This problem solving activity has an algebra focus.
There are 2 pirates and 4 treasure chests on an island.
The pirates have 1 small boat to take the treasure to their ship.
The boat can take 2 pirates or 1 pirate and 1 chest of treasure.
How many trips do the pirates have to take to get all the treasure and both pirates onto the ship?
This problem develops a strategy that works a number of times, as students use equipment or a diagram, and logic to solve the problem.
This problem is an introduction to algebra where the notation gives a way of expressing the repetition of a strategy.
There are 2 pirates and 4 treasure chests on an island. The pirates have 1 small boat to take the treasure to their ship. The boat can take 2 pirates or 1 pirate and 1 chest of treasure.
How many trips do the pirates have to take to get all the treasure and both pirates onto the ship?
What if there are 8 treasure chests?
There are 9 trips from island to ship.
Note that steps 1 and 2 can occur at any time that the small boat is on the land or steps 3 to 9 can be followed by ‘returns to land, 2 pirates go to the ship’.
Each treasure chest requires two trips, one to the ship and one back to the land. So with 8 chests the pirates will need 8 x 2 trips with the chests and 1 trip to take the extra pirate. This means 17 trips.
With c chests and two pirates there will need to be 2c + 1 trips. Note that students are not expected to write these kinds of expressions at Level 2.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/treasure-ship at 8:56pm on the 26th February 2024