1. ECU103 Geography for Schools
Maths matters

2. Geography needs Geometry
Overview
Geographic mapping relies on complex and rich mathematics to describe the 3 Dimensional world on a two dimensional platform (paper or a computer screen).
The elements of maths in geography include the following:
Location - Coordinate systems
Direction/Compass Points
Scale
Geography needs Geometry

3. Geography uses Geometry
Geometry is the area of mathematics dealing with solids, surfaces, points, lines, curves and angles and their relationship in space (Eather, 2013)
Plane geometry is about shapes that can be drawn on a flat surface (so like a map)
Plane geometry uses points, lines, circles and other polygons to represent an object on a flat surface

4. Properties in plane geometry
Source: Maths is Fun, 2013
Dimension refers to length, breadth and height
For example click here

5. Knowing where you are
Plane geometry uses Cartesian Coordinates to mark the position of a point, line or polygon (Lines and polygons are series of points)
Cartesian is a term used to relate to the French Philosopher and mathematician René Descartes who described the system

6. René Descartes (1596 – 1650) Descartes was a creative
Mathematician, philosopher
and natural scientist
Descartes is credited with
many scientific achievements
Including offering a vision of the
natural world

7. Location
A coordinate system is used to provide us with location – where is the object or area of interest?
Coordinate systems consist of a plane (Cartesian plane) with two perpendicular axes and an intersecting point called the origin

8. How does this relate to map coordinates?
Source: acara, 2013
How does this relate to map coordinates?
Can you remember the coordinate systems used locally and globally?
What would the x axis represent and what does the y axis represent?

9. Longitude = Y axis
Is the angular distance in degrees, minutes and seconds in relation to the Prime Meridian
Latitude = X axis
Is the angular distance in degree, minutes and seconds in relation to the equator
Source: Worldatlas

10. Maps and maths in school
Examples of learning and applying location and coordinates in a Year 3 and 4 class
Source: O’Brien & Purcell (2008)

11. Scale Scale is the ration between two sets of measurements
In size transformation the ration expresses the amount of marginalisation
In maps scale represents the ratio of the measurement in the map compared to the measurement of the original object or space being mapped
To understand scale you need to understand ratios

12. Ratios Ratio describes a comparison between at least two objects
Ration may be written as a ration or a fraction e.g. 1:2 = ½
Maps use the term scale to describe the relationship between what is on the map and what exists in space. The scale is expressed as a ratio or a fraction.

13. Denominator Shows how many equal parts are in the whole
Fractions
Denominator Shows how many equal parts are in the whole
Numerator
Shows how many equal parts out of the whole we are considering
In the grid to the left, each square forms 1/25 of the whole
How does this relate to maps?

14. Map Scale
When we talk about large scale maps and small scale maps we are talking about the size of the fraction (or ratio) used
1:10000 is a large scale map (1 cm = 100m
1: 10 million is a small scale map (1 cm = 100 Km)
The terms small scale and large scale are relative since it is about the size of one fraction compared to another
See examples of each scale use here