Intent

In this first POW of the unit, students examine a puzzle based on the movement of chess pieces.

Mathematics

As with many POWs, the most important content addressed in the activity is the problem-solving process itself. In this case, students will work to develop sequences of steps that move a chess piece from one part of the board to another. The problem raises the important mathematical questions of existence, uniqueness, and efficiency of solutions.

Progression

Students do initial explorations during class and then work on and complete a write-up of the activity on their own. Several students will present solutions in a week or so.

Approximate Time

10 minutes for introduction

1 to 3 hours for activity (at home)

15 minutes for presentations

Classroom Organization

Whole class, then individuals, followed by whole-class presentations

Materials

1-inch grid paper

Doing the Activity

Discuss in class how the knight piece moves on a chessboard to be sure students understand the kinds of moves allowed.

Discussing and Debriefing the Activity

Following the POW presentations, you might ask whether other students were able to move the knights in fewer moves, and if so, have them share their methods. (The switch is possible, and the least number of moves in which the switch can be made is 16.)

Ask students to discuss how they kept track of moves so that they did not double-count and why they feel they cannot do the task in fewer moves. They probably won’t offer complete proofs here, but this is a good opportunity for learning to develop convincing arguments.

Key Questions

Did anyone switch the knights in fewer moves?

How did you keep track of the moves?

Why do you think your result is the best possible?

Supplemental Activities

More Knights Switching (extension) is a similar activity that is a bit more challenging and is a good follow-up to the discussion of POW 9: The Big Knight Switch.

A Knight Goes Traveling (extension) is similar to the other knight-switch problems but uses a square chessboard of some unknown size. This is another good follow-up investigation to POW 9: The Big Knight Switch.