I once taught a similar course. I had some success discussing mathematics and voting. Larry Bowen of Alabama has a webpage with some basic ideas and exercises:

http://www.ctl.ua.edu/math103/voting/mathemat.htm

Voting was also the topic for Mathematics Awareness Month April, 2008.

http://mathaware.org/mam/08/

We covered mathematics in music. The magical mathematics of music, by Jeffrey Rosenthal may be a good introduction for the students.

http://plus.maths.org/content/magical-mathematics-music

On this topic, I also recommend the work of Rachel Wells Hall (St. Joseph's). Here is a link to her homepage.

http://www.sju.edu/~rhall/research.htm

We discussed some probability. The students found the Monty Hall problem intriguing.

I hope this helps.