach.

2. Potential for Varied Response. Children’s books should not be worksheets. Instead of being didactic, they should encourage children to think mathematically and invite them to “investigate, discuss, and extend… (and to) engage in research, problem posing and problem solving.” Readers are not directed. They are invited.

Readers of the charming Grandpa’s Quilt by Betsy Franco, are easily tempted to find their own solutions the problem that faces the book’s characters. The 6-square by 6-square quilt does not cover their grandfather’s feet so they must rearrange its dimensions. Children are likely to explore factors of 36 and to get a feel for the relationship between perimeter and area. And the mathematical “invitations” go on from there.

3. An aesthetic dimension “Good books appeal to the emotions and senses of the reader, provide a fresh perspective, and free the imagination.” Here the Whitins look at how well the written language is crafted, along with the quality of the visuals and whether the book actually inspires a greater appreciation of the wonders of the world (including the human world). To earn our respect, the words and visuals of a work of mathematical literature must be just as compelling as those of any other literary genre. Claiming “It’s just a math book!” doesn’t cut it.

In their unique counting book, Spots: Counting Creatures from Sky to Sea, author Carolyn Lesser and illustrator Laura Regan use vivid, evocative language and stunning paintings to inspire awe and appreciation of nature — as well as the mathematics that is so often useful in describing and explaining the natural world.

4. Racial, cultural and gender inclusiveness. My first reaction to this criterion was a bit dismissive. “Doesn’t that apply to all books?” I asked. Of course it does, but we should be especially careful not to let the
mathematical component of literature that perpetuates stereotypes blind us to an unfortunate sub-text. There is a huge push now to attract women and members of ethnic minorities to careers in mathematics, science and engineering, and children’s books can help promote equity. There is more to it than counting boys vs. girls or white children vs. black or brown children in the illustrations. As one of several fascinating examples, the Whitins sing the praises of The History of Counting by eminent archaeologist Denise Schmandt-Besserat, a non-fiction picture book that celebrates the contributions of many cultures over many centuries in developing diverse number systems.

New Visions for Linking Literature and Mathematics goes on to provide myriad examples of books for a wide range of ages, strategies for using them to teach math, and an outstanding annotated bibliography called “Best Books for Exploring.”

Now about that exemplary book the Whitins chose to feature in the opening chapter. I held off identifying it until now for fear of seeming self-serving, but in the interest of full-disclosure, I should say that it’s my book If You Hopped Like a Frog. I’ve written about it in earlier posts so I won’t summarize it now and it would really feel way too “me”-focused to list the ways the authors of New Visions found that it met their four criteria. Instead, I’ll close with a passage from an article published in Horn Book in 1987, quoted by the Whitins. I can think of no better summary of their feelings and mine:

“You can almost divide the nonfiction [that children] read into two categories: nonfiction that stuffs in facts, as if children were vases to be filled, and nonfiction that ignites the imagination, as if children were indeed fires to be lit.” (Jo Carr, “Filling Vases, Lighting Fires” Horn Book 63, November/December 1987.)

Every summer, I think back on my author visits from the previous school year, and many highlights come to mind. Usually one stands out in a slightly brighter typeface than the others, and this past year it was the kindergarteners of Michelle Schaub’s class at Grayhawk Elementary School in Scottsdale, Arizona. They had read my book Where In the Wild? Camouflaged Creatures Concealed…and Revealed, and they decided that when I came to town, they would have a surprise for me: their own performance of a poem from the book.

It was the poem about the coyote.

Wary eyes...

Ears are keen...

Sniff the air...

Seldom seen...

Crouching low...

In the brush...

Standing still...

Watching, hush...

Darkness falls...

On the prowl...

Rising moon...

Yip and howwwwwllllllll

One thing led to another and soon they had a plan to do it on Grayhawk’s schoolwide TV network while I was in the studio and the entire school was watching in classrooms. And there was to be a surprise at the end, when each child lifted a beautiful coyote mask to cover his or her face. They had worked for days on the masks; each one was beautiful and unique. The overall result: spectacular.

You can probably imagine what fun this was for the children, their teacher, the whole school and me. But here’s the important point: Those kinders are not going to forget this poem or facts about this animal (detailed, in prose, later in the book) because they turned what I wrote into something of their own.

I could produce a lengthy resource book about ways that classes have extended my books into projects of their own. Some classes have explored individual statements from my books (perhaps to confirm or dispute what I wrote). Some have created books of their own, modeled (closely or loosely) after mine. Some have performed sections of my books in various ways, or even enacted episodes of my life. Think of the differences in learning opportunities between simply reading a book and extending it into something of one’s own, something to be proud of. “Give a man a fish, he’ll eat for a day. Teach a man to fish, he’ll eat for a lifetime” goes the saying. “Read a child a poem a coyote poem, he’ll learn about coyotes for a minute. Give a child a coyote poem to enact, she’ll learn about coyotes for days.”

