I like the following problem.
It was shown by Alan Schoenfeld in his talk yesterday in Singapore. Among the many things he touched upon, he introduced the Mathematics Assessment Project which has a package of lessons for grades 6 till high school. The above problem came from the lesson on Distance Time Graphs.
Schoenfeld also gave a list of key questions to ask for Mathematics Classes:
1) Was there honest-to-goodness maths in what students and teacher did?
2) Did students engage in “productive struggle,” or was the math dumbed down to the point where they didn’t?
3) Who has the opportunity to engage? A select few, or everyone?
4) Who had a voice? Did students get to say things, develop ownership?
5) Did instruction find out what students know and build on it?
Certainly a tall order!