Tangrams and Geometry

Perhaps you are familiar with Tangrams. This ancient game is said to have originated in China, and is an ingenious-puzzle figure of seven pieces. If you have ever seen a Tangram, you know that it is formed entirely of geometric shapes: isosceles right triangles, a parallelogram and a square. Some of the triangles are congruent, and all of the triangles are similar. Math students will enjoy playing tangram puzzles, and can practice their geometry by creating a tangram puzzle of their own.

In this project, students can follow the instructions below, and solve a tangram. The instructions have been written using geometric terminology. If you have access to geometry software such as The Geometer's Sketchpad, students can design and create their own tangrams on the computer, and then challenge others to solve their puzzles. If you are not using Sketchpad, then print the colored image below and cut out the pieces. In either case, students will become very proficient with the geometric concepts of Reflection, Rotation, and Dilation, as well as Similar and Congruent Triangles.

Instructions for the Tangram Challenges: To solve one of the Tangram challenges below, select one of the original pieces, then move it on top of the challenge. Rotate or reflect it so that it matches the challenge. (If you are using Sketchpad, Create a point for Center anywhere you like before you Rotate, and create a line for a Mirror before you Reflect.) If you are using Sketchpad, hide all the extra figures that may be created in this process, do not delete them..

The Challenge: Create this figure, using the tangram pieces:

The Solution:

And here is another tangram challenge:

And here is the solution:

Once students have had a chance to solve a few Tangram puzzles, ask them to create their own Tangram challenges (and to provide the solution, as well!) This will give them real hands-on experience, and a real sense of ownership of the geometry concepts involved: names and definitions of the polygons involved, practice with the geometric concepts of shape and size as well as hands-on practice with rotations, reflections, and translations.

The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal, James, William (1842 - 1910)