The problem in Algebra 2: too many topics, too many formulas that mean too little to most students.
I propose a partial solution: teach fewer topics, in more depth, to inject meaning into the course; provide access to all students through carefully selected tools, and still try to challenge the strongest students.
Blog post: In Defense of Algebra 2
Available on this site:
Parabolas and Quadratics — Links to many lessons and activities: hands-on introduction using manipulatives (factoring and completing the square), interesting work involving symbol manipulation, three paths to the quadratic formula, and more!
Sequences and Series: links to much material on this topic, plus a ten-minute slide show on the place of formulas when teaching for understanding.
Exponential Functions: using dice, analysis of graphs, and more.
Introduction to logarithms: Super-Scientific Notation
Animation to explain the sine curve.
Introduction to linear programming: Letters and Postcards. This is a concrete approach, and ends with a discussion-provoking applet.
Iterating Linear Functions from The Mathematics Teacher (with Jonathan Choate), and Algebra: Themes, Tools, Concepts (with Anita Wah). This works well prior to work on sequences and series. Also there: links to GeoGebra applets, and a bit on iterating non-linear functions and chaos.
Geometry of the Ellipse (worksheet)
Perspective (lab on inverse variation, similar triangles review.)
Complex numbers (worksheets and games)
Naoko Akiyama and Scott Nelson had designed a one-hour presentation based on the Math 3 curriculum which we've all taught, and which was largely developed by me at the Urban School of San Francisco. I later joined them to expand the presentation into a 3-hour minicourse, which we presented at the California Math Council, Southern Section (Palm Springs, November 2001) and National Council of Teachers of Mathematics (San Antonio, April 2003.) I updated it in 2011 to present at an NCTM summer institute.
Download the slides or view a short version on line. Corresponding handout (3.6 MB).