BIG Numbers

Millionaire. Billionaire. Three hundred million dollars to make Spiderman 3 and $5 billion to clean up the BP oil spill. Nine million people living in Mexico City and 1.3 billion people living in China. More than 100 million homeless people in the world today... We throw these numbers around all the time, but they're so large that they're truly difficult to picture. Leave it to children's book makers to address that problem! A new book about the concept of a million just came out—so how does it stack up compared to earlier books on the same topic? Here's a look at the latest attempt to wrap our brains around big numbers, along with reviews of two its predecessors.

How Many Jelly Beans? A Giant Book of Giant Numbers! by Andrea Menotti, illustrated by Yancey Labat

Let me just start off by pointing out that the book, like the number it honors, is really big—I personally measured it (because this is a full-service book review blog, dontchaknow): we're talking 11 by 14 inches. Definitely going on the oversize shelf!

Where other authors have considered the question of large numbers using different objects and scenarios, Menotti keeps it simple; she merely considers jelly beans in bigger and bigger quantities. Which brings me to the framing plot, one that will appeal to just about any kid... two siblings are trying to decide how many jelly beans they want. Pretty soon they are imagining greater numbers, the question being, "Is there such a thing as too many jelly beans?" Emma and Aiden and their little dog, Murphy, mostly don't think so. Mostly.

How many jelly beans would you like, Emma?
TEN!
How about you, Aiden?
TWENTY!

And the jelly beans are shown in the children's hands. The kids and their dog are presented in strong, simple black lines on a white background, in contrast to the jelly beans, which are brightly colored and are not outlined. An occasional pool of blue and the use of contour in the ink lines add some depth to the rather flat scenes.

Of course, the kids start topping each other with bigger numbers. "He can have twenty? I'll have TWENTY-FIVE!" And we see bigger and bigger batches of jelly beans. "I changed my mind," Aiden says. "I'll have FIVE HUNDRED JELLY BEANS!" Whereupon Emma tells him, "That's too many. You can't eat five hundred jelly beans." Aiden replies that in a whole year he could eat a thousand jelly beans. Next we get a thousand jelly beans parsed out on a dozen calendar pages. As a teacher, I appreciated how Menotti made the number more accessible by breaking it down into pieces again, "two or three a day," as Emma realizes. And when Aiden says he can eat a hundred thousand jelly beans, we are shown the number first as one huge bunch and then divided into different batches by color—ranging from 50,000 grape jelly beans to an amusing "1 lemon."

In this way, Menotti keeps her progression of numbers and questions from becoming entirely predictable. She also throws in a single analogy, with Emma comparing 5,000 stacked jelly beans to the height of a building.

At last, in a feat of tiny computer-generated jelly beans on a REALLY big foldout spread, Menotti and Labat give us all 1 million pieces of candy—along with the punch line to Emma and Aiden's conversation.

I will just note that illustrator Labat's little dog Murphy quietly steals the show as his facial expressions and ears offer commentary on the kids' statements. Being a dog, he is of course interested in all things edible, and he is more than willing to partake in a jelly bean feast.

I suppose my only quibble with this book from a teaching standpoint is that not every number is given numerically. Some are presented only as words. I would have liked to see both forms for each number. Overall, however, this is a very nice addition to a special subgenre of math books for children, offering readers a clear, upbeat take on the big number question.


A Million Dots by Andrew Clements, illustrated by Mike Reed

Clements is best known for middle grade fare such as Frindle, but here he, too, tackles the concept of 1 million. This picture book doesn't include any particular narration or characters, but it does march kids right through a count that goes all the way up to 1,000,000 dots.

So how do the writer and illustrator add interest? On each counting page, we are given an interesting little factoid about just one of the numbers that appears along the way. Here are a few of the facts:

Dot Number 1,860—A person must climb 1,860 steps to walk to the top of the Empire State Building.

Dot Number 24,901—It is 24,901 miles around the Earth at the equator.

Dot Number 87,600—The sooty tern can fly nonstop for 87,600 hours after it leaves the nest—that's ten years on the wing!

Dot Number 134,000—A person blinks about 134,000 times each week.

Each page notes the spotlighted number, and additional signposts indicate how many dots have been counted so far. (I suspect these two numbers might be confusing for some young readers.)

The particular dots that accompany the facts are highlighted, though sometimes this is hard to see. To add visual interest, the background of the mass of ranked dots is rendered on each page as a fairly simple illustration. For example, the backgrounds of the facts mentioned above are the Empire State building, the planet Earth, a sooty tern wearing goggles and carrying a suitcase, and a goat winking in an airplane (we get mountain heights on that page, as well).

