Great Estimations



The New York Times Book Review, Editor’s Choice
Like farm animals and the alphabet, the digits — 1 through 9, along with their extraordinary sibling, 0 — are young readers’ familiar companions. It’s easy to get a feeling for small numbers like 1, 2 and 3; some scientists believe infants as young as 5 months old, like rats, pigeons and monkeys, already understand such numbers intuitively. But larger numbers don’t come nearly as naturally to little humans and animals that go squeak, coo and chee-chee — or, apparently, to the authors and illustrators of children’s books. Showing kids what big numbers really mean and how to use them well requires some mathematical subtlety.

“Great Estimations” is a model of how to do it right. Bruce Goldstone starts with a clearly defined topic, one that many adults have never mastered or even thought much about: how to estimate quantities of things. By the book’s end, attentive readers should have a reasonable chance at winning the next guess-how-many-jelly-beans contest. But he will also get curious readers wondering about many other mathematical subjects, from symmetry to sphere-packing to statistics, whether or not they’ve ever heard those terms.

With its cleanly arranged, stark-against-white photographs, “Great Estimations” is interactive in the old-fashioned way. It invites kids to do what they do best with picture books: stare at the pictures, enter them in their mind’s eye, and get something done while they’re in there. “Begin by looking at some 10s,” Goldstone suggests on a page that shows groups of familiar objects like pencils, dog biscuits and peanuts. “What does 10 look like?” A lot of different things, it turns out, depending on what the objects are and how they’re arranged. As the eye learns to recognize 10, it also explores patterns: lines, circles, rectangular grids, hexagonal tilings. “Try holding this book upside down,” Goldstone advises. “Try looking at things upside down or sideways any time you want a different point of view.” And don’t get caught up in precision. The game here is making a good guess, not counting exactly.

Once he’s done training the eye, Goldstone moves on to estimation techniques: clump-counting, box-and-count. Without belaboring it, he chooses objects that introduce complications for readers to solve. In a photo of wall-to-wall white rabbits, for example, the bunnies shrink with the distance, so clumps of bunnies in the background fill less space than ones in the foreground. In an array of doll shoes, the shoes are different sizes, so the eye has to sort the objects into different kinds.
— Polly Shulman


School Library Journal
Goldstone adds another winner to the growing canon of titles that make learning math concepts both fun and interesting. Combining clear, concise language with colorful photos of countable objects, he introduces estimation, beginning with eye-training exercises to recognize groupings of 10s, 100s, and 1000s. Readers are encouraged to move the book around so they can see the items from varying perspectives. The next few spreads explain how to base an estimate on quantified groups: left-hand pages show clusters of an object (10 cherries, 100 cherries) while right-hand pages present an unidentified amount of the same thing (“About how many cherries are in a quart?”). The author then shows youngsters how to make reasonable estimates when looking at large quantities using clump counting and box counting. The real standout here is the crisp photography of objects and animals, including everything from google eyes to a penguin colony, set against stark white backgrounds that make them almost seem to leap off the page. This well-designed book will add zing to many a math lesson and attract browsers as well.
— Grace Oliff, Ann Blanche Smith School, Hillsdale, NJ


Kirkus Reviews
Math teachers have a new tool for teaching estimation in this manual designed to train the eyes and mind. In the “Eye Training” section, Goldstone uses photos of objects and animals to help readers recognize groups of tens, hundreds and thousands, and then presents several opportunities to practice this type of estimation. In “Clump Counting,” children see how much space ten (for example) of an object takes up, then how many groups of tens there are, to arrive at a good estimate. “Box and Count” is a similar method wherein readers are taught to visually divide a space into one hundred small boxes, count the objects within one and multiply by one hundred. Throughout, a hint box at the bottom of the page gives clues as to where to start, methods for proceeding and possible estimates. Perfectionists beware: Only one exact number is given in the entire book. A list of things to estimate gives readers a chance to practice their new skills in the real world. A must-have resource for school libraries.

Comments are closed.