I had so much fun exploring this site for more math based materials one can easily integrate into the classroom.
Check out the Math of Design, a series of podcasts by Professor Jay Kapraff on 11 different topics such as the structure behind structures, and from tangrams to Amish Quilts. These podcasts are about half an hour long.
Queen Mary, University of London has the Mathematical Magic with 16 short videos on how mathematics relates to magic including two calculator tricks, dicing with destiny, and a short piece on jokers.
If you only have time for shorts, take a look at Math Snacks by New Mexico State Learning Lab. The animation shorts run anywhere from 2 to 6 minutes and address ratios in a variety of situations. The shorts are in both English and Spanish. I watched one on dating where the girl compared the number of words she spoke to the number her date spoke. It took her three dates to finally find someone who spoke the same number of words for a 1:1 ratio. The shorts are cute.
I found an hour long segment on the Mathematics of Juggling in Physical Sciences and Mathematics by Cornell University. It is one hour long and explores the mathematics involved with juggling. I have a few students who are trying to learn to juggle and they just might.
On the other hand, Open University has Mathematical Models: from Sundials to Number Engines. I watched the video on sundials which explained in detail how it works. The particular sundial used as an example showed both the time of day and time of year. I found how they used certain paths to show the time of year. It was cool. In addition, I checked out the video which discussed recording sales on clay tablets in Babylonia. Apparently, they used a base 60 system. The spokesperson indicated writing was developed for mathematical modeling. This site is more of a history of models but it was quite interesting.
Spice up a day by showing students one of three videos in Rollercoaster Design by Open University. The three videos discuss the designing of a ride called Nemesis in England from a mathematical point of view including showing a graph of the ride if you stretched it out completely. Each video has a transcript in case its needed.
For those days your students need a bit more of a challenge, check out Math Challenges by the University of Warwick which has 6 problems for students to solve. Solutions are provided so the teacher knows what to do. I looked at a problem which showed 5 glasses. The first three were filled and the last two were empty. You can only make one move so the classes are alternating, full, empty, full, empty, full. How do you do it.
These are only a few of the collections and courses offered via iTunes University. There are actual math classes such as geometry, algebra, string theory but there are also interesting ones on gliding, etc. There are even some iBooks available. Go look, check things out to decide which ones you want to spice up your class with.
Let me know what you think.