The so-so illustrations and the lack of characters and a narrative frame (however slim) make this one somewhat austere. However, the facts are compelling, as is the diligent build to 1 million.

I mean, come on: Did you know that "a queen-size bedsheet is woven from more than 153,000 feet of cotton thread?"

I will add that this book begins and ends on a page with just one dot—the first dot and the millionth one. I find this especially satisfying, both from the literary standpoint of a framing device and from the mathematical standpoint of recognizing that even a huge number like a million is made up of units, dot after dot after dot.


How Much Is a Million? by David M. Schwartz, illustrated by Steven Kellogg

This one is the gold standard for books on the topic of big numbers. I have read it, not only to first graders, but to third graders, sixth graders, and twelfth graders. So how does is stand up after 27 years? The answer is, really well.

The ambitious Schwartz gives us a series of analogies to help us envision, not only a million, but a billion and a trillion. Kellogg packages it all up using a group of exuberant kids and a mathematical magician, not to mention a dog, a cat, and a unicorn. The book begins:

If one million kids climbed onto one another's shoulders, they would be taller than the tallest buildings, higher than the highest mountains, and farther up than airplanes can fly.

The other analogies are how long it would take to count to each number, how big of a goldfish bowl you'd need to hold that many goldfish, and how many little stars would be needed to reach the number in question.

The stars section shows rows and rows of tiny stars for seven pages. The characters float across the pages in a hot air balloon, making funny little remarks. We're told we would have to take that same journey of seven pages ten times to pass a million. Later in the book, the star pages are referenced for other, larger numbers.

David Schwartz's genius lies, not only in making the idea of a million accessible, but in building a comparative understanding of a billion and even a trillion while he's at it. Steven Kellogg's genius lies, as always, in creating slightly nutsy, appealing characters to humanize the concepts.

I think my favorite pages are the depictions of the counting question: With counting to a million, we get our little cast under a tree and learn it would take about 23 days. But counting to a billion would take 95 years—and Kellogg shows the kids all elderly, with a gravestone for the mathematical magician. Counting to a trillion would take almost 200,000 years. Not surprising, Kellogg gives us gravestones for the entire group this time (after showing the alarmed kids faced with boxes and boxes of calendars.)

I'll admit I am book greedy, and I would want to own all three of these books about big numbers if I were you. If you really must choose, I still think Schwartz and Kellogg's book is the best. But I have to say—I do love those jelly beans. And Murphy!

On a related topic, I recommend Betsy Franco and Shino Arihara's poetic book on the concept of zero, Zero Is the Leaves on the Tree. (See my review from a few years back.)

Note: Chronicle Books sent me a copy of How Many Jelly Beans?

A Review of Animal Aha! by Diane Swanson

Most of the nonfiction I read as a child bored me. The only nonfiction books I remember liking were the World Book Encyclopedia, which I sometimes read randomly to entertain myself, and some books called Animals Do the Strangest Things, Birds Do the Strangest Things, and Insects Do the Strangest Things. In fact, I wondered why, if animals and birds and insects were out there doing such strange things, more of the books in the library couldn’t talk about that, instead of what they did say, which seemed like a whole lot of blah-blah to me.

I’m still more hooked on fiction than nonfiction, but I am happy to report that children’s nonfiction has improved tremendously since I was young. Simply having more photos—and having them be in color—is a great start. The advent of the Eyewitness series has also upped the ante. As a teacher, I love bringing those books to my students, especially reluctant readers. Like my childhood encyclopedias, their pocket-sized pieces of text and wonderful photographs draw kids in. I know some have objected to the way they jump around, but then, science is often sold to us in schools as lists of facts, so what’s the difference?

Fortunately, there are alternatives. After you’ve gotten children involved with books like Eye Wonder and Eyewitness, you can introduce them to some books that don’t, in fact, jump around. Another thing I’ve noticed while teaching is that kids are inclined to think of science as a done deal, with all of those facts conquered and ordered and laid out in boxes beneath pins for their perusal. To show them that science is actually ongoing and constantly changing, we need books along the lines of Animal Aha! Thrilling Discoveries in Wildlife Science. Here’s how the introduction puts it:

Scientists work hard to uncover some of the amazing things that animals do. They spend thousands of hours planning experiments, making observations, spotting patterns, and analyzing results. Their efforts call for plenty of patience and loads of persistence. But that all pays off big time when they discover something new—something no one has ever seen before. As you might imagine, finding an AHA in research is a big thrill.

This book has five short chapters, one for each discovery. The discoveries are told in story form, letting young readers share in the scientists’ aha moments. Further facts and explanations and a history of the research leading up to the key observation follow. For example, the first chapter tells about the discovery of a gorilla using tools, adding that previously, among the great apes, only chimpanzees, orangutans, and humans have been seen doing that. In this case, a female gorilla crossing a swampy area in the Congo rainforest was observed breaking off a tree branch and using it, not only to support herself, but to check the depth of the water as she went.

