Step 1 · Kings face to face
White to move
6k1/R7/5K2/8/8/8/8/8 w - - 0 1The rook has already cut the king off on the back rank. A rook cannot mate alone — put your king opposite the black king.
The move: Kf6-g6
Kings face to face. Yours guards f7, g7 and h7; the black king can only shuffle along the back rank.
Common mistake: The rook is doing its job on the seventh rank. What is missing is your king: step it to g6, opposite the black king.
Into the corner
Black to move
6k1/R7/6K1/8/8/8/8/8 b - - 1 1Black slides into the corner. Now the rook can give the final check.
Step 2 · Checkmate in one
White to move
7k/R7/6K1/8/8/8/8/8 w - - 2 2The rook checks along the back rank while your king guards g7 and h7.
The move: Ra7-a8
Checkmate. The rook sweeps the back rank; your king holds g7 and h7. That is the rook mate.
Common mistake: Not mate: the king still has a square. Give check along the back rank while your king holds g7 and h7.
What you learned
Use your rook to restrict the king and bring your king closer safely. For the final mate, coordinate both pieces to cover the escape squares.