A tessellation is a pattern made from shapes that repeat to cover a flat surface with no gaps and no overlaps. Making a tessellation poster is a fun school project because it combines math, art, and careful observation. Students can use color, symmetry, and repeating designs to create a poster that looks complex but follows simple rules.
Tessellations also appear in tile floors, quilts, honeycombs, and many works of art.
Key Facts
- A tessellation covers a plane with no gaps and no overlaps.
- Regular tessellations can be made with equilateral triangles, squares, or regular hexagons.
- For shapes to fit around a point, the angles meeting there must add to 360 degrees.
- Square tessellation: 90 degrees + 90 degrees + 90 degrees + 90 degrees = 360 degrees.
- Hexagon tessellation: 120 degrees + 120 degrees + 120 degrees = 360 degrees.
- A translation moves a shape without turning or flipping it, keeping the same size and direction.
Vocabulary
- Tessellation
- A tessellation is a repeating pattern of shapes that covers a flat surface with no gaps or overlaps.
- Tile
- A tile is one shape used again and again to build a tessellation.
- Pattern
- A pattern is a design that repeats in a predictable way.
- Translation
- A translation is a slide that moves a shape to a new position without rotating or flipping it.
- Symmetry
- Symmetry means parts of a design match after a movement such as a flip, turn, or slide.
Common Mistakes to Avoid
- Leaving small gaps between tiles: this is wrong because a tessellation must completely cover the surface without empty spaces.
- Letting shapes overlap: this is wrong because overlapping hides part of a tile and breaks the rule that each shape fits edge to edge.
- Changing the size of the tile as you trace it: this is wrong because the repeated shape should stay identical for the pattern to fit correctly.
- Coloring before checking the layout: this can make mistakes harder to fix, so lightly trace and test the full pattern first.
Practice Questions
- 1 A poster has 6 rows of tessellation tiles with 8 tiles in each row. How many tiles are on the poster?
- 2 Four square tiles meet at one point. Each square angle is 90 degrees. What is the total angle around that point, and does it tessellate?
- 3 A student designs a shape that leaves small white spaces between copies when repeated. Explain why it is not a tessellation and describe one way to improve the design.