Math Books for Children of All Ages!

Montessori Thrive • May 8, 2020

In Montessori schools, children tend to really love math. It’s no wonder, with gorgeous materials created to appeal to their senses and developmental stages. While work with the materials is best left in the classroom, one fun way parents can support their children’s love of math is by reading to them about it. This month we have created a list of books that will appeal to children of all ages, whether they are learning to count or discovering the magic of Pi. Check out these titles and let us know what you think!


Numbers

by John J. Reiss

There are some iconic early counting books out there, but if you’re looking for something fresh to inspire a love of numbers, check out this beautiful little book. With bold illustrations and sturdy pages, children can learn to count to ten and beyond (there’s even a page for 1000!).


How Much Is a Million?

by David M. Schwartz, illustrated by Steven Kellogg

Is your child ready to expand their understanding of place value? Are you looking for a way to help them conceptualize larger numbers? This charming book is both fun and educational, giving kids concrete ways to visualize one million. How tall are a million children? How long does it take to count to a million? How much water would a million goldfish need? Find the answers to these questions and more!


The Grapes of Math

by Greg Tang, illustrated by Harry Briggs

Adding, subtracting, multiplying, and dividing are important skills for all young children to learn. Finding different ways to look at groups of numbers can make operation work a breeze. The Grapes of Math uses clear illustrations and catchy rhymes to challenge children to find new ways to count larger numbers. Your child is sure to have fun figuring out these math riddles with you.


One Hundred Hungry Ants

by Elinor J. Pinczes, illustrated by Bonnie MacKlain

Everyone loves a picnic, including ants! In an attempt to get to the food as soon as possible, the ants keep rearranging themselves into different groups. Two lines of 50 is surely faster than one line of 100, right? What about five lines of 20?


Measuring Penny

by Loreen Leedy

Lisa’s teacher asks the class to go home and measure something. What could be more fun than measuring your pet dog? This book discusses multiple standard units, nonstandard units, comparisons, and a myriad of ways to measure. Lisa and Penny have fun at the park, where there are plenty of other dogs to measure, too!


The Lion’s Share: A Tale of Halving Cake and Eating It, Too

by Matthew McElligott

An ant attends the Lion’s annual fancy dinner, along with a number of other animals. The sweet ant is shocked by the terrible behavior of the other guests. Beyond their awful table manners, they divide a cake with no regard for fairness (although they do give readers a great lesson about fractions along the way!). When the ant offers to bake the king a cake, the other animals try to outdo her, with each doubling the offer of cakes. Kids will be amazed and amused!


Math Curse

by Jon Sciezka, illustrated by Lane Smith

What would you do if your math teacher told you that basically everything in life could be a math problem? If you’re the main character in this book, you might feel like you have a math curse. When life is suddenly numbers, fractions, and word problems, how can you possibly think about anything else? When even the character’s dreams become math problems, they realize they have to find a solution.


Sir Cumference and the Dragon of Pi

by Cindy Neuschwander, illustrated by Wayne Geehan

When Sir Cumference has a stomach ache, his son Radius runs off to find some medicine. He accidentally turns his father into a dragon, and finds a mysterious mathematical poem to help him undo the magic. While searching for answers, Radius sees circles everywhere, but he needs to figure out how to measure circumference in order to save his dad. He does, of course, and what better way to celebrate than with some pie?


The Boy Who Loved Math: The Improbable Life of Paul Erdos

by Deborah Heiligman, illustrated by LeUyen Pham

Young Paul did not live his life like most people. He struggled with seemingly simple tasks, yet he was always thinking about math. As a four-year-old, he enjoyed mentally calculating how many seconds old people were. This story highlights the fact that there is a place in this world for all of us. The genius of this one boy was realized as he traveled the world collaborating with other mathematicians.


What’s Your Angle, Pythagoras?

by Julie Ellis, illustrated by Phyllis Hornung

While we don’t actually know anything about the childhood of the famed Pythagoras, Ellis imagines the types of mischief (and learning!) he may have gotten up to. Curiosity can lead us in many different directions, and Pythagoras goes on a voyage with his merchant father. His passion for buildings leads him to learn about angles, and how a knotted rope helped early builders calculate precise measurements. He explores some more, and uses patterned tiles to discover the concept of squaring.


