Maps and Grid Reference System

Lessons

Senior 4 · Geography

Maps and Grid Reference System

3 lessons

Lesson 1 of 3

Maps: Meaning, Elements and Scale

25 min

Reading a real map critically

The map below was made in September 2020 to show forecast rainfall in Rwanda for the short rainy season. Before you read the rainfall, check what the map tells you about itself: what it shows, for when, which way is north, how far one centimetre is on the ground, and what each colour means. Then look for what is missing or wrong.

"Rainfall Forecast: September to December 2020", a map of Rwanda by Mugisha Cosma. It has a title, a north arrow, a linear scale from 0 to 180 km, a legend, district boundaries with their names, Lake Kivu, and tick marks of longitude and latitude on the frame. Look closely at the legend: the classes 250–350 and 300–350 mm overlap. Map: Mugisha Cosma, CC BY-SA 4.0, via Wikimedia Commons.

Definition

Map: a drawing, usually on a flat surface and reduced to scale, of the whole or part of the earth's surface, showing selected features by symbols and colours.

A map differs from a photograph (which shows everything the camera saw, unselected) and from a sketch map (which is drawn without an accurate scale). A plan is a map of a very small area, such as a school compound, at a very large scale.

The elements of a map

Element	What it does	On the rainfall map
Title	Says what the map shows, where and when	Present: "Rainfall Forecast: September to December 2020"
Frame (border) and margin	Encloses the map; the margin carries information	Present, with longitude and latitude ticks
Key (legend)	Explains every symbol, line and colour	Present, but its classes overlap
Scale	Relates distance on the map to distance on the ground	Present: a linear scale, 0 to 180 km
North direction	Shows orientation, by an arrow or by grid lines	Present: a north arrow
Grid or graticule	Grid lines (eastings and northings) or lines of latitude and longitude, used to locate places	Ticks only, labelled in degrees
Marginal information	Sheet name and number, publisher, date, edition, projection, contour interval, magnetic north	Missing: no source of the data, no projection
Inset or location map	A small map showing where the area lies in a bigger region	Absent (not essential for a national map)
Conventional signs and labels	Standard symbols and names of places and features	District names and boundaries

Warning

Legend classes must not overlap. On the rainfall map, a district forecast to receive 320 mm belongs to both "250–350" and "300–350", and to "300–400" as well. Good classes follow on without gaps or overlaps: 250–299, 300–349, 350–399, 400–450. When you draw a thematic map, check your classes this way.

Scale

Every map is smaller than the ground it shows. The scale states how much smaller, and it can be written in three ways (Figure 1).

Figure 1: one scale, three forms. On the bar, the zero sits one division from the left: whole kilometres are read to the right of 0, tenths of a kilometre to the left.

Definition

Scale: the ratio between a distance on the map and the same distance on the ground.

Statement (verbal) scale: in words, "1 cm represents 0.5 km".
Representative fraction (RF): a ratio with no units, because both sides are in the same unit: 1:50 000 means 1 cm on the map is 50 000 cm on the ground (and 1 mm is 50 000 mm).
Linear (bar) scale: a line divided into ground distances, which stays correct if the map is enlarged or reduced.

\text{RF} = \frac{\text{map distance}}{\text{ground distance}} \quad \text{(both in the same units)}

Worked example 1: from statement to RF and back

(a) Write "1 cm represents 2.5 km" as an RF. Change the ground distance to centimetres: $2.5\ \text{km} = 2.5 \times 1\,000 \times 100 = 250\,000\ \text{cm}$ . So the RF is 1:250 000.

(b) Write 1:25 000 as a statement. 1 cm represents 25 000 cm, and

25\,000\ \text{cm} = \frac{25\,000}{100\,000}\ \text{km} = 0.25\ \text{km}

so "1 cm represents 0.25 km", or "4 cm represent 1 km".

Worked example 2: measuring a distance

Problem. On a 1:50 000 map, two schools are 6.8 cm apart in a straight line, and the winding road between them measures 9.3 cm with a piece of string. Find both ground distances.

