The Running track

Purpose

The purpose of this multi-level task is to engage students in an investigation that requires them to define the dimensions of the parameters necessary to construct a described locus.

Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.

Activity

Task: A group of students have been given the task of marking out the inside of a 400m running track on the school field. To mark out a locus in the shape of this track the students are provided with a thick rope to peg down in the middle of the field. A thin rope can be looped around this and used to mark the locus. 

Work out how long each of the lengths of rope need to be to mark the track.
 

The arithmetic approach (show more)

  • The student is able to construct and use a scale diagram of the locus in order to solve the problem.

The procedural algebraic approach (show more)

  • The student is able sketch the locus and calculate the parameters required to solve the problem.

The conceptual algebraic approach (show more)

  • The student is able sketch the locus and calculate the parameters required to solve the problem.

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