I have discovered the most important item in the chess teacher's toolbox: the lollipop.
Specifically, I recommend "ring pops," since they are less likely to end up on the chessboard and because they most resemble a pacifier, which is the main function that they serve in my teaching. Ring pops make a good reward at the end of activities ("solve these three problems and we will break open the candy!") -- providing useful motivation to stay on task. But, more importantly, they magically create the most essential ingredient to a successful chess class for kids: peace and quiet!
The first time my entire class of ten 10-year-old boys had their "pacifiers," the room grew suddenly silent and I could lecture at the demonstration board for a full fifteen minutes, keeping their focus on the lesson at hand. In fact, our group became so quiet that parents in the next room, used to hearing a constant staccato of competitive outbursts from the boys, punctuated by occasional raucousness on the verge of riot, had to peek in to see what magic I had wrought....
In our past two sessions, I have used the ring pop moments to show my students some games, beginning with Morphy vs. the Count and the Duke (I know, I know: "old hat"--but very effective) followed by a few other games from my Mating Patterns I: Bishops and Rooks collection (especially Reti-Tartakower, Vienna 1910, and Onderka-NN, Austria 1913). Taken together, they all illustrate the concepts of Development, Initiative, and Attack on the King while helping to reinforce the "Morphy's mate" motif. I was amazed at how quickly they began putting these lessons to use in their own games: opening with the d- or e-pawn, developing pieces toward the center, castling to bring their Rook to open files, actually trying to attack their opponents' King, and even (in one instance) pulling off a mate with Bishop and Rook that was directly inspired by our lessons. Looking at games has had a powerful effect.
In the end, nothing teaches chess faster than playing over games. I remember being told that by IM Mike Valvo when I was a kid myself, just starting out with chess and playing weekly at the Westfield Chess Club (which we both frequented in the 1980s.) During one of his lectures, he said, "Just get a games collection and play over as many games as you can. The most important thing is that they be great games. You don't need detailed notes -- in fact, no notes might be best. Just play over the games until you start to see the patterns!" Of course, you should play them over with focused attention, trying to understand and absorb as much as you can. But even playing them over with little conscious effort has some effect.
At that time, I remember playing through every game in The Golden Treasury of Chess before getting hold of a Chess Informant. Today, kids can get the same effect by just browsing through Chessgames.com or NICBase or one of the many free game database sites. I often recommend websites like that to the kids and their parents, but I'm not sure how many of them have tried them out. There is no question, though, that simply playing through a lot of games will teach them a tremendous amount about the standard patterns of the game -- from pawn formations to the best squares for the pieces. By seeing all of the stages of the game, from opening, to middlegame, to endgame, kids begin to see how the stages fit together, practically like a story. They see pieces and pawns get exchanged, lines open, attacks develop, king's field sacrifices blow open castled positions, and mating patterns or passed pawns rushing to the queening square finish things off. If they look at several hundred games (which they can do in an amazingly short amount of time online, just spending an hour or two each night), they will make an incredible leap forward toward real chess mastery.
For now, I have enough of their attention for games as the ring pops allow. Maybe it's time to switch to "everlasting gob-stoppers."