I get tired of trying to think of activities for my math classroom. To quote a lot of friends, "Borrow what is already done and tweak it." So I do that and I found a site with great activities for a variety of classes and topics.
There are 15 different activities with instructions and worksheets. Some I will use, some I won't because of my student population but they all look fun.
For instance, there is one on Stylometry where you analyze the word length, the sentence length, and word repetition. This information is often used to settle disputes over ownership of material. This exercise has students graph distribution of words, sentence length, etc for an author. It is suggested students do this for an author who writes under their own name and a pseudonym to see if the writing styles change or remain constant. This is a cool application of math and it connects literature to math.
Another uses Voronoi Diagrams which are often used to create boundaries such as you have a town with 5 schools and you need to establish boundaries so all students will go to the school closest to their residence. This activity makes full use of perpendicular bisectors so it would be a good activity to use in Geometry.
I love the tangent experiment which looks at finding the slope of the line of a ramp, or stairs. It has students moving around to the steps or a ramp, measuring, and calculating the slope. My school has a ramp but it goes down and part way down changes direction. I have steps in the front and back of school but I'd have to get permission to go to the steps that head up to the server room so they can measure those.
All activities come with the worksheets, instructions, information on the activity itself and where it come from along with some suggestions of what to use. Just looking at the activities shows me three I can use in Geometry, a couple in other math classes for statistics and probability. There is also information on using Excel to crunch some of the math. Go check it out and enjoy.