I made this page when I was a High school teacher. I never liked calling on students because I would always choose the good students who knew the answer to any question I ever asked them. I was always self-conscious of appearing to "pick on" the lazy kids, so I decided the only fair thing to do would be to create utter chaos (thank you Harvey Dent).
My first idea (the prototype of this page) was to assign each student a number, then draw cards out of a deck, but that got boring real fast (actually it was quite entertaining, but it would waste a good deal of time and create a mess on my desk) and a new solution had to be found.
My favorite thing about this page (an idea I randomly came up with halfway through the project) is the "Chances of Getting Picked" feature. What it does is pretty obvious: it shows the students that haven't been called on yet what their odds are of being the next one chosen. I always took pleasure in seeing the fear in students' eyes as the percentage got bigger and bigger, the questions got harder and harder, and they had NO idea what was going on. What makes this section my favorite is its unique combination of "statistics" meets "sadistic" [insert evil laugh].
Another reason why I made this page was to share it with other teachers at the school, so I made it very easy to customize: all you have to do is replace "Student 1", "Student 2", etc. with your class roster (the size of the class does not matter). I had 5 copies on my classroom desktop: one for each of my classes. I was planning on some additional features, but I stopped being a teacher and this project got put on hold indefinitely.
I know what you're thinking: "Why go through all this trouble? Why not just call on students in alphabetical order? Or go through the class chair by chair?" Well I thought of that, but ultimately decided I don't want students to know when they're being called on (why make it easier for them?)