How did the chicken cross the road? – Model with Mathematics

Q: How did the chicken cross the road?

A: One step at a time. 

In various Twitter conversations with @Foizym, @ddmeyer, @MathMinds,  @gfletch, and @Simon_Gregg, the question of what mathematical modeling could or should look like at the elementary level has been a recurring theme. I want to explore this question a little bit in this post and offer a few ideas that may