That's called problem soloving. You see the problem, see that it is a combination of smaller problems, you solve them.
Lots of problem solving at school was teaching exactly that: how to transform a problem into the ones you can solve with step-by-step approach. This was true not only for math, but for physics and chemistry too.
Yes, but I would agree with dvt that there are professors who consider themselves "clever" for putting material on the exam that looks nothing like what showed up in lecture or in the homework.
Kinds of problems that can justify being on an exam are surely important enough to be in lecture or on the homework. Putting a special kind of problem on the exam that must be deconstructed before it can be transformed in a problem that showed up in the homework is a "trick".
