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?
Fairytales: 3 Bears and 5 bowls of porridge (Baby Bear taking bowls of porridge to the dining room table);
3 Pigs and 10 bricks (Porky Pig moving bricks).
These problems also extend the pirate problem in that they require the same strategy but use larger numbers. The problem can be further developed using any number of people (or animals) and any number of objects to be transported.
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 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.)
Printed from https://nzmaths.co.nz/resource/treasure-ship at 7:36am on the 20th May 2022