ECU103 Geography for Schools Maths matters

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

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

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

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

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

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

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?

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

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)

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

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.

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?

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