This issue of viable and engaging contexts is complicated for a couple reasons. Many of the students in my high school classes came from situations that many of us would find hard to imagine; the last thing they cared about was how to balance a checkbook or figure the balance on a savings account. But they loved solving problems. For another thing, reality is relative.
Also, Deborah Loewenberg Ball on real-world context:
So I do think, on the question of context, it's worth remembering that mathematics itself is a context and that puzzle-like problems are often both very engaging for kids and good equalizers because kids looking at those diagrams aren't shaped by some of those same inequities about kids' experiences.
A facilitator at one of the workshops I went to this summer, Laura Kent, said that context is “anything that gives the students access to the math.”