In a recent post, I wrote about questions children ask of authors – at least this author. Now I want to explore a question I have heard but did not mention in that post: “What do you do about writers’ block?”

It’s a good one. It shows that the questioner is truly thinking about the writing life, and perhaps hoping for enlightenment that will help his or her own writing life. I have also noticed that the children who ask about writers’ block seem to be just a bit self-satisfied (some might say smug) for knowing about so sophisticated a concept. I harbor no resentment toward their attitude. I confess to having felt a bit smug as a child when I learned something esoteric, and I did not hesitate to bandy about my newfound knowledge.

But in this case, I am slightly troubled. It is not that children want to hear a few tips for getting the writing process restarted when it’s stalled. The problem is that, like many adults, they view writers’ block as a handy, even respectable, explanation for why nothing has been produced. It’s not me, it’s my writers’ block.

The view is supported by a hefty collection of books on writers’ block by authors who apparently conquered the ailment long enough to get the job done. In Outwitting Writers’ Block and Other Problems of the Pen, Jenna Glatzer opens by warning readers of a pestilence: “Writer’s block is an insidious pest—a beady-eyed rodent hiding under the floorboards of even the hardest working writers, waiting to rear its hideous head at the most inopportune times.”

For over half his working life, my father was a furrier. He operated a sewing machine on the floor of a factory in New York City. I have not asked him, but I’ll bet he would have had Furriers’ Block from Monday to Friday of every work week if he could have gotten away with it. He went to that factory and sat at that sewing machine so his son and daughter could have something to eat and a place to call home. My mother was an English teacher at Syosset High School on Long Island. She probably found the working conditions more pleasant than those my father’s workplace, but she loved to read, she liked to play tennis, she enjoyed Broadway matinees and word games and I don’t remember what else – and I’ll bet there were plenty of days when she would have relished a bad case of Teachers’ Block.

In my opinion, writers who regularly find way to pass their time other than by putting words on paper – a large subset that includes myself – do not deserve to take refuge in so dignified-sounding a condition as “writers’ block.” We should call it what it is: procrastination. And we should teach our children and our students that it is best conquered by force: Forcing ourselves to sit down and get the job done. Not knowing what to write and struggling over it is not writers’ block. It is writing.

On April 8, Garrison Keillor devoted his daily “The Writer’s Almanac” radio show to honoring novelist Barbara Kingsolver on her birthday. “She took a job as a technical writer,” Keillor said of her early adulthood, “which forced her to sit in front of a computer for eight hours a day and do nothing but write. She later said, ‘I learned to produce whether I wanted to or not. It would be easy to say oh, I have writers’ block, oh, I have to wait for my muse.’ I don’t. Chain that muse to your desk and get the job done.”

In writing non-fiction, I have noticed a subtle way in which writers’ block manifests itself: over-researching. There is no bell that goes off telling a writer it’s time to stop researching and time to start writing, so the author having an “I-can’t-do-it” moment (the root cause of much writers’ block) can extend the research phase indefinitely. That’s what I do, and I must say it is very effective in its two main goals: putting off the moment when I must put words on the page, and enabling me to feel OK about myself for not putting those words on the page (since, after all, I’m partaking in the essential task of researching – never mind that I already have way more information than I need).

And now I must close this blog entry and get to work on the sequel to Where in the Wild?, tentatively entitled Where Else in the Wild? Hmmmm. Maybe What in the Wild? would be a better title. I wonder what Mom thinks. I will call her. As soon as I clean out the refrigerator.

People often ask, “What age children do you write for?” Because my books are picture books, they are surprised when I say, trying not to sound smug, “pre-school through high school.” It would actually be more truthful to say, “pre-school through college” because on two occasions I have met chemistry professors who use How Much Is a Million? in their introductory courses when teaching Avogadro’s Number, an enormous and important quantity defined numerically as 6.02 X 10 to the 23rd power.

I, too, would have been surprised early in my writing career if anyone had told me that some of my books were destined for use in classrooms throughout the grades. This has happened so often with How Much Is a Million? since its publication in 1985, that I am no longer surprised when I hear of fifth, sixth or even tenth grade students devising their own problems and doing calculations modeled after mine.

More recently, I published If You Hopped Like a Frog and a sequel, If Dogs Were Dinosaurs. As soon as Frog came out in 1999, it was déjà-vu all over again. The book explores the principles of ratio and proportion by comparing animal abilities to those of humans. To use the title example, a 3-inch frog can hop five feet, or 60 inches, thus hopping 20 times its own length. Applying that ratio to a 4’6″ child jumping proportionally, I came up with the statement that introduces the book: “If you hopped like a frog… [page turn]… you could jump from home plate to first base in one mighty leap.”

