I've been saving these up, I guess ...
I keep hearing about thought experiments in physics lately. Here's a good post on that idea.
This post is mostly about John Conway, the game of life, and how that relates to segregation (watch the video).
Here's a post on the n-queens problem. (For n=8, put 8 queens on an 8x8 chessboard so none are attacking any others.) On Sunday evening I played around, trying to find a solution, and couldn't. On Monday morning I showed the problem to Artemis (the boy I tutor), who said, "That has 92 solutions, unless you don't count rotations and reflections. Then it has 12 solutions." I wanted to get past his memory and work with thinking about it. He put 4 queens on a graphpaper board, and said "now go from there". I told him I'd done that much and gotten stuck. He and I crossed out places queens couldn't go, and I suddenly saw a solution. I told him he was a good teacher. [He also showed my his attempt to multiply out (A+B)^5. He isn't yet grounded in why you do the steps you do; he did all the right steps plus a bunch more. We'll get there... :^) It sure doesn't feel like work, tutoring him.]
This one is not really math. NASA is planning to crash something into the moon tomorrow, and it should be visible with garden-variety telescopes. Lesson plans available, and I might do something with the kids I teach, if I can pull it together in time.
Tanya Khovanova doesn't like IQ tests, and has made a funny question up that she's pretty sure won't appear on anyone's IQ test.
This woman knows how to take learning into her own hands! She had a concussion, and decided to create a multi-player role-playing game called SuperBetter to help herself recover. Wow! (Thanks, Dan, for pointing me there.)
Sweeney Math has a nice systems of equations project for an algebra II class, or a stat class. "Students find data online that they are interested in comparing. (Sales of video games v sales of movies, Wins of their favorite sports team v wins of their friend's favorite sports team, Women's race times v Men's race times, Success of movie with many sequels v another, Sales of Abercrombie v sales of American Eagle, etc) They graph and find best fit lines for each set of data, then answer some thought provoking questions about the results." One of the questions is the point of intersection and what it means. I like it.
At God Plays Dice, there's an interesting (to me) book review post titled Counterexamples in X, where X is a field in mathematics.
I don't have an interactive whiteboard available where I teach, but I do have a 'smart classroom' (computer hookup and internet projection). Most of the examples in this Interactive White Boards interview can be used in my classroom, I think.
I can't remember now why I did this, but I'm still intrigued... I went to Wolfram Alpha and typed: factor 1782^12+1841^12. It's just a bunch of big numbers. Why do I like it?
Oops! There was one more. I remember from when I was young, a letter to Ann Landers, claiming that you get wetter in the rain when you run than when you walk. Here's a good physics analysis debunking that.