The largest Jesuit high school in the country, this 2,113-student North Shore institution seems in many ways like a classic Catholic school: Students are required to take theology classes every semester, and Mass is celebrated daily at 7:10 a.m.

But then there’s the emphasis on innovation: Take the two-year-old entrepreneurial career program, which culminates with students presenting their ideas, Shark Tank–style, to a panel of alumni. The winners of last year’s competition, who conceptualized a bicycle with a built-in tracking device, won a week of tours and informational meetings at places like Twitter, Google, 1871 Chicago, and Groupon to help flesh out their idea.