The age ranges given are just my best guess.
The Opposites, by Monique Felix (ages 2 to 6)
One of the earliest math skills, more basic perhaps than counting, is noticing attributes. This book has no words, and yet it tells dozens of stories, each about opposites. Noticing the one attribute that shows opposites in each detail-filled picture is a math game your child will want to play again and again.
Quack and Count, by Keith Baker (ages 2 to 7)
This is a board book – good for the youngest child who will sit and listen to a story. It stays good because it’s so luscious – great illustrations, fun rhythm and rhyme, cute story, and good mathematics. Seven ducklings are enjoying themselves in every combination. “Slipping, sliding, having fun, 7 ducklings, 6 plus 1.” (And then 5 plus 2, etc.) It would be great to have a book like this showing all the number pairs that make eight, and another for nine, etc. If I ever get to teach math for elementary teachers again, I’d love to get my students to make books like this one.
Anno’s Counting House, by Mitsumasa Anno (ages 2 to 7)
Everything I’ve seen by Mitsumasa Anno is delightful. There is so much to see in his books, many of which have no words. In this book, ten people are moving from one house to another. In each two-page spread you can see one more person who’s moved from the left house to the right, along with lots of furniture and other small items. For slightly-older kids, there is Anno’s Mysterious Multiplying Jar, showing us one island with two counties, which have three mountains each, and so on, until we get to ten jars within each box – a lovely, very visual representation of factorials. In Anno’s Magic Seeds, the story does need words – we learn of a plant whose seed, when baked, will keep you from being hungry for a full year. The plant grows only two seeds in a year, one of which must be used to grow a new plant. The story explores the conflict this causes. You may also enjoy Anno’s Math Games. Anno has written over forty books, most available in English.
Two of Everything, by Lily Toy Hong (ages 3 to 7) A poor old farming couple in China find a mysterious pot. When a hairpin drops in, they scoop two out. The math isn’t discussed in the story, but it’s pretty easy to add your own thoughts to this delightful tale of doubling.
How Hungry Are You?, by Donna Jo Napoli and Richard Tchen (ages 3 to 12)
There are lots of great of great books on sharing equally. My favorite used to be The Doorbell Rang, by Pat Hutchins, but this one is even more delightful. The picnic starts with just two friends; Rabbit is bringing twelve sandwiches and Frog is bringing the bug juice. Monkey wants to come: “My mom just made cookies. I could take a dozen.” They figure out how much of each goody each friend will get. In the end, there are thirteen friends at the picnic, and the sharing becomes more complicated. One of the delights of this book is the use of little icons showing who’s talking. It would make for a good impromptu play.
I Love Math!, a series by Time-Life (ages 4 to 12)
My son loves these. Each book has a wide variety of stories (fiction and non-fiction), puzzles, games, and more. It’s like a very cool math magazine, but hardcover. Titles include our favorites, Right in Your Own Backyard: Nature Math and The Case of the Missing Zebra Stripes: Zoo Math, along with ten others.
One Grain of Rice, by Demi (ages 5 to 12)
The greedy raja is gently outsmarted by a wise village girl named Rani. This is a very sweet take on the story of grains of rice put on a chessboard. (One grain on the first square, two on the next, then 4, 8, 16, …, until the board is filled. How much rice is that, anyway?)
The Cat in Numberland, by Ivar Ekeland (ages 5 to adult)
The story starts when Zero knocks on the door of the Hotel Infinity. He’d like a room, but they’re all full (with the number One in Room One, and so on). It turns out that’s no problem – the Hilberts and their number guests are able to make room for zero. The cat who lives in the lobby gets confused – if the hotel is full, how can the numbers make room for Zero just by all moving up one room? Things get worse when the fractions come to visit. This story is charming enough to entertain young children, and deep enough to intrigue anyone. Are you ready to learn about infinity with your five-year-old?
You Can Count on Monsters, by Richard Evan Schwartz (any age)
Each number from one to one hundred is a monster, and each one gets its picture on its own page. All of the numbers (except poor one) are made up from their prime parts. The pictures are amusing, colorful, and packed with intriguing details. The pages in the front and back that explain prime factorization are unassuming, waiting for the reader to decide it’s time to find out more. This and Powers of Ten would both make great coffee table books, to peruse over and over.