Shapeshifting and Storytelling with Tangrams

600px-Tangram_set_00This week’s book added tangrams into our math story time. The tangram is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective is to form a specific shape (given only an outline or silhouette) using all seven pieces, which may not overlap.

In this NPR article*, tangram is described as the “EverReady battery of puzzles. It just keeps going and going.” The article includes a history of the puzzle (quoted from Alex Bello’s Here’s Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math) and includes this Tangram video illustrating the magical shapeshifter in action. 

While I’m familiar with tangrams as teaching tools and toys, I recently discovered they can be used in storytelling as well. This week’s magical math book uses tangrams to tell a tale of two fox fairies.

The Book

Grandfather Tang’s Story (Dragonfly Books) written by Ann Tolbert and illustrated by Robert Andrew Parker in 1990.

The story begins with Little Soo asking her grandfather for a story. Grandfather Tang arranges the tangram pieces and two magic fox fairies spring to life. As Grandfather Tang tells the story, the foxes change from rabbits to dogs to squirrels and geese, each time trying to one up the other. When one fox fairy faces a hunter’s bow,  their competitive shape shifting ends and second fox fairy springs into action to save his friend.

The Math

Tangrams are geometric shapes. There are 5 isosceles right triangles (two large, 1 medium, two small), 1 square and 1 parallelogram. As a child uses tangrams to match a silhouette like the ones below, they  attend to how the shapes are related. Tangrams are an excellent way for children to develop their spatial reasoning. [Here is a nice summary of spatial reasoning written by Ontario Ministry of Education]


Discussions about angles, congruence, and transformation geometry concepts of slide, turn and flip come up naturally in tangram play.

Go here for a great article from Parenting Science that includes resources about tangrams and math. Here for an Illustrative Math lesson incorporating tangrams, or here for Ms. Jacoby’s creative use of tangrams in her classes. 

The Magic

Before reading the story, I watched as Liam and Siena free played with the pieces. A favorite activity was forming symmetric designs. During her play, Siena pointed out she made a “shape out of shapes.” (See parallelogram below made from two small triangles which is congruent to the parallelogram tangram)


After they played, I asked if they could form a square with the seven pieces. They got to work and found ways to use 2 tangram pieces to make a square, 5 tangrams, and 7 tangrams. Questions we are still working on: Can you use 3 pieces to form a square? what about 4? or 6?

When Liam found a 5 tangram square, I watched as he measured to make sure all four sides were equal using the green tangram to check. [See slideshow below.]


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At first, I was surprised to see him verify he had in fact made a square. But realized after chatting with him, that he was recalling an experience he had last week when a squarish shape wasn’t a square (i.e., didn’t have four congruent sides).  In Triangle by Mac Barnett and Jon Klassen, the main characters are Triangle and Square.   While reading this book, I noticed a page on which the character Square is not actually a square (his sides are 5.5cm by 6.3 cm in our copy).  I had Liam and Siena search through to find this non-square Square and prove it it wasn’t a square. This illustration error in the book provided a nice opportunity to check whether something was a square and wonder how this might happen (e.g., maybe the illustration was accidentally scaled only in an horizontal direction in the editing process).  Note:  Square is a square on the other pages.

Image from Triangle by Mac Barnett and Jon Klassen

After playing, they took turns forming the characters with the tangrams as we read.

See if you can guess what they are, the answer key is above In black and white image

After reading the story, Siena told her own story with the tangrams about a mom and a baby, Liam interrupted, “Wow Siena how did you do that?”  marveling at how she made the people. I loved his surprise at how his younger sister could wield the tangrams shapeshifting power and create an image he immediately recognized.

Grandfather Tang’s Story is a great way to share a story with children. If you are interested in tangrams or book here are some links to amazon products.

Grandfather Tang’s Story (Dragonfly Books)

Classic Tangrams

Tangoes Junior

*The cover photo for this post is also from the NPR article referred to above by Robert Krulwich.

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Thanks and see you next Monday! #mathbookmagic


  1. Tangrams provide many opportunities for students to enjoy learning about math. See how to start with a square and cut shapes to end up with the tangram shapes. Fun part is having students put the pieces back together. There is also an IPad App TanZen as well as some games with the OSMOS that use tangrams.

    Liked by 1 person

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