To master chess, you need more than just knowing the pieces and their moves - you need to be able to make notations of your moves. To make a short notation, write the piece name and square it moved to; for example, Bd2 for bishop on d2. Pawns don't need the piece name, just the square; e.g. g5. Show your kids how to draw lines to the board for the moves given.
Teach your child the rules of castling: no castling if the king is under attack or will move onto an attacked square, or cross an attack line. To prepare for a game of chess, help your child complete the exercise of identifying when the king can castle – check the pictures.
Chess is a great game for sharpening math skills, strategic thinking, and knowledge of how each piece moves. If your child is interested, introduce them with this worksheet. It demonstrates how the queen can capture opposing pieces, such as another queen, and take their place.