I love to see examples student work that derive from and extend my books, and Frog has resulted in a wealth of material from the pencils and pens of clever children guided by inspiring teachers. What strikes me is how the book is enjoyed and used across a wide range of ages, and how teachers across many grade levels have incorporated it into their classrooms to support the curriculum.

I will give a few examples of diverse student work related to If You Hopped Like a Frog but I am hoping that this post will open a discussion of books by many authors that are used throughout the grades. As much as any measure, a book’s ability to be appealing and thought-provoking to a wide age range could be (should be?) an indicator of success. I certainly feel successful when I witness the same book loved by five year olds and thirteen-year olds alike.

“If you flicked your tongue like a chameleon,” I write in Frog, “you could whip the food off of your plate without even using your hands. But what would your mother say?” (Something about bad manners, I suppose.) As with all the assertions in the book, a section in the back explains both the facts and the math. Kids are always asking me, “Is that true or did you just make it up?” Well, when you write non-fiction, I tell them, you’re not supposed to make it up! If they read the pages at the back, they can see why I wrote what I did and how I did the math. In this case, it is based on the tongue length in some chameleon species being half as long as the chameleon’s entire body. (In fact, there are species in which the tongue is several times the length of an individual’s body, so this is a modestly endowed chameleon we’re talking about.) When I speak about this book at schools, I love to flick out a red paper “tongue” as a demonstration, adding comments like, “Yum, I just love those fat, juicy flies.”

Without even approaching words like “ratio” or “proportion,” a first grade class in Fair Hope, Alabama, used this as the basis for exploring the concept of “half.” Each child was assigned a length in inches. He or she was to draw a chameleon of that length, then figure out half of its length and cut out a tongue from red paper to be attached in the appropriate place. At the end of the tongue, a fat, juicy fly was be affixed. Yum.

Fourth graders in Hanford, California, did something similar with their own heights except that they did the measurements in both “customary” (American) units and in SI (metric) units. (Finding half of a height in feet and inches usually proved harder than in centimeters – a fabulous demonstration of metric superiority.) Then they made tongues for themselves and assembled for a novel class picture.

In Nashville, fourth graders drew upon my example of a flea jumping straight up to an altitude 70 times its own height. (“If you high-jumped like a flea… you could land on Lady Liberty’s torch.”) Instead of each child comparing his or her prodigious high jump to a landmark in far-off New York City, they used structures in their own city, including the Ryman Auditorium (the original Grand Ole Opry) and the Bell South Tower (known to all Nashvillians as “The Batman Building.”) I like the way Genny calculated not only how far up the Batman Building she could jump, but also how far she would have yet to go before reach the summit.

At Marymount School in Paris, fifth graders got similar results but they compared their prodigious jumps to the heights of l’Arc de Triumph and the Cathedral Les Invalides.

In a most impressive class project, sixth graders in Hobson, Montana, created a class book modeled after If You Hopped Like a Frog. Each child researched the abilities of one species, found a proportional relationship between some ability of their chosen animal and a human, wrote and illustrated the text, and explained the whole shebang in detail at the back. (How cool is that?! This was their variation on the less inspired “animal report” that does little more than get kids to rehash an encyclopedia.)

The example voted by the class to be on the cover of this magnificent class-created book is “If your tooth was as long as a narwhal’s tusk…” I must refrain from editing it into the subjunctive to make it say, “If your tongue were as long as a narwhal’s tusk…” Never mind the grammar: this young author’s contribution is fabulous.

To appreciate it, I will have to summarize his explanation before telling you the rest of his sentence: A narwhal is a whale that lives near Greenland; it is approximately 20 feet in length. One tooth develops uniquely, spiraling straight out to a length of about ten feet. Hence, the narwhal’s tusk is half as long as its entire body.

The author of this exposition tells us that he himself is 5 feet tall, so if he had a narwhal-like tusk, proportionally, it would be 2’6”. Now I can provide his entire sentence: “If your tooth was as long as a narwhal’s tusk…[turn page]… you could roast six marshmallows over a campfire without burning your face!” How does he get that? He reports that he “did an experiment to see how close to a campfire I could put my face. The answer was two feet.” That means that the six inches of tusk hanging over the campfire would make a perfect skewer for marshmallow roasting. How big are the marshmallows? He says he measured them to learn that each has a diameter of one inch. Hence, six marshmallows could fit on the six inches of tusk positioned directly above the hot coals. S’mores anyone?

This particular class project included many other spectacular examples of creativity in concert with mathematical thinking (and magnificent art). One of my favorites is, “If you spit like an archerfish…” (this Amazon basin fish spits 16 times its body length to knock insects off of branches above the river; it can then gobble them up) “…you could nail the second baseman from home plate.” Please don’t try it at home. Or at school. But do the math. You’ll have to use the Pythagorean Theorem to figure out the distance from home plate to second base.

And you thought picture books were just for little kids?