When coaching at the local school's chess club, I try and keep things simple and understandable. As most of the kids aren't deep calculators, trying to explain that one side or the other one because of a deep combination doesn't always work.
Instead I often treat demonstration games as little 'morality plays', where the loser did something 'bad' (in chess terms) and that is why they lost. For example the following game from the current US Championship shows Black being punished for (a) pawn hunting with the queen, (b) leaving the king in the centre, and (c) falling behind in development. But if I used this as an example game I would simply pose the question 'Which side moved the least number of pieces?'. Of course this is an over simplification (and I could find plenty of counter examples where the less developed side eventually won), but it at least drives home the message that trying to win with one or two pieces only helps your opponent.
Christiansen,Larry M (2586) - Seirawan,Yasser (2636) [B12]
ch-USA GpB Saint Louis USA (2), 16.04.2011
1.e4 c6 2.d4 d5 3.e5 Bf5 4.Nf3 e6 5.Be2 c5 6.Be3 Qb6 7.Nc3 Qxb2 8.Qb1 Qxc2 9.Qb5+ Nd7 10.Rc1 a6 11.Qxb7 Rb8 12.Qxa6 Qb2 13.Bb5 c4 14.0-0 Qa3 (D)
15.Ba4 Be7 16.Nb5 Qb2 17.Bd2 Be4 18.Bc3 Qe2 19.Rfe1 Bxf3 20.Rxe2 Bxe2 21.Nd6+ Bxd6 22.Qxd6 Rb7 23.Bc6 1-0