Magically Miraculous Math: Day 3

Today in class, we learned about fractals. To help students understand the concept better, we made our own Menger sponge (see photos below). I had each student make a single cube. Then we combined 20 of them to create the 1st iteration. To make the 2nd iteration, we would need 400 of the cubes, so we were not able to go further. Students learned that the surface area of the sponge approaches $latex \infty$ and the volume approaches zero. This led to a discussion of the concept of limit (often first introduced in a precalculus or calculus course).