Activity: Tukutuku Tile Challenge

Materials

• Coloured tiles or squares of paper (e.g., red and yellow)
• Graph paper

Challenge 1: The Poutama Pattern

The Poutama (stairway) pattern often shows steps. Let's build one.

1. Rule: Your pattern is based on the rule 2n + 1.
2. Build Stage 1: Let n=1. The number of tiles is 2(1) + 1 = 3. Build it.
3. Build Stage 2: Let n=2. The number of tiles is 2(2) + 1 = 5. Build it next to Stage 1.
4. Build Stage 3: Let n=3. The number of tiles is 2(3) + 1 = 7. Build it.
5. Record: Draw your first three stages on graph paper.
6. Predict: How many tiles will be in Stage 5? And Stage 10?

Challenge 2: Create Your Own

Now it's your turn to be the designer.

1. Create your own algebraic rule for a growing pattern (e.g., 3n, n + 5, 3n - 2).
2. Write down your rule.
3. Build the first three stages of your pattern using the tiles.
4. Swap your pattern with another group. Can you figure out their rule?