Lesson 2: Symmetry Investigations

Year 9 60 mins Geometry

Learning Intention

I can identify lines of symmetry and rotational symmetry in 2D shapes and patterns.

Success Criteria

  • I can draw lines of symmetry where a shape matches exactly if folded.
  • I can determine the order of rotational symmetry (how many times a shape fits onto itself in 360°).
  • I can create a simple motif with exactly 2 lines of symmetry.

Lesson Sequence

1. Warm Up: Mirror Mirror (10 mins)

Use handheld mirrors. Place them on letters of the alphabet (A, B, C...). Which letters have a line of symmetry? Which have two?

2. Concept Builder: Line vs Rotation (20 mins)

Line Symmetry (Reflectional): "The folding line."

Rotational Symmetry: "The spinning match."

Activity: Show a square. How many fold lines? (4). If I spin it, how many times does it look like a square? (4). Order of rotation = 4.

Contrast: Show a rectangle. Lines = 2. Order = 2.

Contrast: Show a Kōwhaiwhai spiral (koru). Does it fold? (Usually no). Does it spin? (Often order 2).

3. Creator Task: The Symmetry Designer (20 mins)

Brief: On grid paper, design a "tile" that meets these specific rules:

  • Must have at least 1 line of symmetry (vertical or horizontal).
  • Must use only straight lines (for easy drawing).
  • Must NOT be just a square or cross (be creative!).

Challenge: A neighbour tries to find the order of rotational symmetry for your design.

4. Reflection (10 mins)

Why do cultural patterns (like in churches, marae, mosques) use so much symmetry? (Balance, beauty, order, storytelling).