Maybe you have this same problem: the AP exam is in May, but your school goes right along into June? Mine does this for about a month before the final exams start. So from May 17th-ish through June 20th-ish I have a group of juniors who must adopt the identities of the greatest leaders from all time and who then enter into a competition to see who the greatest world leader of all time is.
I usually have a small number of seniors and they become my accomplices in setting this up before they depart early. They create a list of leaders we've covered during the class. Their parameters are that they must be leaders who impacted more than just their immediate region, and American and European leaders are limited to 4-5. Once they compile the list, it gets cut up and juniors draw names at random out of a hat. Once the leaders are established for each class, the seniors then have to rank the leaders from 1-20 (-ish. This depends on the size of the class.) I then make up a single elimination bracket for each class on big paper, place the leaders into their numbered slots and the competition is on! Each class generates a champion, and they meet in a final round after school on the last day of classes.
All students must create a biography of their leader, and a VoiceThread (www.voicethread.com) in the first person explaining why he or she is the all time greatest leader of world history--they treat it like a campaign ad for themselves. The great thing about VoiceThread is that students can post responses through writing, drawing or recording. The website is very intuitive to use, and the iPad app retains nearly all the functionality of the website.
Students move through different debate styles with different scoring rubrics. Defeated leaders must become the minions (or lackeys...terms vary with my mood) of the leader who won, thus building up a stable of assistants to do opposition research and assist in the debates.
I share results via Twitter with the #maymadness and update the brackets in my classroom and on the class blog.
The handout describing the project is linked up here.
The description of the rounds is linked up here.
I'll share the scorecards and brackets in a bit. They have some flaws that I'll be working on next spring, so I'll come back to link them up once they are done.