# Where is the epicentre?

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

The background knowledge and skills that should be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.

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.
nb A useful map of the North Island can be found on the following link: