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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.

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    $\begingroup$ What is their exposure to geometry? Although you may not want to teach them fallacious proofs in geometry (although a visit might be sufficiently cautionary), you could try Archimedes-type approximation and Cavalieri's principle to give them some geometrical background, and show how certain mensuration formulae serve as reminders of differential and integral formulae. Gerhard "Some Prefer Curves To Squiggles" Paseman, 2015.08.05 $\endgroup$ – Gerhard Paseman Aug 5 '15 at 17:34
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It sounds like all or part of a standard class in Finite Mathematics may help.

Finite Mathematics is a grab-bag class, including multiple topics that do not require trigonometry or calculus. Some of the topics are occasionally taught in an Algebra 2 class but are usually left out of that class. Here is a list of the chapters in the Finite Math textbook that I have sometimes used in my current high school:

  • Linear functions
  • Systems of linear equations and matrices
  • Linear programming: The graphical method
  • Linear programming: The simplex method
  • Mathematics of finance
  • Logic
  • Sets and probability
  • Counting principles: Further probability topics
  • Statistics
  • Markov chains
  • Game theory

When I teach this class, I get a list of interests of each of my students, discuss the topics, and get votes on each chapter. That way I tailor the class to the interests of my students, and they know the teaching is geared to help them. I add some more to subjects my students really want: for example, I added reading the book How to Lie with Statistics to the statistics chapter. The feedback I have gotten from former students tells me that this class is greatly appreciated by my students, much more so than my calculus class.

This textbook is geared to students who have taken Algebra 2, but you could skip the topics and homework questions that are too advanced for much of your class. One advantage of this class over some other options: there are many textbooks available and curricula will be easy to find.

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  • $\begingroup$ I had considered most of these to some extent, but Markov Chains/Game Theory are really great additions! Wow great idea! I wish that I could 1 up your question right now at least. Haha. $\endgroup$ – Loonuh Aug 5 '15 at 17:56

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