Combinations of Transformations and Tessellations
One transformation moves a shape. Two or more transformations applied in order create intricate patterns. Tessellations—patterns that tile a plane—use these combinations to fill space perfectly.
Sequential transformations
Apply one transformation, then apply another to the result. Example: Translate triangle ABC right 3 units, then rotate the new triangle 90° counterclockwise around the origin. The final position is different from either transformation alone.
Order matters (usually)
Translating then rotating usually gives a different result than rotating then translating. Students discover this through exploration and learn to describe transformations precisely.
Tessellations
A tessellation tiles the plane with no gaps or overlaps. Regular tessellations use one type of shape (e.g., squares, equilateral triangles, regular hexagons). Semi-regular tessellations use multiple shapes. Transformations create the pattern.