Chess 960 popularised by Fischer could be useful to teach opening principles (mainly because the players has to think about development consciously). LaPingvino asked "What other games or chess variants are useful to improve your chess skills?" (by the way, its current answers include blindfold chess and Japanese chess).
I am interested in exercises and games that are useful to teach chess. This is beyond the scope of LaPingvino's question since exercises are included. There are exercises and games already used to teach chess especially to complete beginers, such as maze and capture the stars (e.g. lichess). Feel free to include exercises and games you create (provided they are useful in chess coaching).
Please post only one exercise or game per answer, and mention its utility in a chess coaching program as bullet points. You are welcome to write cons as well. Many chess variants are discouraged to use in chess class because of game dynamics being very much different from chess.
Also, I request to vote the answers based on the utility in a chess coaching program, not by the appeal of the exercise/game of itself.
PS: To chess coaches interested in including chess-like games, I would recommend to select a small number of chess-like games, and to ensure that they are visually different from each other and from chess.