Camp Euclid is an online math research program for middle and high school students age 13 - 19. It runs for six weeks. It provides a virtual research environment for participants. Mentors are undergraduate and graduate math students who are active researchers. Students will be assigned into groups; each group has mentors assigned to it. There are 4 hours per week of seminar meetings and 6+ hours per week of informal collaboration. The tuition is $1250 in 2014.
You can find out more about the program here: http://euclidlab.org/programs/camp-euclid