By request, we had a chess week. But not regular chess. We played Dice Chess! Pieces move and capture in the normal way, but a role of the die determines which piece is moved. 1 = pawn or king. 2 = pawn or king. 3 = queen. 4 = bishop. 5 = knight. 6 = rook. If a piece is missing or cannot legally move then the die is rolled again. A player wins by capturing the king. A player can check the king, but with the version we played the king is not obliged to move out of check (although it would be a gamble not to). You do not win by checkmate but by capturing the king. This variation is quicker than normal chess as there is less time spent agonising over which piece to move.
We also played a game I call Chess Four.
It is played on a 4×4 grid, with only one pawn, knight, bishop and rook each. The aim is to be the first to make a 4 in row. Pieces move and capture in the normal way, but a captured piece is given back to the player who lost in, who gets to reintroduce in when they choose. This is a good game for introducing children to how chess pieces move and capture.