I run a high school outreach program at UCLA called DMAP: Diversifying Mathematics And Physics (webpage: http://dmap.pbworks.com), which focuses on exposing groups underrepresented in advanced maths and physics to these fields. There are two groups in this program: a non-calculus group, and a calculus and beyond group. The problem that I am running into is that the students in my non-calculus group are from mathematics levels from Algebra through Pre-Calculus, and thus their skill levels vary greatly. The club meets weekly, and right now I don't have a well defined curriculum for my non-calculus group because I can't seem to solve this problem of entertaining students with a wide skill-set variation; currently I have taken a bit of a shortcut with this dilemma and I am teaching my non-calculus group introductory computational mathematics since most of them do not have considerable exposure to this. Does anyone have a suggestion for curriculum that I can use that students from Algebra through Pre-Calculus will find entertaining but not too over their heads? (i.e., specific links to coursework, and/or suggested topics?)
One possibility that I was thinking was to try teaching basic probability, number theory, and proof techniques because these are easy enough for anyone to learn, but are not often taught in high schools formally.
An important note perhaps is that these students come to this club voluntarily, so they are on the upper-end of the motivation level, I don't suspect that their motivation levels will be an issue; I am more concerned with suiting the variation of their skill-levels.