Analogies: Making Math Meaningful

Math is an esoteric subject for most people. Good instruction makes information meaningful. One method for making information meaningful is to connect new information to prior experience. 

In this situation the new information involves determining whether shapes are similar (see photo below). One example of student prior experience with this topic would be shrinking people down. In the photo above I use Mini Me and Dr. Evil and their respective (and fabricated) weights and shoe sizes as measures that will eventually give way to measures of sides of a polygon (below). When working on the problem below the students can be prompted by recalling the analogy of Mini Me and Dr. Evil.