Problem
Captain Blackheart had buried his treasure and committed the biggest sin a pirate can commit – he had lost his treasure map! But all was not lost. His trusty crew all remembered different bits of the map.

"I remember drawing it with 5 squares each way", said the Captain. ("He can’t count over 6", the cabin boy John said.)

"There was a row of three trees running due East from the square (1,1)", Peg Leg Pete said. "You put each one of them on a different square."

"Weren’t there four granite boulders going due South from (5,5)?" John asked. "I think you put one of them each in a square too."

"Ah!. Now I remember!" yelled the Captain. "I buried the treasure half way between the first rock and the first tree!"

Where is the treasure?

What is this problem about?
This is a problem about drawing and interpreting maps but it lays the foundations for graphs and Cartesian geometry that will be important in secondary school and at university.

Achievement Objectives
Geometry (Level 3)
- draw and interpret simple scale maps

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).

Resources
Grid paper (at least 5x5)
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- follow instructions using grid and compass references on a map

Teaching sequence

1. Set the scene for the problem. This could be done by displaying a 5x5 grid (burnt at the edges) and telling the class that this is the map that the pirate lost and when it was found no details remained.
2. Discuss the details that might be found on a pirates map – landmarks, compass directions (N,S,E,W).
3. Pose the problem.
4. Brainstorm for ways to solve the problem – (draw, use equipment).
5. As the children work on the problem check that they understand the use of grid references and the compass directions.
6. Wait until all the children have located the treasure before sharing solutions.

Extension to the problem
Write clues for their own treasure map. Post as a challenge for others to solve.

Solution
We have put all the information from the story on the map below.