Handout: Kōwhaiwhai Patterns

Finding the algebra in Māori art.

Pattern 1: The Koru Swirl

This pattern starts with one swirl and adds another one each time.

Stage 1: (

Stage 2: ( (

Stage 3: ( ( (

1. Draw Stage 4.

2. Complete the table:

Stage (n)123410
Swirls123??

3. What is the algebraic rule for this pattern? Rule: n

Pattern 2: The Pitau Branch

This pattern grows by adding two branches each time.

Stage 1: /\

Stage 2: /\_/\

Stage 3: /\_/\_/\

1. Draw Stage 4.

2. Complete the table:

Stage (n)123410
Branches246??

3. What is the algebraic rule for this pattern? Rule: _________

Challenge: The Rafter Pattern

This pattern starts with 3 lines and adds 2 more each time.

Stage 1: |||

Stage 2: |||||

Stage 3: |||||||

Can you find the algebraic rule for the number of lines in stage 'n'?

Rule: _________