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.

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.

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.