Lesson 1: Patterns as Mathematics

Year 9 60 mins Geometry

Learning Intention

I can identify and describe geometric transformations (translation, rotation, reflection) in patterns.

Success Criteria

  • I can look at a pattern and say "what repeats" and "what changes".
  • I can use the words translation (slide), rotation (turn), and reflection (flip) correctly.
  • I can label these transformations on a simple pattern.

Lesson Sequence

1. Hook: Notice & Wonder (10 mins)

Display: Show a large image of a Tukutuku panel or a complex tiling pattern.

Think-Pair-Share:

  • What shapes do you see?
  • How do the shapes move across the board?
  • Is it the same shape repeating, or does it change?

2. Explicit Teaching: The Language of Movement (15 mins)

Introduce the three key rigid transformations using physical movement:

  • Translation (Slide): Move a book across a desk without turning it. "It just slides."
  • Rotation (Turn): Pin a piece of paper in the middle and spin it. "It turns around a centre point."
  • Reflection (Flip): Hold your hands up like a mirror. "It flips over a line."

Cultural Connection: Look at a Kōwhaiwhai rafter pattern. Is it sliding (translation) or flipping (reflection)?

3. Investigation: Pattern Detective (25 mins)

Task: Students are given a worksheet with 4 different patterns (2 Māori, 2 generic geometric).

  1. Circle the "base shape" (motif) that repeats.
  2. Draw arrows to show where it moves.
  3. Label the movement: Translation, Rotation, or Reflection.

Extension: Find a pattern in the room (e.g. carpet, exercises book grid) and describe it.

4. Wrap Up (10 mins)

Exit Ticket: Draw a shape (like a triangle). Draw it again after a Translation.