Though they may have existed for generations, the earliest known printed reference to tangrams appears in a Chinese book from 1813. Tangrams became very popular in 19th century Europe and America as sailors brought the puzzles back home from their trading voyages to China. The origin of word tangram is still uncertain, but one theory is that it comes from an old English word "tramgram," which means puzzle or trinket.

The tangram puzzle consists of seven pieces, called tans, which are cut from a large square. The pieces include five right triangles (2 small, 1 medium, 2 large), one square, and one parallelogram. The original objective of a tangram puzzle was to create a “work of art" using the seven pieces, but in formal games today, players are asked to form a given shape, such as a rabbit, house, or boat. The pieces must all touch, but none may overlap.

In trying to recreate a given shape, you are allowed to move the pieces by sliding them around the flat surface or rotating them. In some cases you may also have the option of flipping the pieces. In mathematical terms, these changes to the shape are called transformations. There are three primary geometric transformations. Dragging or sliding a shape from one position to another without turning it is called a translation. Turning a piece is called a rotation, and flipping a piece is called a reflection. Moving the tangram pieces around gives you an opportunity to work on spatial reasoning skills. You have to think about how a whole figure is made up of its parts, and sometimes you find that there can be more than one combination of pieces that will work. Once you start working on the puzzle, you start to see how two shapes can fit together to make a new, larger shape—for instance, the two small triangles can be positioned next to each other to form a parallelogram, a square, or even a larger triangle. Similar arrangements can be made from the two large triangles as well (as shown below).

You can make your own tangram set out of many different types of materials, such as paper, cardboard, wood, glass, or metal. All you need is a piece of material in the shape of a square, a ruler, and a tool to cut the material. After you have experimented creating some of the given shapes, you can think about creating your own figure and then asking another person to try to re-create it.

To learn more about transformations and arranging shapes, check out Wallpaper Tessellations, Squares, Hexagons, and Triangles.

For a lesson plan involving tessellations, check out Investigating Tessellations Filling 2-D Space.