I ran a session of the Boston Teachers Math Circle on the topic of modeling. The example we looked at was that of choosing the ideal placement of a park, knowing that four towns are sharing the costs of building it.
The objective of the session was to discover the process of modeling, and discuss the Common Core State Standards's Standard of Mathematical Practice: Modeling with mathematics. But along the way, we explored various math topics, and even delved into politics, economics, and other topics!
You may see here the slides I used in my presentation, and my notes (including post-session reflections on how it went).