How Many Will There Be? Stairs

Objective

Students will use the patterns they find in the first four steps to predict the 100th step.

Inspired by the website Visual Patterns.

Steps

1. First, students count the squares in each step, search for three patterns, and predict Step 5.
2. Next, they use their patterns to predict Step 10.
3. Finally, students try to predict Step 100.
4. We review the answer and I introduce two extensions: Triangular Numbers and Carl Friedrich Gauss.

Resources

• Worksheet (PDF)
• Worksheet (Google Slides)
• The Stairs (PDF)
• The Stairs (Google Slides)