A tessellation is a repeating pattern of shapes that covers a space completely with no gaps between the shapes. We can think of making a tessellation like tiling a floor using geometry, a type of math that’s all about shapes.
sheet of paper
small, square piece of paper or a post-it note
The small, square paper will become your tile. You can change this paper’s shape by cutting a pattern out of one side of the square using the scissors and taping that pattern piece onto another side of the square. You can do this to two sides, so that all four sides have a pattern either cut into it or taped to it.
Above: a 3-panel image of a square piece of paper being turned into a tile. The left panel shows the paper with the patterns drawn on it. The top right panel shows the patterns cut out of the square, and the bottom right panel shows the patterns taped to the uncut sides.
Once your tile is done, place it anywhere on the 8x11 paper and carefully trace its outline onto the paper.
Above: an image of a sheet of white paper with the tile design traced onto it, with the tile itself sitting to the right.
You can then place your tile next to your drawn shape so that the edges line up perfectly and trace another tile. Think of it like you're putting together a puzzle as you put your tile tracings together. Keep going until your whole paper is filled with tiles!
To make your tessellation complete, color in the tiles with whatever colors you like, and check out the pattern you’ve made with your tiles!
Above: a paper filled with traced tiles, forming a tessellation
To extend your learning, think about these questions and activities:
What tessellations do you see in your daily life? How many can you find in your home?
What other tile shapes can you make?
Try making a tessellation with two different tiles, but still creating a repeating pattern and fills up the whole page. How is this different from using just one tile?
You can download a printer-friendly version of this activity below. Note: there are no images in the printer-friendly version, all guide images are posted above.