Lesson 5: Tessellations

Year 9 60 mins Geometry

Learning Intention

I can create tessellating patterns and explain why some shapes tessellate and others do not.

Success Criteria

  • I can define a tessellation (a pattern of shapes that fit together with no gaps or overlaps).
  • I can show that angles around a vertex point must add up to 360°.
  • I can create a semi-regular tessellation using more than one shape.

Lesson Sequence

1. Investigation: The Floor Tiler (15 mins)

Give small groups a set of plastic polygons (triangles, squares, pentagons, hexagons, octagons).

Challenge: Which ones can tile a floor perfectly? Which ones leave gaps?

Findings: Triangles (Yes), Squares (Yes), Pentagons (No - gap), Hexagons (Yes), Octagons (No - unless you use squares too!).

2. The "Why": Angle Sums (15 mins)

Why do hexagons work but pentagons don't?

Looking at a Vertex point: A full circle is 360°.

  • Square (90°): 90 + 90 + 90 + 90 = 360. Fits!
  • Hexagon (120°): 120 + 120 + 120 = 360. Fits!
  • Pentagon (108°): 108 + 108 + 108 = 324. Gap stays!

3. Escher-Style Art (20 mins)

Demonstrate the "Nibble" technique:

  1. Start with a square card.
  2. Cut a shape out of the LEFT side.
  3. Tape it to the RIGHT side.
  4. Now the new weird shape will still tessellate!

Students create their own unique tessellating creature.

4. Cultural Connection (10 mins)

Look at Tāniko weaving patterns. They rely on a triangular grid (often diamonds). Discuss how this grid supports different designs compared to a square grid.