How Many Will There Be? Triangles Within Triangles
Students will make mathematical predictions about an infinitely repeating sequence of triangles.
Inspired by the website Visual Patterns.
- First, students simply count up triangles in the first three steps (1, 3, and 9). Then they predict what the 4th step will be like.
- We reveal that step 4 has 27 triangles. I ask students to predict step 6.
- After revealing that step 6 has 243 triangles, we will try to predict all the way up to step 20!
- I discuss the pattern of repeating 3s and show how exponents are the key to quickly finding any step. And students confirm that, yes, step 20 has over a billion triangles!