# Tessellation

## Background vocabulary

A tessellation is a plane (flat surface) of tiles with one or more geometric shapes (tiles) that fit together with no overlaps and no gaps or spaces between the tiles.

## Example of how to create a tessellation

• Start with a square:
• Cut part of the left side of the square and slide it directly to the right side of the square.
• Cut part of the bottom side of the square and slide it directly to the top side of the square.

## Tesselation extensions

• What other shapes can you tessellate?
• What different shapes can you combine to make a tessellation?
• What are the properties of shapes that tesselate and do not tesselate?
• Someone said. What is changes in one place must be made up for elsewhere. What do they mean?
• Does this assume the starting shape must be able to be tesselated?
• How do the areas of the shapes before the change and after the change compare?
• They suggested to start with a shape, which can be tesselated, (square, equlateral triangle, equalateral hexagon, ...) cut away a part and move it along the perimeter to the remaining part of the shape. Repeat as desired and the new shape should be the same area and tesselate.
• Draw a pattern on a square gird. Use the grid to cut and reshape the pattern as suggested above.