Sometimes issues of privacy and messiness make it difficult to ask students to bring their real life problems to math class. Well, life inside the classroom is also real, and everyone can see what the parameters are. Look around for problems at school that students could take part in solving. Where is your institution spending money that students might have some input? Some examples follow, but really, it is a question of keeping your ears and eyes open.
It would be a total fantasy to ask everyone to imagine that they were going to spend $1000 decorating a room in their house, or even $200. Yet they can see that some part of the building where classes are held needs work—perhaps the foyer is shabby, or the coffee room doesn’t have enough seating, or the smoke pit is damp and cold, or somewhere there is not enough storage, so boxes of various supplies are sitting around the hallways or classrooms.
Take a space in your program—the lobby or lounge area, the cafeteria or a classroom, or an outside area where students hang out, and ask them to make a plan for refurbishing it.
Ask them to make a scale diagram of the space and show placement of various elements they would bring in. Go on a field trip to price paint, hardware, furnishings, etc., with a camera so students can take pictures of things they would like to incorporate into their design. Back in class, ask them to figure out how much things would cost and present a budget and their design to their classmates. The class could decide to present some or all of their ideas to administrators, or to other student groups, although the administration is likely to be a more sympathetic audience, whether or not they actually agree to some of the changes.