Ying and the Magic Turtle

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Ying and the Magic Turtle is a story book that invites readers to experience mathematics, problems solving, and the rewards that come with perseverance. Children ages five and up, parents, and teachers can enjoy the book for its rich beauty in mathematics and as an ancient legend.

Ying and the Magic Turtle

96 pages. ISBN 978-1-945899-06-5

Beautiful paperback for your learning library. $24 $19 It comes with ePub, Kindle, and PDF files of the book.

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Crowdfunding Video

111 crowdfunders fully supported the book’s production – thank you! Here’s a memento from the campaign:

About the book

“Long ago in the land of China, there were many rain storms … and the land of China was slowly sinking into the sea. This is the story of how a wise emperor, an observant girl, and a magic turtle saved the villages of China from the great flood.”

So begins the story of Ying and the Magic Turtle.

Children ages 5 and up, parents, and teachers can enjoy the book for its rich beauty in mathematics and as an ancient legend. It is the kind of story to revisit over and over again. This book is perhaps best experienced with someone, as a read-aloud or read-together. When reading, we learn of Ying’s trouble, and we root for her to find her solution. We find ourselves drawn into the life problems that Ying is facing, but also drawn into the inherent mathematics of the story. It is through the beauty of the pattern of the dots on the turtle’s shell that the solution is finally found and the land is saved.

We can appreciate each scene as we read, and then pause and predict what might come next. We can play with the mathematics, solving right alongside Ying. We can delve deeper into the power of magic squares by working with puzzles presented at the end of the story. There are unsolved problems in number theory even a young child can try, such as finding all the possible magic squares of a given size.

Ying and the Magic Turtle mock-up

Ying and the Magic Turtle is about the excitement and rewards that come with solving a challenging and interesting math problem. Ying, the heroine of the story, shows others what it means to enjoy and productively struggle with a mathematical problem. She is patient, persistent, and curious. She uses these qualities to stick with a perplexing problem. She demonstrates the attributes of a problem solver. She sketches things out. She ponders and wonders. She walks away and then returns to the problem. She searches for patterns and clues. Ying takes her time to notice the pattern and use the hidden structure. Most importantly, she does not give up! 

Following the story, there are magic square puzzles inviting readers to continue to play with the mathematics. Solving puzzles together is a wonderful way to connect with one another through mathematics. We can experience the joy that comes both during the process of problem solving, and with finding a solution. 


The puzzles at the end of the story are designed in a progression of levels of challenge to provide multiple entry points. Some tasks are specific in nature, while others have various solutions. All tasks encourage creativity in mathematical thinking. While ages are suggested, readers can choose how they wish to engage with the mathematics in a way that they find joyful.

For young readers, ages four to six, they might solve a magic square by studying Ying’s drawing and counting the dots. They might notice how many dots are in each box on the grid, and look for any patterns. They might create their own pattern on a grid.

Ying And The Magic Turtle 2

Readers ages six through twelve can be drawn into the fascination of how magic squares “work.” They can play with the placement of the numbers on the grid and look at various sums using three addends. They can also play with rotations and symmetry to find multiple solutions.

If we look even further into creating magic squares, readers age twelve and older can explore and derive the formula for generating not only a three by three magic square, but also larger magic squares. As they do so, they are working with algebraic thinking and the study of functions.

All too often people equate mathematics with rote exercises that are lifeless. Ying and the Magic Turtle shows us that a mathematical journey can indeed be magical. 

Meet the Team

Sue Looney

I am Dr. Sue Looney, the author of Ying and the Magic Turtle. Even as a young child I have been full of curiosity – especially about how numbers work. I continue to be that curious ever-questioning child. Perhaps I am a bit like Ying!

I discovered this legend over twenty years ago, and it sparked a strong ongoing interest in magic squares. I have continued to be fascinated by the properties of mathematics and pattern seeking that can be uncovered through studying and solving magic squares. I have had great fun and success engaging learners of all ages with activities for magic squares. I now have the opportunity to more widely share my enthusiasm through Ying and the Magic Turtle.

Educating children and adults, and encouraging them to question, to pursue understanding, and push their boundaries of learning has become my career. I am passionate about spreading the joy of mathematics to all learners – from experienced educators to the youngest of children. I am the founder of Looney Math Consulting, a professional development agency devoted to supporting educators in the important work of inspiring learners to believe in themselves as powerful mathematicians.

I also love adventures, imaginative stories, and nature. When I first heard this ancient Chinese legend, I became fascinated by its combination of magic and beauty. The main character, Ying, is a role model for children to pretend-play a mathematician. Just like a mathematician, Ying is patient, persistent, curious. And just like Ying, a child faced with a difficult math problem will draw sketches, ask questions, search for patterns, make conjectures, and test ideas. Our world’s challenges are more complex than a single puzzle. Yet fantastic adventures like Ying’s can inspire real future scientists, engineers, and mathematicians.

I am fortunate that I was able to include my children, Jessica Looney and Joey Looney, as illustrators for this story. As artists, they seek out the beauty in expressing the world that they see. They create with a variety of mediums including drawing, painting, writing, and photography. 

Thank you, team! Cover design by Mark Gonyea ~ editing by Ruthann Raitter, Cristy Bertini, and Maria Droujkova ~ layout by Michael Del Purgatorio.

Bonus Puzzles

Print out this PDF of bonus magic square puzzles that go with the book.

Ying Puzzle Card

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, beautiful, and kind math to your child’s life? Will it be fun? So that you can say YES to all of these questions, the Natural Math community has developed a unique publishing process.

Our publishing gives authors, artists, and even readers a lot of creative control. A book starts with amazing authors who deeply care about their work in mathematics education. Each author spends many hours improving every aspect of the manuscript by testing the book with children, families, and classes.

Next, Natural Math invites 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 parents, principals and classroom teachers, as well as leaders of math circles, learner coops, museum activities and other extracurricular programs. They come from all learning backgrounds and all continents (except Antarctica). Their input is how Natural Math books become so real.

Crowdfunding comes next. Our crew of professional editors, proofreaders, and designers is paid with the crowdfunding money. They make the paper books a joy to hold, and ebooks flow on all devices. Natural Math books have been featured by The Atlantic, The NY Times, The NPR, and many lovely sites dedicated to learning, parenting, and mathematics.

And One More Thing

As all our previous books, Ying and the Magic Turtle is published under a Creative Commons license. That means that people all over the world will be able to access its content, translate it into different languages – and share their ideas based on the book. The Creative Commons site features an interview with the Natural Math founder in its celebration of innovative projects in education.

If you already are a part of the Natural Math community, thank you for your continuing support. If you are new to Natural Math, thank you for checking out our latest project. Please join the math adventure!

Thank you for your interest! Please help us spread the word about this book to support young problem-solving.