I visited my son’s first grade class the other day, and brought along a branch I found in our yard debris pile. The kids didn’t take long to realize the big branch was made from smaller branches, which were made from still smaller branches. After establishing that a self-similar shape like that is known as a fractal, we set about making our own using a template I made. (The template has two equilateral triangles with vertices and midpoints marked, just to get everyone started)
For this “Sierpinski gasket” fractal activity, I wanted them to follow these steps:
1. connect the midpoints of a white triangle’s sides
2. color the triangle you created in step 1.
3. Go to step 1. 
At the end we taped their triangles together in progressively larger groups of three. Judging by the results, not everyone grasped the iterative process, but they seemed to have fun with the idea, which is arguably more important.
