You Can Count on Monsters

by Richard Evan Schwartz

Using a unique teaching tool designed to motivate kids to learn, this volume visually explores the concepts of factoring and the role of prime and composite numbers. The playful and colorful monsters are designed to give children (and even older audiences) an intuitive understanding of the building blocks of numbers and the basics of multiplication. The introduction and appendices can also help adult readers answer questions about factoring from their young audience. The artwork is crisp and creative and the colors are bright and engaging, making this volume a welcome deviation from standard math texts.

CRC Press Author and NPR's Math Guy Keith Devlin spoke with Scott Simon about how the book makes finding prime numbers fun.

"This is one of the most amazing math books for kids I have ever seen…," Devlin says. "Great colors, it's wonderful, and yet because [Schwartz] knows the mathematics, he very skillfully and subtly embeds mathematical ideas into the drawings."

Genres: Mathematics, Picture Books, Nonfiction, Childrens, Education, Art

244 pages, Paperback

First published January 1, 2010

About the author

Richard Schwartz grew up in Los Angeles. He wore only blue clothes between the ages of 7 and 11. He spent his youth obsessively playing tennis until video games distracted him. He majored in math at UCLA, got a PhD in math from Princeton, and is currently the Chancellor's Professor of Mathematics at Brown University. His research interests lie in geometry and dynamics. He likes to do mathematical experiments on the computer and then find proofs for the results he discovers.

Rich was an Invited Speaker at the 2002 International Congress of Mathematicians, a Guggenheim Fellow in 2003, a Clay Research Scholar in 2009, and Simons Fellow in 2012. He is the author of a number of books, including Spherical CR Geometry and Dehn Surgery, Outer Billiards on Kites, You Can Count on Monsters, Man Versus Dog, Unnecessary Surgery, and The Extra Toaster. He lives with his wife and two daughters in Barrington, Rhode Island. In his spare time, he listens to music, writes comic books, cycles on the bike path near his house, walks on the beach, or spends time with his family.

Reviews

[Ragheb · Rating 5 out of 5]

الكتاب جميل جدًا بالرسومات التي يحتويها
في الواقع إنّ الكتاب يحوي القليل من الكلمات مقارنة بالرسوم
الكتاب مناسب لتعليم الأطفال العد والحساب وبعض المفاهيم الحسابية البسيطة بأسلوب جذاب
وهو يركز على ولع الأطفال بالوحوش ذات الأشكال الغريبة
لذلك جعل لكلّ عدد وحشًا مميزًا يدلّ عليه
فهو يحاول إيجاد ثغرة لإدخال حب الأعداد إلى قلوب الأطفال الذين يجدون الرياضيات صعبة

[Jasmine · Rating 2 out of 5]

Okay I read this entire book. No for real I read the introduction and the afterword about how to find prime numbers under 100. *

Here's the thing this book does not make math easy. I mean multiplying is complicated enough without jumbling up a zillion monsters. I think the book is interesting in a graphic design kind of way for adults.

But giving this book to a child... that would just be mean.

*I thought if I read the introduction the book wouldn't be confusing anymore, not that children read introductions

[Julie Smith · Rating 4 out of 5]

The author has written a wonderfully illustrated book about the first 100 numbers and their characters (prime monsters). All you need to know is how to multiply whole numbers together (like 2 and 3), and this book will put you well on your way to understanding factor trees, primes and composites, and how to find prime numbers. With imaginative monsters and colorful drawings, this would be a great book for homeschoolers and educators to have on hand to make factoring not-so-scary. (except for those weird-looking, colorful monsters, that is!)

[Megan · Rating 5 out of 5]

I forgot how much math blows my mind. This book is amazing. Each prime number gets a "monster" and then to illustrate factor trees, the monsters combine to create new and different monsters.
PRIME NUMBERS ARE CRAZY.

