2. The “Rational Tangle Dance” is a simple, yet deep, activity in knot theory that is a favorite amongst math circles and can be adapted down to high, middle, or even elementary school. In the activity, four people hold two ropes that connect them as pairs. The group moves in a series of twists and rotations, eventually creating a complex knot between them. It is the objective of the group to better understand the dynamics of the system, and eventually undo any knot that they have created. It was first introduced by John Conway, but explored by many mathematicians. Here is a link to a video: http://www.mathcircles.org/node/798, instructions: http://www.geometer.org/mathcircles/tangle.pdf, and a paper: http://www.mathteacherscircle.org/assets/session-materials/JTantonRationalTangles.pdf
3. Chris introduced us to The Art of Problem Solving by Richard Rusczyk. The text is designed to prepare students for mathematical competitions, but is highly applicable to the general high school setting. Its goal is to teaching concepts and problem solving methods not traditionally taught in school. One of the main concepts is to take an old problem and list all of its attributes. Then, change or remove an attribute to see what effect it has on the solution. Rusczyk also publishes a set of middle and high school textbooks modeled after his philosophy. http://www.artofproblemsolving.com/
4. Inside Mathematics is a website that houses a number of model lessons, videos of teachers, performance assessment tasks, and classroom resources that grew out of the Noyce Foundation’s Silicon Valley Mathematics Initiative. Cathy Humphries (from “convince yourself, convince a friend, convince a skeptic” fame) is one of their teacher mentors. Take a look: http://www.insidemathematics.org/
6. (Extra Credit) A dilation by a complex number is equivalent to a rotation. Huh…
7. (Extra Credit) Olympic Park, near Salt Lake City, is an active training facility for ski jump and freestyle aerial as well as an outdoor adventure park. When there is no snow, the ski jumpers land on wet turf and the freestyle aerial skiers land in a pool with jets pushing them back up. Besides watching the athletes practice, we completed couple of ropes courses, raced down the alpine slide twice, and were first in line for the extreme zip line. The perfect day finished with a trip to a High West Saloon in Park City.