Here is a statistics question I asked on a recent exam:
How high should the doorway be to allow 97% of men to fit through it?
I got a very large number of answers like "3 inches" or "0.0001 feet". This makes me sad. I'd like to know if these students notice that their answers are nonsense, and reward them if they have this level of sense-making.
How can I set up my grading scheme to reward people who notice their answer is nonsensical? Is there any way to do this besides the side benefit that nonsense answers are a clue that the work is probably wrong?