I agree. Good old functional decomposition made me a fine living for years. Those three bullets I started out with could have turned into three methods as well as three classes. But that wasn't the question.
BTW: This topic of how to decide how many classes you have and how they interact expands into the entire field of OO design. It's huge, there's never a "right" answer (though some other peoples' answers are clearly wrong) and you'll struggle with it the rest of your career. The good news is that that's the really fun part.
For a light-hearted look at some of it, see
Knight's Principles. If this kind of discussion is interesting, scroll on down to the OO, UML etc. forum.