I've always been a big fan of games and puzzles as teaching tools. They develop logical thinking and problem solving, they remind us that learning is supposed to be an enjoyable activity, and more often than not, they have a dirty, little secret.
Doublets are a great example. Developed by Charles Dodgson (writing as Lewis Carroll), they were, for a while, the rage of the Victorian party scene. The rules were elegantly simple: take two words with the same number of letters; change the the first word to the second one letter at a time with the condition that each transition is also a word (think Scrabble rules -- no slang, no proper names). Though not required, the two words would usually have some logical connection.
Scores are determined by how many steps it takes. As in golf, low score wins.
Here's how a doublet player might go from FOOT to BALL:
Of course, FOOT BALL is an easy one. the doublets Carroll created tended to be far more challenging. Here are some examples from Carroll's Doublets: a word puzzle (available in cut-and-paste friendly plain text here)
Change OAT to RYE.
Get WOOD from TREE.
Prove GRASS to be GREEN.
Change CAIN into ABEL.
Make FLOUR into BREAD.
Evolve MAN from APE.
Now we get to the secret of doublets.
After you've used them as time fillers at the end of class and handed out the puzzle sheets and maybe even given some bonus points to the first student to solve a particularly challenging example, only then do you reveal the dirty little secret:
Specifically, it's graph theory.
That's right, you've tricked all of those poor, innocent kids into doing math and, worse yet, thinking they enjoyed it. You've introduced a sophisticated mathematical concept, reinforced it with a memorable example and laid the groundwork for future lessons.
Naturally, the patron saint of math teachers, Martin Gardner, was here first.