The given in a problem is like your golden ticket in a way, because it can make things a lot easier for you. Especially if there are multiple ways to solve a problem, choose the path of least resistance. For instance, suppose you are asked to calculate the coefficient of determination. You notice that the teacher included the values for SSR and SST, two very nasty statistics to calculate from scratch- use it. What I have found 9 times out of 10, the teacher includes an easy way to approach an equation in your homework. You just have to find it. Now it depends on the course too. If you are in a course that is entry level, the teacher will not expect you to derive equations from mathematical proofs- not for a general population type class. A course that is for your average human being, will include some level of given information so that you can focus on statistical application.
So if someone gives something to you – take it! Use it!
-Moore to follow-Amy