Peaceful Pieces
How it works
Imagine that we want to place as many rooks as possible on a chessboard. However, these rooks are peaceful rooks — they don't want to be placed in a square where they're threatening or being threatened by any other rook on the board. (A rook is "threatening" another rook if it can move to the square where the other rook is on its next move.) What is the maximum number of peaceful rooks we can place on a chessboard? What about kings, bishops, knights, and queens? Can you fit more of some types of pieces than others? Which type of piece can you fit the most copies of?
In this activity, students try to figure out how to place the maximum number of peaceful copies of the different types of chess pieces on a chessboard. They start with a 4 x 4 board and work their way up to larger boards.
Why we like this activity
- It’s fun! Students enjoy thinking about how the different pieces move and trying to place the maximum number of pieces on the board.
- It helps students to develop spatial reasoning.
- It helps students to develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Using logic and finding and using strategies when trying to figure out how to place the maximum number of copies of a piece on a board.
Looking for patterns and making and testing predictions when trying to predict the maximum number of copies of a piece that can be placed on a board.
- It has a low floor and a high ceiling: It's easy for students to start placing pieces by trial and error, but in order to find the maximum, students need to think more strategically.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.