How Many Will There Be? Courtyard

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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.


  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 Γ— 4 = 256 – Step 97: 98 Γ— 4 = 392 – Step 821: 822 Γ— 4 = 3288


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