[Charles · Rating 5 out of 5]

This colorful book uses a set of initial diagrams to explain the factoring of the first 100 positive integers into prime factors. Each prime number is represented by a figure that is a "monster" and the figures for factorable numbers are compositions of the prime monsters. The author has gone to great lengths to make the shape of the monster one that conforms to the number, for example the monster of the number two has two very large eyes. The number three is a smiling triangle with triangular eyes and five is a five-pointed star. Two pages are devoted to each number; the one on the left shows the number and the factor tree if the number is not prime and the right side displays the figure for the number.
This book would be an excellent reference for elementary school classes teaching basic factoring, the children would love looking at these imaginative figures and trying to extract the monster factors. I personally "wasted" significant time in doing just that.

Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon

[Susie · Rating 4 out of 5]

This book was recommended to me by an English teacher; her 9-year-old son was fascinated by it. Each number is depicted by a monster; composite numbers have the accompanying factor tree on the left side, with a composite monster on the right. Prime numbers have more unique monsters that are not simply divided into smaller parts, like composite numbers that can be factored.

This book could be used on several different levels, and in some cases, I wasn't sure how the monster (prime ones in particular) represented the number. (EX: 79) The book could be used with many different ages; much more complex explanations are in the back of the book. Teachers could simply show a page or two and have students off to the races! It's a different, colorful way to look at numbers.

The NPR interview with the author is interesting, as well.

[Heidi · Rating 4 out of 5]

This creative book teaches about prime numbers using not-at-all scary "monsters"! Using simple drawings and terms, it explains factoring, whole numbers, and prime and composite numbers.

Each page has its own monster and corresponding number, from 1-100. If it's a prime number, it is its own unique "monster", which are just silly characters. The composite number monsters are made up of their prime number monsters (factors). It's fun to figure out how the different numbers are making up the monsters. For example, the drawing of the monster for 27 is made up of three 3 monsters.

Along with her skip-counting songs, my kindergartner is understanding the basis of multiplication because of this book!

[Beth · Rating 5 out of 5]

My son is currently obsessed with math and this book fueled his fire even more! If this book was around when I was a kid I may have actually enjoyed math! It begins with a few drawings of numbers as monsters and then progresses into delightful drawings showing addition, prime numbers and factor trees. The book breaks down multiplication into several visual methods. 3 x 3 = 9 OR images of 3 items in 3 rows OR images of 3 groups of 3 items. The illustrations are phenomenal! We both enjoyed this and read it several times!

[Mary Ann]

I'm torn between loving this book and wondering whether it complicates the whole issue of factoring. I love the visual, playful approach to math. I love the monsters, and the way of using the monsters to help show the factors that make up a new number. And yet... and yet the final illustrations don't help me see the way factors help make up a larger number.

I want to share with some math teachers and see what they think. So for now, no stars - still undecided.

[Debdanz · Rating 5 out of 5]

I'm so happy Jen recommended this book to me! I loved, loved, loved it!! It is juvenile nonfiction, and in a delightfully whimsical and artistic manner explains prime numbers and factoring. Absolutely adorable and clever. My fav was number 87 with its factors of 29 and 3. Check it out and tell me you favorite! If my boys were younger, this definitely would have been a Christmas gift.

[Marcie · Rating 5 out of 5]

Learning about prime and composite numbers should be this much fun. Although some of the monsters are difficult, I can see students spending fun time with this. The preliminary and supplemental materials should help parents and teachers who use this with children.

[Lissie Moore · Rating 3 out of 5]

I would have loved to have a book like this when I was younger. It is a great and fun way to teach kids about numbers and math where they can be intersting. This would be a great book for probably 3rd graders. A great interactive book that kids can read together!

[Jen · Rating 5 out of 5]

Coolest math book ever.

[Kelly · Rating 5 out of 5]

Amazing visual explanation on how to grasp prime numbers, composite numbers, and the basics of multiplication. Brilliant. Each and every classroom should have this book.

