Hi Guys- So just want peoples opinion. We change classes every trimester, during which I need to come up with my own class ideas - own syllabus, calendar, ect. Wondering if anyone has any good ideas for math classes that could be taught to lower level students? I've already done a graphing class, a geometry class, a consumer math class, and also going to be teaching a trig class. I can't rely on any background, because it could be completely different students each trimester. Any ideas for fun classes that are interesting?

Probably not "fun" but you could cover quadratics: Factoring (GCF, Difference of squares, Trinomials, Trinomials with a leading coefficient, factoring by grouping-- you could even throw in the sum and difference of cubes.) Then you could teach quadratic formula. You could devote one whole class to graphing polynomial functions: synthetic substitution, Descrartes's Rule, behavior at thee extremes, and so on. How about probability? And or statistics? You could do a whole course on circles: - Area and circumference - Arcs and angles: central, inscribed, two chords, tangents, secants... - Length of Arc - Area of a sector - Area of a segment. Or a whole course on Area: - triangle (1/2 bh, 1/2 absinC, s^2/4 * sqr3, Herons' formula) - paralleleogram (absinC) - rhombus (1/2 d1*d2) - square (1/2 d squared) - trapezoid (1/2h(b1+b2), height*median) - regular polygon (1/2 apothem * perimeter) - sector and segment of a circle (I'm sure I've forgotten some, but it's a Friday afternoon; you get my drift.)

I would do something with basic number theory. For instance, the distribution of the primes/primality testing, diophantine equations, modular arithmetic, basic cryptography etc. That would be a blast for me.

Okay, I love the idea on stats and probability. Students love this and you could even do a sports theme and bring in the newspaper. Maybe have a fantasy league based on stats. We had a week long class on writing music using different mathematical functions and different bases (I think we liked base 13 the best). This was incredibly fun and we learned to work with a base system other than 10 and we worked on writing and solving functions.

Scroll down to unit 8 here and see if there's anything you can use: http://regentsprep.org/Regents/math/algtrig/math-algtrig.htm#m9