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Montessori education has been in existence for over a century, but does it actually work? Dr. Angeline Stoll Lillard spent years researching this question, and her book, Montessori: The Science Behind the Genius, is a must-read. In her book, Dr. Lillard identifies eight principles at the heart of Montessori education. What’s key is that these Montessori principles align with what developmental science tells us about how humans actually learn. The remarkable thing is that Dr. Maria Montessori arrived at most of these insights through careful observation of children, decades before the research existed to corroborate how children learn. In this two-part blog post, we’ll examine these eight principles and the connected research. PRINCIPLE ONE: Movement and Learning Are Deeply Entwined In most traditional classrooms, children are still expected to sit still, as if stillness is a prerequisite for learning. In Montessori, we understand how movement and thinking are intertwined. And research backs this up. Studies have found that physical activity improves cognition, judgment, memory, and social reasoning. Moving the body isn't a break from learning. Rather, the movement is often the learning (and this is even more so for younger children!). Montessori materials are designed to be touched, carried, sorted, and manipulated. Children working with the knobbed cylinder blocks are actively perceiving, making judgments, and reasoning through their hands. The same is true when children sort fabric squares by texture, shake and compare sound cylinders, or lay out bead bars to represent quantities. Every material helps children integrate their minds and bodies. Practical life activities take this even further. When children learn to pour, button, fold, or prepare food, they are engaging in organized sequences of purposeful action that develop concentration and executive function skills. What the Research Shows A Milwaukee study found that high school students who had previously attended Montessori programs significantly outperformed peers on math and science assessments, subjects that rely heavily on the kind of reasoning that, in Montessori, is first built through hands-on materials. PRINCIPLE TWO: Choice Improves Both Learning and Well-Being The freedom to choose is at the heart of Montessori education, but this isn’t just about enjoyment. Having choice measurably affects how well children learn and how they feel about themselves. In a striking series of studies, children aged seven to nine were given anagram puzzles to solve. Those who chose their own category of puzzle solved twice as many as children whose category had been chosen for them, even though the actual puzzles were identical. Those who had a choice also spent far more time voluntarily working on puzzles during free time. The key finding is that the perception of control (even in small things) activates a fundamentally different relationship to the work. Children who feel in control tend to engage more deeply, persist longer, and take more ownership of their learning. In a Montessori classroom, children choose their own work throughout the day. Importantly, Dr. Lillard notes that this freedom is always paired with responsibility, and that too many choices can be as demotivating as none. The Montessori environment offers meaningful, bounded choice. Rather than an overwhelming array, each classroom has a selection of purposeful materials designed to match children’s developmental readiness. Choice and concentration are closely connected, too. When children choose work that genuinely engages them, they're far more likely to reach a deep state of focus, or what psychologists call a “flow state.” PRINCIPLE THREE: Children Learn Best When They're Genuinely Interested This sounds obvious, of course! It makes sense that we learn better when we are interested. However, think about this in terms of how classrooms are typically structured. If interest is one of the most powerful drivers of learning, then organizing a school day around a single curriculum delivered to the whole class at once works against almost every child in the room. Dr. Montessori understood children's interests as biological signals pointing toward what their developing minds most need to engage with at that moment in their lives. These windows of opportunity, or "sensitive periods,” are particular stretches of development during which children are uniquely primed to absorb certain kinds of learning. During these windows, learning that matches the child's inner readiness can be extraordinarily effortless and lasting. The role of interest is why Montessori materials are designed to be beautiful, engaging, and self-correcting. The sensorial materials, for example, aren't only teaching discrimination of size or color. They are designed to help children become more interested in noticing the world around them. The adult’s role is to observe carefully and offer new lessons at the moment a child's interest is most alive. PRINCIPLE FOUR: Rewards Undermine the Motivation They're Meant to Build Offering children external rewards (e.g., stickers, prizes, praise for being smart) for activities they already enjoy reliably reduces their intrinsic motivation to do those things later. What the Research Shows Researchers identified preschoolers who loved drawing with markers. They then told one group they would receive a "Good Player Award" for drawing (a fancy certificate with a gold star). Weeks later, the children who had expected the reward used the markers far less than they had before, and half as much as children who had never been offered a reward at all. Expecting a reward had turned something they loved into something they did for a prize. And when the prize was gone, so was much of the pleasure. Rewards like sticker charts, gold stars, and even grades and honor rolls, shift children’s relationship to learning from "I do this because it interests me" to "I do this to get the reward." When the reward is taken away, children’s inner drive has often already weakened. In Montessori classrooms, feedback comes through the work itself, which includes many self-correcting materials, so children discover their own errors without external judgment. The goal is to keep children's relationship to learning intrinsic, personal, and durable. This doesn't mean feedback is absent, though! What matters is the kind of feedback. Research by psychologist Carol Dweck found that praising children for effort (e.g., "you worked really hard on that”) produces dramatically better outcomes than praising ability (e.g., “you’re so smart”). Children praised for effort choose harder challenges, persist longer after failure, and actually improve their performance over time. Children praised for their intelligence begin avoiding challenges, fearing that failure will expose them as not as smart as they were told they were. In our following blog post, we’ll look at the next four Montessori principles outlined in Dr. Angeline Stoll Lillard’s book, Montessori: The Science Behind the Genius: Children Learn Powerfully from Each Other Meaningful Context Makes Learning Richer and More Lasting How Adults Interact with Children Shapes Everything Order in the Environment Supports Order in the Mind In the meantime, schedule a tour here in North Austin to see the principles in action! And let us know if you would like to borrow a copy of Montessori: The Science Behind the Genius by Dr. Angeline Stoll Lillard. 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