Logic: the game

It's often easier to understand logic by noting its absence.
All men are mortal.
Socrates was a man.
Ergo, Socreates was mortal.

That's a fairly simple and obvious syllogism.  But what about this one:

Everything that is rare is expensive.
Cheap horses are rare.
Ergo, cheap horses are expensive.

The game of logic then is to teach a particular logical concept, then have students create examples where they flout the rule and see if their classmates can spot the mistake.