Activity Planning: Logic and showing conditions hold.

A big part of Calculus is showing certain conditions hold. The big example is continuity. There is a very natural interpretation of the idea (If you can draw the graph of a function without picking up your pencil, it is continuous.) but then there is the very technical. (Left and right limits agree, function value must exist, and the limits must agree with the function value.) Just the idea of showing conditions hold is sometimes difficult for students, primary because they have never been asked to do this before.

For the first week of my Calculus I course I am doing a lot of review. I know, I know, some of you might yell "But they're in college, you shouldn't have to review." Let's get into that in another post, for now, let's talk what I want them to know before we talk about continuity. I want them to be able to show conditions are satisfied for a definition or theorem. How do we do that? Below are a few ideas, but I would love to hear your thoughts. Share them below!

• Using plane figures and classification of parallelograms to show whether certain conditions hold or not. 
• Giving a variety of pictures where some are classified as a 'thing' and others are not classified as a 'thing' and asking them to create definitions. 
• Something to do with the law and fulfilling certain contractual obligations.