For raw students I always start with K & Q v K and K & R v K mates.
It is essential they know this before anything.
For K & Q I like this position.
Their task is to mate the Black King on a1 and you are not allowed
to give a single check. Just checkmate and the Black King must
be the square a1 when it is checkmated.
Explain the trick is to give phantom Knight checks with your Queen.
But NEVER when the King is cornered.
After they have done that, get them to mate the Black King on h1.
You can put across quite a lot with this one example.
Thinking ahead, an endgame technique, stalemate, mating patterns...
Now they can mate a King on any of the 28 edge squares on a chessboard
against anyone (or computer) in the whole world by force -
- and without giving a single check!
I bet they never thought they could that 15 minutes before the lesson started.
Their confidence rises and suddenly this game does not seem so difficult at all.