International Baccalaureate (IB) programs are turning up in a diverse mix of school districts, an attempt to add rigor and depth. For rich and for poor, for big schools and small ones, IB has become a way to add rigor and depth to public school curricula. But each school district has adapted IB for its own needs. Some use it in all schools for all students from kindergarten through 12th grade. Some limit it to just those high school students ambitious enough to strive for the demanding IB diploma, which requires good grades on six major tests, a 4,000-word research paper, a critical thinking course, and community service. However they use it, educators give much the same reason for adding IB to their schools. They say the program will give their students a head start in an era of intense international competition.