Most of our high school students participating in Math Circles do so on Saturday afternoons, and as I recently mentioned, UIC’s Alexander Furman runs the UIC Math Olympiad Project on Friday evenings. The natural question is–how do I fill my time in between? 
Good news! Registration is open for Fermi Lab’s Saturday Morning Physics program until October 14th! Sessions start on 9/30 and then sessions continue most Saturdays until December 9th. They suggest that you have some high school Physics and exposure to Algebra 2 to participate.
I admit that getting back to UChicago or Payton for math circles on Saturday afternoons may be a challenge, but this is such a great opportunity that I had to mention it. Plus, Fermi Lab seeks 15-25 interns each summer for their TARGET program, a paid internship (and they do help Chicago kids with transportation during the summer, picking up and dropping off at the end of the blue line).