Shorter game for play with kids I am teaching my children (5 and 7) to play chess, and we are pretty much at the which piece can move where phase. However while they do enjoy the game, they don't really have an attention span that can play a full game. 

What I would like is some way to make changes to the game that will cut game time down so that my kids can enjoy the game, as quality time with Dad and hopefully learn something.
A few ideas:


Michael Goeller's Pawn Battle  which introduces a checkers-like game (that still follows the rules of chess) that wonderfully folds in key pawn concepts like break moves, sacrificing to clear a line and even zugzwang. This exercise also helps kids learn to appreciate calculating outcomes beyond just "Hope Chess"-ing it out.
Some of the handouts at ProfessorChess.com contain exercises and drills that are fun and instructive.
Basic won endgames :  These can be fun, simple positions which very direct goals and often gets done within minutes as they start to figure out how to solve them.  Start up with KQ vs K setups and move up the ladder of complexity to KR vs K and even KP vs K.  These fundamental skills stay with them as they progress with their chess.


An added funsy way of doing the above is to use 2 x 8-sided dice to randomly assign squares for pieces in the starting position (e.g. K goes here, other K goes there, the Queen goes here. Play to win!). You could go all out and even create a roulette wheel of different drills to perform!