Where is the epicentre?

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Purpose

The purpose of this activity is to engage students in using mathematical constructions to locate a position on a topographical map.

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
GM3-5: Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
Description of Mathematics

This activity assumes the students have experience in the following areas:

  • Using a scale on a map to find actual distances.
  • Using a compass to draw circles and arcs.
  • Construct a locus (set of points with a common property).

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.

Activity

 
Seismometers have been installed in many schools around New Zealand. When an earthquake is recorded, there are two main peaks in the series of squiggles the seismometer makes. The distance between those peaks can be used to tell how far away the the epicentre of the earthquake was. In one event, three North Island schools detected an earthquake and found the epicentre to be:

  • 100 km from Napier
  • 60 km from Gisborne
  • 180 km from Taupo

Find the epicentre of that earthquake. 


The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.

Make sense

Introduce the problem. Allow students time to read it and discuss in pairs or small groups.

  • Do I understand the situation? (Students may call on their knowledge of earthquakes. Media often report the centre of the quake. You might investigate how the centre is located.)
  • What is the important information? (The distance of the epicentre from each town is the important data.)
  • Do I know where in New Zealand each town is? How could I find this information?
  • What will my solution look like? (The solution will be a precise location for the epicentre supported by evidence that the location is correct.)

Plan approach

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.

  • What strategy or strategies will be useful? (Accessing a scale map will make the problem easier to solve.)
  • What maths will I need? (Interpreting scale on the map as actual distance is essential.)
  • What tools might I access to help me? (Google Maps has a distance from a point function. A drawing compass and ruler will be helpful for manual strategies.)
  • Do I already have a sense of where the epicentre might be? How do I know that?

Take action

Allow students time to work through their strategy and find a solution to the problem.

  • Am I showing my workings in a clear, step-by-step way? Am I using the map correctly? 
  • Do I know how to use my tools, or should I ask for help?
  • Is my strategy giving me sensible answers? Do the answers match my prediction of the epicentre location?
  • Does my answer seem correct? Is it close to my estimation?
  • How could I make sure that I haven’t missed anything?
  • How do my results look the same or different to others? Why could this be?
  • Is there another possible way to solve it that is more efficient?

Convince yourself and others

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.

  • What is the solution? Does the solution meet the requirement?
  • How could I check my solution?
  • Is my working clear for someone else to follow?
  • How would I convince someone else I am correct?
  • Could I have solved the problem in a more efficient way?
  • How might I apply what I learned to other problems?

Examples of work

Work sample 1

The student uses a scale map of the North Island. They draw circles an appropriate radius from each town by using the scale on the map. The student finds the epicentre by looking for the common point of intersection of the circles.

Click on the image to enlarge it. Click again to close. 

Work sample 2

The student develops a sense of the location of the epicentre from the given distances from each town, particularly Taupō and Gisborne. They use arcs and ruler measurements to scale to find a more accurate location for the epicentre.

Click on the image to enlarge it. Click again to close. 

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Level Three