This easiest way to think of it is someone tiling a floor. All the pieces fit together perfectly, without any gaps. There are some beautiful examples of tessellations in nature, such as the cute little hexagon array that makes up honeycomb, as well as in architecture around the world. Tessellations were used a lot to create beautiful decorative tiling patterns in ancient Roman and Islamic art, such as the Alhambra Palace and Reales Alcázeres. Today, we see tessellations used to create decorative effects in quilts.
Research some different examples of tessellations around the world. You can look at works by M. C. Escher, or one of the examples mentioned. Or you can find some cool ones of your own.
Share the different tessellations you find with your class.
There's a cool site that has created Tessellation Town, a world where things fits together perfectly. Have a play around and see what kind of patterns you can create. It's pretty fun!
Tessellations have led to the creation of other kinds of geometrical puzzles, such as jigsaw puzzles and tangrams. A tangram is an ancient Chinese puzzle, created by cutting a square cut into seven pieces (as shown in the picture below) which can then be arranged to make various other shapes.
It can be really fun to create your own tessellating piece, and it is surprisingly easy to do.
Use the invariant properties of figures and objects under transformations (refl ection, rotation, translation, or enlargement)