Even in high school, if you get your kids hooked on the challenge of mathematics as mental play, they will never be satisfied with mere textbook math. There is always something fascinating just around the corner.
Alcumus: Art of Problem Solving’s innovative online learning system adjusts to student performance to deliver appropriate problems and lessons.
Better Explained: Intuitive, often visual, explanations of high school math topics.
Don Cohen’s Map of Calculus for Young People: Hands-on activities featuring advanced ideas, for students of any age.
Discovering Trigonometry: A basic introduction to trigonometry, starting with sticks and shadows.
Gallery of Data Visualization: A collection of the world’s best and worst statistical graphs.
GeoGebra: Download software for playing with geometry and algebra, and the website offers a wealth of user-created instructional materials.
How to Read Mathematics: “A math article usually tells only a small piece of a much larger and longer story.” Learn to read between the lines.
How to Think like a School Math Genius: James Tanton’s series of videos about five key principles for mathematical thinking for students approaching high school math.
Interactivate: Lots of projects to try, from middle school math to calculus.
Interactivate Mathematics: (A different site from the above.) From algebra and money math to higher calculus, this website (by the author of SquareCircleZ blog) has interactive Flash-based activities that help the user to understand what is going on.
Invent Your Own Computer Games with Python: Each chapter gives your student the complete source code for a new game and then teaches programming concepts from the example.
Karl’s Calculus: Karl Hahn has a creative way of explaining the ideas of calculus. Includes sample problems.
La Habra High School’s Math History Timeline: Math discoveries, publications, and other tidbits from paleolithic number bones to the present.
MacTutor History of Mathematics Archive: My favorite place to begin any foray into math history.
Mathematical Problems of David Hilbert: With a link to Hilbert’s 1900 address to the International Congress of Mathematicians in Paris, surely the most influential speech ever given about mathematics. Wolfram MathWorld has an annotated list of all twenty-three problems.
Muslim Rule and Compass: The Magic of Islamic Geometric Design: An article by Alex Bellos, with instructions for constructing a beautiful geometric pattern.
A New Algebra: Henri Picciotto offers a selection of interesting activities for algebra students.
Project Euler: A list of programming challenges for advanced students.
Proofs Without Words: I love these.
Purplemath: A good source of supplemental explanations in prealgebra and algebra. When your textbook just doesn’t make sense, look here for help.
Statistics Every Writer Should Know: Robert Niles’s introductory statistics tutorial for math-phobic journalists.
Statistics and Probability Tutorial: From Stat Trek.
Tips for All Your Math Courses: Articles by Stan Brown about how to succeed as a math student, how to use a graphing calculator, what it means to “show your work,” and other topics from algebra, trig, calculus, and statistics.
Trig Without Tears: “Or, How to Remember Trigonometric Identities.” How to learn and understand trig without memorizing a gazillion identities. Check out the author’s other mathematics articles, too.
What’s Special About This Number?: Distinctive facts about several numbers, 0-9999 the last time I looked.
Virtual Math Lab: Algebra tutorials from West Texas A&M University. Includes practice tests.