Grade 4 · Unit 8: Location and transformation

Translations and tessellations

Slide, flip and fit shapes together.

Hexagon tiles fit together with no gaps.

Tiled floors

Look at tiled floors: the same shape repeats again and again. Each tile is slid, flipped or turned into place. A pattern with no gaps or overlaps is a tessellation.

Translation

In a translation, every point moves the same way. The corner (1, 1) moves to (5, 3); (3, 1) moves to (7, 3). These are corresponding points: 4 right, 2 up.

Reflection

A reflection flips a shape over a mirror line. Each vertex is the same distance from the line on the other side. When the shape is slanted, reflect each vertex carefully, one by one.

Which shapes tessellate?

Regular triangles, squares and hexagons tessellate on their own. Regular pentagons leave gaps. Octagons need small squares in between – look at many bathroom floors!

What I learnt