A tangram is a set of seven pieces that all fit together to form a square. The fun — and the spatial orientation challenge — is to rearrange the five right triangles, the square, and the parallelogram to form a variety of shapes. An optional challenge is to find the area of each piece and of each arrangement created. Work with shapes and their areas relates to both Geometry and Measurement Standards. You’ll find that all the online activities below can be adapted to the offline classroom by reproducing the seven pieces for hands-on use.

Tangrams: Geometry (grades 6-8)
Using this applet for the Chinese tangram puzzle, students can experiment with the placement of the seven tangram blocks to form 14 different shapes. Students move, flip, and rotate each tangram block.

Build a Shape with Tangrams
Using this applet, the student can observe spatial relationships found by placing polygons in different arrangements. The goal when working with this applet is to replicate examples of different shapes formed using the seven pieces found in a traditional tangram.

Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams: Tangram Challenges
This NCTM site offers tangram challenges such as: Make a square using only three tangram pieces. Use all seven tangram pieces to make a trapezoid.

Tangrams
A Problem of the Week that will engage your class in work on area and percentage. One example: If the smallest triangle costs 5 cents, based on its area, what would each of the other pieces cost?

Archimedes’ Puzzle
The Stomachion is an ancient tangram-type puzzle. Believed by some to have been created by Archimedes, it consists of 14 pieces cut from a square. In this lesson, students learn about the history of the Stomachion, use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces.

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