# Tangram Chess: Transformation Math Games

Have you ever played with a tangram before? No one knows exactly when the tangram was created but its design was inspired by a table used in the Tang Dynasty in China. This customizable banquet table, called the yanqi, could be rearranged to fit the number of people sitting around it. A traditional Chinese tangram is made up of seven shapes. The seven shapes are a parallelogram, five right triangles of various sizes, and a square. When these pieces are rearranged to fit together they create a larger square. Sometime in the 19th century, seafaring tradesmen discovered tangram puzzles in China and brought them to Europe. They became very popular because endless games and designs could be made from them including human figures, animals, and flowers as well as geometric patterns. In a way, they are similar to origami but just 2-dimensional instead of 3-dimensional.

You’ll notice that the tangram for this challenging game of Tangram Chess is a more simplified tangram composed of only five shapes: a parallelogram, a square, two different right triangles, and an isosceles triangle. There are so many potential springboards for classroom exploration when you begin with this game. You can start by teaching students congruence based on the different moves on the board, such as translations (slides), rotations (turns), and reflections (flips). It’s also a great opener for discussing a proof of the Pythagorean Theorem using a tangram. In addition to the strategies students will use to move their pieces across the gameboard and reassemble their tangram on the other side, they’ll also notice relationships among the pieces as well, such as the fact that the isosceles triangle is made up of two right triangles.

Another fun idea is to make different shapes using your tangrams and create a story. Have one student put together a human or animal shape and the other assemble another character to go with the first shape. In this way, both math and storytelling are working hand in hand.

Think about creating an entire teaching module to go with this game. Begin with the history of the tangram. Then give students worksheets with different tangram silhouettes and have them figure out how the different shapes could be placed together to create the figures. The pieces must be placed with their edges together, but they must not overlap. There are some free worksheets with tangram designs online but you can also have students make their own designs. Have 1/2 of the class create the silhouettes and the other 1/2 of the class explore with the tangrams to see how the shapes were created. Then play the Tangram Chess game and talk about the different moves that could be made on the chessboard so that your tangram can be reassembled as a square on the other side of the board. Finally, for older or more advanced students, talk about proofs using tangrams to display the Pythagorean Theorem. Perhaps given the appropriate pieces they can create the visual proof themselves without a finished picture to review.

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#### Common Core Mathematical Standards

8.G.1 Verify experimentally the properties of rotations, reflections, and translations
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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