The purpose of this activity is to engage students in an investigation that requires them to define the dimensions of the parameters necessary to construct a described locus.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
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 following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student constructs and uses a scale diagram of the locus in order to solve the problem.
Click on the image to enlarge it. Click again to close.
The student sketches the locus and calculates the parameters required to solve the problem.
Click on the image to enlarge it. Click again to close.
The student sketches the locus and calculates the parameters required to solve the problem.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/running-track at 8:53pm on the 26th February 2024