Pirate Math

Today was a snow day for us, and when the school buses don’t run there are far fewer students who come to class. Today I wanted to explore a problem that I hadn’t led before, it’s one of Peter Liljedahl’s good questions.

10 pirates are disbanding, and although they could easily split their gold, they cannot split a very precious diamond. The pirate captain wants to rig a “fair” way to decide who gets the diamond. They all stand in a circle and the pirate captain points to someone in the circle who is out of the running (they take their gold and leave). The person to their left is in the running, but the next in the circle to the left is out. Every alternate person to the left will leave the circle until only one person remains. Who should the pirate captain point to so that he himself ends up with the diamond.

The extensions are: what if there are 12 pirates, or 11 pirates, or 18 pirates, or 5 pirates, or 6 or 7 pirates.

We needed to decide on a common way to discuss the issue, and came up with tracking how many spots to the right or left of the captain that he should point to start the eliminations. We worked on ways of drawing and tracking information, and then looked for patterns.

Without too much prompting students (grade 9 and 10s and 12s) dug in and modelled the problem, then made some connections. Some tried to make equations and graphs and extend their thinking and test predictions. We ran into some challenges, but persevered! Some teachers even came to try out the pirate math.

Pretty good for a snow day!