The school year has started. I have read Ish to my classes and talked about math-ish numbers. It was a huge hit. Some of the kids recognized the book and some did not know it. It was the perfect introduction to needing number sense and math-ish numbers. I love incorporating story books into middle and high school math classes. Today I have another one to share with you. It tells the real-life tale of a woman with no mathematical background who solved a very old mathematical problem and not just once! The book is The Five Sides of Marjorie Rice: How to Discover a Shape by Amy Alznauer and illustrated by Anna Bron. It is recommended for ages 7 to 9. I am going to share some related math activities to go with the book for different ages!
About the Book:
When Marjorie Rice was a little girl in Roseburg, Oregon, in the 1930s, she saw patterns everywhere. Swimming in the river, her body was a shape in the water, the water a shape in the hills, the hills a shape in the sky. Some shapes, fitted into a rectangle or floor tilings, were so beautiful they made her long to be an artist. Marjorie dreamed of studying art and geometry, perhaps even solving the age-old “problem of five” (why pentagons don’t fit together the way shapes with three, four, or six sides do). But when college wasn’t possible, she pondered and explored all through secretarial school, marriage, and parenting five children, until one day, while reading her son’s copy of Scientific American, she learned that a subscriber had discovered a pentagon never seen before. If a reader could do it, couldn’t she? Marjorie studied all the known pentagons, drew a little five-sided house, and kept pondering. She’d done it! And she’d go on to discover more pentagonal tilings and whole new classes of tessellations. In this visually wondrous tribute, Anna Bron’s intricate art teems with patterns, including nods to M. C. Escher, and radiates the thrill of one woman’s discovery, playfully inviting readers to approach geometry through art—and art through geometry. Back matter offers more on the story of five and suggestions on how to discover a shape.
From Me:
Oh, the math teacher in me loves this book. Here is a woman who was interested in math and art as a child but was pushed into a more "female" career and then became a homemaker with five children. However, her brain longed for more. When she read her son's Scientific American magazine about shapes that tessellate and then later about the problem of pentagons and someone finding a new solution she began her own search for a tessellating pentagon. Yes, a homemaker takes the time to find several new tessellating pentagons and submits them! What a great story!!
I love how the book shares some of the history of tessellating shapes and a bit of the math behind them. I also love that Marjorie was honored by the Mathematical Association of America at a meeting and then the floors of the lobby at its building and the entrance to the National Museum of Science and Technology in Sweden. At the end of the book there is information about how the story of convex pentagons is in fact over. They have all been found with the help of Marjorie. There is also a page of how readers can discover shapes with ideas on shapes to explore in making tessellations. There are mentions of M.C. Escher in the story as well as at the end of the book. This book is perfect for any classroom studying shapes, tessellations and even art. It is full of math--geometry in particular but it is also full of art and history. It could be featured in Women's History Month or as a study of pentagons. I can see kids enjoying it and perhaps Marjorie can be a role model for some young readers! This book is going to be living in my classroom so I can share it with my high school geometry class each year!
Activities to Go with the Book:
For the young readers there are various tessellation coloring pages available on-line. Candlewick Press also offers a Teacher's Tips Page under the resources for the book.
Some of my favorite coloring pages:
- Free Collaborative International Dot Day Tessellation Project Math Activities from Inspire Math Matematyka on Teachers Pay Teachers
- STEM Activities for Kids offers a free download of 5 Tessellation Coloring Pages
- The Ed Kins offers a pentagon tessellation to color
- Super Coloring has a Pentagonal Flower Tessellation Coloring Page
- Free Fish Tessellation Coloring Page from Green T Studios on Teachers Pay Teachers
This summer we went to New York City for my birthday and one of the places we visited was the National Museum of Mathematics. They had an exhibit called Miles of Tiles where you could use magnet tiles to create tessellations. They had monkeys, rabbits, and dinosaurs that tessellated! They reminded me of lizard magnets I used to have (and gave away when I stopped teaching). You can buy various tessellating items including these magnets at the gift shop. If you are near NYC, I highly suggest visiting!!
For older kids you can have them try to make their own tessellation. I suggest a translation one for the younger kids.
- What Do We Do All Day? shares a wonderful tutorial video for translation tessellation.
- Little Bins for Little Hands has a free paper cutting tessellation project.
- Teach Beside Me shares a heart tessellation to draw using graph paper.
- Frugal Fun 4 Boys and Girls shares a printable leaf tessellation for kids to make and a fun fish tessellation you can print or make your own template!
- To see how a rotation or reflection tessellations differs you can check out this great free Tessellation Handout from Sheena Kohlmeyer on Teachers Pay Teachers.
- Artsy Craftsy Mom shares a roundup of different tessellation activities using all sorts of different mediums.
For high school geometry class, I would first discuss why a regular pentagon does not tessellate. Using information about the angles in a regular pentagon (each angle measures 108 degrees), it becomes easy to see that no number of these angles can create a perfect 360 degrees needed to tessellate.
However, there are different types of pentagons that do tessellate. You can see some pictures of them on this archived post over at American Mathematical Society's blog. I would then see if the kids could come up with a pentagon that does tessellate.
For more about Marjorie Rice and her tessellating pentagons:
- Math Munch even shares a bit about Marjorie Rice and her discoveries with pictures.
- Quanta Magazine also shares about Marjorie Rice and her discoveries.
And, of course, a discussion of tessellations is not complete without talking about M.C. Escher and his amazing work!
- There is a free M.C. Escher Tessellation from Art Projects for Kids on Teachers Pay Teachers for grades 3-5.
- The Crafting Chicks also have a great M.C. Escher Tessellation Project for kids.
