When I introduce electronic response systems (clickers) to teachers I often use my favourite problem: The Monty Hall Problem. This is a famous problem on probability that is easy to explain, yet its solution appears to be counter-intuitive (at a first glance). If you have never heard of this problem, watch the beginning of the video below and try to answer it yourself. Many of us find this problem either very easy or very difficult. I know it from experience, as I was able to track responses of students and teachers using clickers. I also remember that it was a hard problem for me, before I understood it conceptually. However, if you have clickers in your classroom, you can turn this problem into a very exciting experience for your students. Let them vote on the problem (anonymously) and then ask them to turn around and to discuss their answer with a neighbour, then ask them to vote again. It is your choice as a teacher to show the first histogram to the class or not, but you will be amazed to see the engagement of the students… You can also use online simulations of the problem or do `real life`trials in the classroom. This is an example of a `simple` problem that lends itself perfectly to be used with clickers.
For more information on active classroom check Stephanie Chasteen`s blog: http://theactiveclass.com/2012/01/30/using-clickers-with-experiments-and-demos/