[lalunenoire · Rating 3 out of 5]

Can I be honest? As a child, I found this book about as unhelpful as every other math purchase my parents made to support my learning on the subject - only gaining a real interest in middle school, when out of a dirth of school maths, I started reading out of my father's college textbooks. Reading this book now so many years later, I really began to appreciate what they, and Schwartz were attempting to do. A visual breakdown of the concepts I found so frustrating: primes, composites, units...Now, I'd love to share this with my students, or least the conceptual visual breakdown, as I found the associated 'monsters' to be a bit too complex for early readers/learners to be eased into the subject.

[Julie Culver · Rating 5 out of 5]

I love this book! Each prime number has a monster picture and each composite number is a picture made up of parts of the primes it is made up with. It is an excellent early introduction to primes, multiplication and just the numbers from 1 to 100.

[Blair · Rating 5 out of 5]

This is a superb introduction to multiplication and division, in the form of the prime factors of composite numbers. My four year old grandson used this book for months before I had to return it to the library.

[Valorie Zonnefeld · Rating 5 out of 5]

I LOVE this book! It's beautiful and mathematical.

[Amelia · Rating 2 out of 5]

Didn't work AT ALL for my math-loving first grader who had asked for a book about this exact topic. Not sure who the target audience for this is.

[William · Rating 5 out of 5]

Features some awesome art.

[Sarah · Rating 5 out of 5]

I love this visual book on multiples so much!!!

[Lbrown107 · Rating 2 out of 5]

This book is about prime numbers and factoring using numbers up to 100. I really did not enjoy the illustrations in this book because each monster has a defining feature that relates to its number and I found a few monsters whose characteristics were not clear enough to tell the corresponding number. I think it would be a little difficult for young children to keep track of the corners of the monsters while counting. I did like how the author had visuals of factoring, using groups of dots to show multiplication.

[Phil Scovis · Rating 5 out of 5]

From the other reviews, I see there is some question of whether prime factorization is suitable material for picture-book-aged children. My opinion is that it's always good to begin with the assumption that children are able to understand.

Maybe it depends on the child. All I can say is that my own children (ages 5 and 7) spent the evening drawing factor trees, and creating their own monster pictures for numbers past 100. They also loved counting the tentacles/edges/hairs on the prime-numbered monsters, and trying to guess what the next monster would look like.

[Heather · Rating 4 out of 5]

Thanks friends for the suggestion. This is exactly how my sons brain appears to think about numbers & he ate it up. He has looked at it numerous times. Even quizzed me, I asked him why he was quizzing me, as the numbers & factors were right in front of him, he said to ensure that it was accurate!! Ha!

[Mary Conroy · Rating 4 out of 5]

This is a great resource for teaching and reviewing number facts! The text is fun and colorful, and the monster illustrations are really cute. This book explores the relationship between numbers and the different fact families. It would be great for a read-aloud or to lead into a lesson about number relationships.

[Robu-sensei · Rating 3 out of 5]

A cute math book for precocious children, You Can Count on Monsters illustrates the concept of prime factorization by combining "monsters," representing the prime numbers, in strange and silly ways to form composite numbers. Also includes an carefully explained version of Euclid's proof that the prime numbers are unbounded (i.e., that there is no largest prime number).

[Lorena · Rating 4 out of 5]

I bought this book for Shari Brooke because she is obsessed with numbers and counting. It's actually quite clever in that it displays the factors of each number to 100. Grant, who also loves math and numbers and clever things, really likes this book. It has a several pages of mathematical explanations at the beginning. It's not my favorite book, but these two kids of mine really love it!

[Christine Turner · Rating 4 out of 5]

Presents numbers 1 through 100 and multiples.

Great visual guide for learning prime numbers and factoring.
I would give this 5 stars but I find the "monster" illustrations to be strange. Other than that, it's a winner for people who are visual learners.

[Elizabeth]

As seen on NPR (via Game Theorist).

[Marya · Rating 3 out of 5]

Schwartz draws each prime number as a monster, and then all the composite numbers as, appropriately, composites of the prime numbers that they factor into. So 14 is the 7 monster eating the 2 monster. It's really a beautiful book, but what age group is it really for?