Walk the line


The purpose of this multi-level task is to engage students in using grid references as co-ordinates on a plane along with scales and bearings to solve a problem.

Description of Mathematics

This background knowledge and skills that need to be established before and/or during this task are outlined in the diagram below:

This task may be solved using only practical measurements of lengths and angles, or by using trigonometry to resolve the co-ordinates of a vector. The approach should be chosen in sympathy with their skills and depth of understanding.


Task: A group of outdoors enthusiasts are planning to walk the Motatapu track.

The track is clearly marked on the Department of Conservation guide, but does not appear on the topographical map. They have been advised that, while the terrain is relatively open, the track is not clearly marked between Fern Burn Hut and Highland Creek Hut.

Mark the route that follows these bearings, on the map and work out how much further the group will have to walk than is visible on the map, to get to the second hut.

The procedural approach (show more)

  • The student is able to measure lengths and angles on a map (guide) and calculate these to scale giving a bearing, to solve a problem.

The conceptual approach (show more)

  • The student is able work with measurements and calculations of co-ordinates, to solve a problem involving maps, bearings and displacement.

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