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The treasure map

Student Activity: 

Captain Blackheart buries his treasure but loses his treasure map! But all is not lost. His trusty crew remember different bits of the map.

"I remember drawing it with 5 squares each way", says the Captain. 

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

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

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

Where is the treasure?

Achievement Objectives:

Achievement Objective: GM3-5: Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
Follow instructions using grid and compass references on a map
Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
Description of mathematics: 

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.

Required Resource Materials: 
Activity: 

Problem

Captain Blackheart buries his treasure but loses his treasure map! But all is not lost. His trusty crew remember different bits of the map.

"I remember drawing it with 5 squares each way", says the Captain. 

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

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

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

Where is the treasure?

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 students work on the problem check that they understand the use of grid references and the compass directions.
  6. Wait until all the students 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.

 
 
 
 
   
 
 
 
 
 
 
 
 
 
 
 
treasuretree.
treasuretree.
treasuretree.
 
 

The treasure is in (3,3).

AttachmentSize
TreasureMap.pdf145.46 KB
TePouakaTaonga.pdf205.21 KB