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?