I just got a book by Kathy Ceceri called Make: Paper Inventions. Yes I realize that this does not seem to fall under math but it turns out there is a wonderful chapter in the book called Paper Math. After reading through the material, I realized this is the perfect thing for those days where you have something going on that is going to mess up part of the day.
The chapter starts off with paper fractals. It goes a wonderful job of defining a fractal and then promptly has students creating a dragon curve fractal which when done resembles a fire breathing dragon. The author even explains where this idea came from.
Next is the box pleat which is used to create the Action Origami Robot Worm. There are tons of pictures showing each step of the process. The photographs are so good, you actually see where all the folds are so its much easier to follow. There is even a trouble shooting section on it.
Third is a lovely section called the Math of Cut Paper. This one is based on the idea that you can cut any two dimensional shape with straight sides from a sheet of paper using only a single cut. I learned to cut a rhombus from a single sheet of paper when I took Math in a Cultural Context but this one shows how to cut a star using a single cut.
This is followed by a very in depth section on creating a Mobius strip and possible variations to the single cut. They suggest you add an extra twist. It even has a page later in the book you can check to see if you ended up with what you are supposed to.
The finally section is on making a Hexaflexagon is created out of a strip of paper, making a six sided figure. As you play with it, you end up looking at different sides facing up to the point, you can color in areas on the strip so you have multiple colors facing upward at different times. This is so cool, I've got to try it myself this weekend.
The best thing of all is that there are links to websites on each and every one of these topics. I want to check out the website to learn more about fold and one-cut patterns. The side has printable patterns available for downloading to use in class.
Most of these topics are so easy to slip into a Geometry class so students have fun and enjoy making these creations. I have a few days to play with some of these things before I can let my students play with these in my Geometry class on Monday.