I would suggest the article I wrote for Chess Tutors called "Pawns vs Pieces".
Young people do not have the ability to stay focused on something that is complicated and soon lose their concentration. Hence, if you start out with teaching openings you will either lose their attention or immediately make them hate the game! When I started teaching a class of young students I set up the board position and said, this is the game we are going to learn how to play well. But to make it more fun we have to break it down and play a "game within the game."
You start out by giving the value of all the chess pieces and explain that the basic unit is "1". That is what the pawn is valued at and the pieces have a "fighting value" based on a reference to the pawn at the beginning of the game (even Kings have a "fighting value" reference based on the unit of pawns!).
"Pawns vs Pieces" by Don Vandivier
Knight vs Pawns
Start with placing only 1 knight on the White side on b1 and 3 Black pawns across from it on a7, b7, c7. The piece always moves first and the rule is for the Knight to be able to capture all the pawns. Kings are not on the board. The player with the pawns must try to queen a pawn without it being captured. If he/she can do so then they win. If the knight captures all the pawns then that player wins.
Once you play this out a few times then you switch sides and play the lesson again. After you come to the conclusion that 3 pawns always win against a knight, then try the lesson by using only two pawns. The knight should always win against 2 pawns!
Bishop vs Pawns
Same idea as the previous lesson. Place a bishop on it's original square and give the other side 3 connected pawns across from it. Remember that the piece always moves first!
You will discover that the bishop always wins against 3 pawns! No need to drop down to 2 pawns as you did in the knight lesson. If you can not play well enough to demonstrate that the bishop always wins against 3 pawns and a knight always loses against 3 pawns, but can stop 2 of them, then you are not qualified to give chess lessons. I recommend that you study your endgame if you cannot do this.
Moving forward, your student will learn how to play their pawns against a piece such as, not creating weaknesses, and the value of a passed pawn. It is a quick and fun lesson and will hold the child's attention. When you have finished the two lessons above (meaning that you tried 3 pawns against the knight, switches sides, and then determined that the knight can not hold 3 pawns and so went to 2 pawns and then switched sides again - then did the same exercise with the bishop against 3 pawns and switched sides) the lesson is nearly over.
All you have to do is give a quick reference that if a rook is valued at 5 points then a rook should be able to beat 5 pawns! Same thing for the queen - it can beat 9 pawns! (of course no kings are on the board and you will have to double a pawn row for the 9th pawn).
I recommend you stop your lesson after this and the next lesson you will talk about checkmating the king with queen and rook and king vs lone king and then 2 rooks and king vs lone king. If everything is going well then teach checkmate with queen and king vs king and rook and king versus king.
Once the student grasps the interaction between pawns and pieces and understands checkmate then you can start showing them some chess opening ideas and maybe even play a game. Don't do all of the above in one lesson.
Good Luck!
Don
I'm going to tutor a 3rd grader, who's around a 1200~ rating.
I dont know what to do as I am in highschool & this is my first time tutoring. I am around a 1800~ uscf rating, and I've had a couple of tutors of my own throughout my chess career.
Should I just go over opening, puzzles, or what? I'm being payed 25$ an hour so i'm gonna be ballin