The treasure map

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Purpose

This problem solving activity has a geometry focus.

Achievement Objectives
GM3-5: Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
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.

Decorative image of a treasure chest.

"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?

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. It lays the foundations for understanding graphs and Cartesian geometry, which is important in the later years of schooling.

Required Resource Materials
Activity

The 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.

Decorative image of a treasure chest."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), coordinates, scale.
  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

Ask students to write clues for their own treasure map. You could provide a 5 x 5 grid for students to use (paper or digital) and make links to instruction writing. Pose these as a challenge for other students to solve.

Solution

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

 
 
 
 
   Granite boulder at (5,5).
 
 
 
 
Granite boulder at (5,4).
 
 
Treasure Chest at (3,3).
 
Granite boulder at (5,3).
 
 
 
 
Granite boulder at (5,2).
Tree at (1,1).
Tree at (1,2).
Tree at (1,3).
 
 

The treasure is in (3,3).

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Level Three