Multiplication Explorers, the book

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Natural Math was one of the first web pages in the world about multiplication, circa 1996. We were the first in the world to offer open online courses for parents in the early 2000s. Our most popular, longest running course is about multiplication as the cornerstone of algebra and calculus. Our quick, powerful pattern-based method of learning the times tables and our creative art activities have been tested by thousands of families, math clubs, and classes. We’ve adapted advanced, beautiful math to make it kind and radically accessible. “You should write a book,” people would say.

We wrote the book!

Multiplication Explorers LIVE 2016

(A mini-poster from one of our courses.)

A Powerful Method to Learn Times Tables – Now a Book

Based on our longest-running, most popular online course, this book features
  • Pattern-based approach to learning times tables
  • Engaging activities that explore the beauty of algebraic and calculus reasoning
  • Radical accessibility – anyone from 3 to 103 years old can enjoy the book’s projects
  • A kind and thoughtful path to advanced mathematics

Want to communicate with the authors, receive sample activities, and be the first to hear the news? Sign up.


Sample Art from Chapter 1, “Inspired by Calculus”

Star Fractal by NaturalMath

More Fractals NaturalMath

Multiplication Towers Math Circle

Sample Art from Chapter 2, “Inspired by Algebra”

Combinatorics Animals NaturalMath

MathLexicon NaturalMath

Spirolaterals NaturalMath

Ancient merchants’ finger trick from Chapter 3, “Times Tables”

Ancient Merchants' Multiplication Trick

Download the printable PDF of “Ancient Merchants’ Finger Trick”. 

This amazing trick was first recorded around 15th century. Back then, merchants used finger reckoning to calculate prices and profits. A calculating device took half a room, while finger math was easy to take on a trip. Merchants twiddled their fingers away from the prying eyes of their competitors: that’s where the phrase “under the table” came from. Try this for a party trick, or to check your memory of the hardest multiplication facts. Once you practice enough, you can do the trick like a merchant of old, under the table.

Does the trick always work? Even a young child can prove that it does. Check every multiplication fact from 6 x 6 to 10 x 10, and the answer will come true. But that proof is not very satisfying.

How about formal algebra? Click to read a formal algebraic proof. During the crowdfunding campaign for the book, we’ll be collecting and sharing various joyful proofs.

Meet the Publisher

nm_logo_100pxAs a parent, teacher, or math circle leader, you want books that are helpful for your children. Will the book make sense? Will it add rich and beautiful math to your child’s life? Will it be fun? So that you can say ENTHUSIASTIC “YES!” to all of these questions, the Natural Math community has developed a unique publishing process.

A quality book takes professional artists, editors, and designers – we got them! Yet great books start with dedicated authors who care enough to spend dozens of hours improving each little activity by testing it with many children, families, and classes. Then early drafts go through revisions when authors of other books help to refine the new project. This is more work and nurture than most math books ever get, but we are not done!

Next, we invite beta readers – brave community volunteers who field-test the draft in their own families and classes, without the authors on-scene to help. Our beta readers are new parents and veteran homeschoolers, principals and classroom teachers, leaders of first-time math playgroups and long-running math circles. They come from all learning backgrounds and all continents (except Antarctica). Readers tell us where to add examples, which activities need more ‘wow’, which terms to explain, and what children’s questions were tough to answer.

That’s how Natural Math books become so real. 

And One More Thing

Our book will be published under Creative Commons license. It means that people all over the world can access its content, translate it into different languages – and share their ideas based on the book with you. The Creative Commons site Team Open features Natural Math in its celebration of innovative projects in education. 

Thank you for your interest!