How Many Will There Be? Courtyard

Objective

Students will use the patterns they find in the first few steps to predict a step much further along.

Inspired by the website Visual Patterns.

Steps

1. Students begin by looking for patterns and predicting the number of squares at step 5.
2. I reveal the solution (it's 24) and students work on predicting step 12.
3. After revealing the solution (it's 52), I reveal an algorithm to predict any step and challenge students to calculate much larger steps. Answers – Step 63: 64 × 4 = 256 – Step 97: 98 × 4 = 392 – Step 821: 822 × 4 = 3288

Resources

• Worksheet (PDF)
• Worksheet (Google Slides)