What: Take your students somewhere [literally or figuratively] where they will serve children. Preschoolers are the most fun, elementary age may be where they both connect the best.
Why: Teenagers usually love serving little kids and they usually have a blast doing it. You'll see some kind of sparks when they go out of their way to make something fun for kids. Kids need to see high school students living bigger lives. And, just in case, you didn't realize, kids are a different culture - use this as a launching point for discussing culture. Even better, get your students to talk about the world to the kids they are serving. Students inspiring kids is the Kingdom on an exponential order.
How I've seen it: Impromptu park ministry [be smart about this though - always in groups, have official contact info to give to parents, etc.], volunteer at some kind of community event, help run some vacation Bible schools, church summer camps, etc.
Extra Credit: Form a deep, consistent partnership with the children's ministry from your church. Experiment with the intersection of students and kids and make sure you fall flat on your face at least once.
My Never Implemented Dreams: Use our students to do some "teaching" in children's Sunday mornings for exposure to the world and their experiences; setup consistent partnerships with local elementary schools and our students to assist in scheduled and routine ways [although this did happen with one school]; SPACE camp - a three day once in the summer day camp with elements about world cultures, global issues and ways for elementary kids to make a difference.
ExCalibur - in Aix, France
Illuminate, a creative arts camp from Mosaic LA