A tessellation is a pattern of shapes that covers a surface with no gaps and no overlaps. In this school art project, students start with a square cardstock tile and transform it into a new repeating shape. The project connects geometry with creativity because the final design can look like animals, monsters, leaves, or abstract Escher-style art.
It matters because students can see how math rules help create beautiful patterns.
Key Facts
- A tessellation covers a plane with no gaps and no overlaps.
- A square tessellates because 90° + 90° + 90° + 90° = 360° around each vertex.
- An equilateral triangle tessellates because 60° x 6 = 360° around each vertex.
- A regular hexagon tessellates because 120° x 3 = 360° around each vertex.
- In a slide tessellation, a cut piece moves by translation: same size, same direction, no turning.
- Area stays the same when a piece is cut from one side of a tile and taped to the opposite side.
Vocabulary
- Tessellation
- A tessellation is a repeating pattern of shapes that covers a flat surface without gaps or overlaps.
- Tile
- A tile is one shape that repeats again and again to make a tessellation.
- Translation
- A translation is a slide that moves a shape without turning it, flipping it, or changing its size.
- Vertex
- A vertex is a corner point where sides or edges meet.
- Symmetry
- Symmetry is a balanced pattern where parts match by sliding, flipping, or rotating.
Common Mistakes to Avoid
- Rotating the cut piece before taping it is wrong because this project uses a slide, so the piece should move directly to the opposite side without turning.
- Leaving gaps between traced tiles is wrong because a tessellation must cover the page completely with no empty spaces.
- Overlapping the traced tiles is wrong because each tile must fit edge to edge like puzzle pieces.
- Changing the size of the template while tracing is wrong because every copy must match the original tile exactly for the pattern to repeat correctly.
Practice Questions
- 1 A student traces a custom tessellation tile in 5 rows with 6 tiles in each row. How many total tile shapes are traced?
- 2 A square tile has side length 8 cm. A piece is cut from the left side and slid to the right side. What is the area of the transformed tile?
- 3 Explain why sliding a cut piece from one side of a square to the opposite side can still make a tessellation, but randomly taping it to a different side may create gaps.