We had a discussion about this at the sbparty. The conclusion I came to is that I would cover the following three topics.
- Basic numeracy. The main goal of this portion of the class is to convince people that 1 million dollars is a small amount of money, but 1 billion dollars is a large amount of money. (For example, if you won a million dollars tomorrow you should not drop out of school, but if you won a billion dollars you should do whatever you want to do.) Related topics include Fermi problems, understanding the scales of things, etc. If there's enough time then this unit would finish with explaining how exponential growth is much faster than linear.
- Basic statistics. I actually don't know that much statistics so I'm not totally sure what this should cover, but the goal is for people to be able to understand polling, sampling, and common statistical fallacies. People should leave this unit understanding what the margin of error means in a poll, some rough idea of standard deviations, and why sampling would improve the accuracy of the census.
- Why is math fun? The goal of this section is to show people some cool things that illustrate what mathematics is as practiced by mathematicians. The student's would not be expected to really learn anything here, but instead would hopefully be persuaded that mathematicians do some interesting things. In particular, it would be nice if a person in the class who would enjoy advanced math classes (but doesn't know that yet) could see that math is something they would like. If I were teaching this class I'd probably do Farey Fractions since that's my go to topic, but there are lots of good options (platonic solids, Cantor set theory, RSA, etc.).
The third section would be shorter than the first two and less heavily covered in the exams.