Understand the sign of work

At some point, we are all confused by the meaning of the sign of work; at least I did. 

Here is how I interpret the sign of work.

We all know that W=P times change of V.

Let's think of a situation in the perspective of a system (cylinder with a piston on top of it).

When the final volume is less than the initial volume, we have negative work. What does this mean?

It means that the system is not doing work! It is not investing any energy (negative work). So, work is being done on the system!

What if final volume is greater? that means the system is doing work! The system is investing energy to do work (positive). We describe this as work is being done by the system!