Thank you, Robert. As Jonathon mentioned, the grading of this exercise would be difficult; I don’t think it could be standardized. In principle, I’d try to use it to gauge the understanding of the subjects taught, and the students capacity for abstraction. Then I’d look at the connections or applications, as you mentioned, probably with emphasis on quantity over depth (because what I would be trying to do is foster a habit, not “being right”).
But above all, it would be a great thing to discuss in class. “Why did you think that?” “How did you come up with that?” etc.