This summer I will be teaching a math course at the Summer Camp for Academically Talented Middle School Students (http://www.wku.edu/gifted/scats.php). I plan to discuss the concept of infinity (using debates between the students to help understand the idea properly), magic squares, Bridges of Königsberg, Möbius strips, graphs, prime numbers, etc.
I taught the same course two years ago and found that infinity was a highly misunderstood concept for the students. I would pose questions to the class and have the students separate into groups depending upon their understanding of the concept.
If you were teaching a course like this, what topics might you include?