Animal Aha! provides an appealing array of animals and discoveries: we go on to read about elephants looking at themselves in mirrors, dolphins demonstrating simple math skills, parrots speaking with meaning, pythons growing bigger hearts in order to digest their prey, and cockroaches learning better at night than in the morning—kind of like some people. Perhaps most intriguing is finding out how the scientists set up viable experiments for verifying things such as animal thought processes. I especially like the way the elephant research illustrates how a poorly designed experiment can yield inaccurate results: Earlier attempts to find out if elephants could recognize that they were being reflected in mirrors had used smaller mirrors so that elephants could only see their faces. Once scientists offered the pachyderms jumbo-size mirrors, the elephants quickly conducted their own experiments and concluded that they were seeing themselves.

Each chapter in Animal Aha! begins with a small sidebar of summary points titled Fast Facts and includes plenty of nice photos of the subject, some from the actual experiments. Each chapter then ends with a sidebar called Fun Facts. The book has an index, as well. My two favorite Fun Facts are “Like your fingerprints, a gorilla’s noseprints are unique” and “An elephant’s ear can weight as much as a slim woman, about 50 kilograms (110 pounds).”

Besides offering up active science about intriguing topics, Animal Aha! is written in a friendly, clear way at a second or third grade level. Diane Swanson is apparently the author of many other nonfiction books, so I’ll be keeping an eye out for them. For now, I am happy to report that animals are still doing the strangest things!

A Review of Secret of the Singing Mice...and More! by Ana Maria Rodriguez

Secret of the Singing Mice has one of the coolest titles ever, but how does it compare to Animal Aha? The books are very similar in design, actually. This one also presents five cases of animal research in five small chapters. The title chapter is especially compelling. Like bats, whales, certain insects, and a few other rodents, mice make some sounds that are so high-pitched humans can’t hear them. These songs are produced by male mice when they meet female mice, and scientists recorded them and were able to play them back and analyze them at a lower decibel. To their surprise, they found out that a mouse’s “love song” isn’t just a single note, but a little pattern—and each male mouse’s song is unique. (I’m picturing American Idol for mice now.)


Three of the five chapters in this book are about animal sounds. Like the mice, Richardson’s ground squirrel sometimes makes ultrasonic noises. The calls are part of the ground squirrel’s repertoire of warning signals, and the book details how scientists figured out when these calls would be advantageous to use—or not, depending on how near a predator might be. The third chapter about animal calls also focuses on an animal that can make ultrasonic noise: bats. It turns out baby bats “babble,” playing with sounds the way human infants experiment with vowels and syllables before learning to make words and sentences.

The two chapters which aren’t about sound give us case studies involving smell and vision. The star-nosed mole is already a bizarre creature, but it turns out to have an intriguing habit discovered by scientist Kenneth Catania: while looking for food underwater, the bat breathes bubbles out of its strange nose to touch potential food in the murky water, then snorts the bubbles back in to check them for smells. The chapter about vision introduces us to a little rodent called the degu that can see ultraviolet light—but what for? The answer has to do with the degu’s urine, which is bright with UV rays!

I was a little thrown by this book’s emphasis on sound in three of the five chapters. Part of me wanted to see a chapter for each of the five senses. But then, describing three sound experiments gives students the opportunity to compare different scientists’ approaches to similar questions, which is certainly valuable.

Singing Mice is written on a second or third grade level. The book offers us various sidebars, though some contain information that could have been worked into the text. I especially liked the idea of sidebars called Meet the Scientists, but was disappointed by their lack of detail. The font size in this book is quite small, which might be overwhelming for reluctant readers. Some chapters seem a little short on photos, as well. I was pleased to discover experiments at the end of the chapters until I realized that only chapters one and five had them. Of course, it would have been nice to see an experiment for each chapter. In addition to an index, Singing Mice provides chapter notes at the end of the book, giving us specific sources for the information in the text. This is not only useful, but is also good modeling for students being asked to document their own report writing. The book is part of a series called Animal Secrets Revealed, and I’m going to try to track down some of the other titles, particularly Secret of the Puking Penguins...And More.

Secret of the Singing Mice gives us a clear picture of how five science teams conduct their animal research. Again, these science stories are powerful examples for students who might not otherwise understand how all those “science facts” they encounter in school are generated. In the midst of recent talk in the news regarding problems with education in the United States, I’ve read that pursuit of careers in the hard sciences is on the wane. Good nonfiction showing kids dynamic, creative science engagement should be part of the solution.