Solution. Each centimetre is 50 000 cm = 0.5 km.

\text{straight line} = 6.8 \times 0.5 = 3.4\ \text{km} \qquad \text{road} = 9.3 \times 0.5 = 4.65\ \text{km}

The road is $\frac{4.65}{3.4} = 1.37$ times the straight-line distance: a typical result in hilly country, where roads wind along the contours.

Worked example 3: finding an unknown scale

Problem. A straight stretch of road known to be 3 km long measures 12 cm on a plan. Find the RF.

Solution. $3\ \text{km} = 300\,000\ \text{cm}$ .

\text{RF} = \frac{12}{300\,000} = \frac{1}{25\,000} \;\Rightarrow\; 1:25\,000

Worked example 4: area on a map

Problem. On a 1:50 000 map a lake covers 3.2 cm². What is its area on the ground?

Solution. 1 cm represents 0.5 km, so 1 cm² represents a square 0.5 km by 0.5 km:

1\ \text{cm}^2 \;\to\; (0.5\ \text{km})^2 = 0.25\ \text{km}^2 \qquad 3.2 \times 0.25 = 0.8\ \text{km}^2

Warning

Areas scale by the square. At 1:50 000, 1 cm² is not 0.5 km² but ${0.5}^{2} = 0.25$ km². Halving a map's linear scale makes each feature cover one quarter of the paper, not one half.

Tip

Units ladder for scale work: 1 km = 1 000 m = 100 000 cm. To turn an RF denominator into "km per cm", divide it by 100 000: 1:50 000 gives 0.5 km per cm; 1:250 000 gives 2.5 km per cm.

Geography with Dave: "Geography Mapwork: Map scale". Fraction, ratio, line and word scales, with examples of measuring on a topographic map. Pause after each example and work it before he does.

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Practice

Name six elements of a map and give the purpose of each.
Convert to RFs: (a) 1 cm represents 1 km; (b) 2 cm represent 1 km; (c) 1 cm represents 10 km.
Convert 1:20 000 to a statement scale in km per cm.
On a 1:50 000 map, a footpath measures 7.6 cm. How long is it on the ground?
A field 400 m long is drawn 8 cm long on a plan. Find the RF.
On a 1:25 000 map a forest covers 18 cm². Find its ground area in km² and in hectares (1 km² = 100 ha).
A photocopier reduces a map to half its size. Explain why the linear scale is still correct but the RF printed on it is not.

Show answersHide answers

For example: title (what, where, when); frame (encloses the map); key (explains symbols); scale (map to ground distance); north arrow (orientation); grid or graticule (locating places); marginal information (source, date, projection).
(a) 1:100 000; (b) 1:50 000; (c) 1:1 000 000.
1 cm represents 20 000 cm = 0.2 km.
$7.6 \times 0.5 = 3.8$ km.
400 m = 40 000 cm; $\frac{8}{40\,000} = \frac{1}{5\,000}$ , so 1:5 000.
1 cm represents 0.25 km, so 1 cm² represents ${0.25}^{2} = 0.0625$ km²; $18 \times 0.0625 = 1.125$ km² = 112.5 ha.
The bar shrinks with the map, so it still matches the ground. The printed RF does not change, but 1 cm of paper now covers twice as much ground: a map printed as 1:50 000 has really become 1:100 000.

Quick check

Key points

A map is a selective, scaled drawing of the earth's surface; its elements are the title, frame, key, scale, north direction, grid, marginal information, inset and labels.
Scale is written as a statement, an RF or a linear scale; RF = map distance ÷ ground distance, in the same units.
1 km = 100 000 cm; at 1:50 000, 1 cm is 0.5 km and 1 cm² is 0.25 km².
Read every map critically: check that the key's classes do not overlap and that the source and date are given.

Sources and credits

Map: Rwanda rainfall forecast, Mugisha Cosma, CC BY-SA 4.0, via Wikimedia Commons.

The rest of the lesson, Figure 1, the worked examples and the exercises were written and drawn by Ganzaa.

Video: "Geography Mapwork: Map scale", Geography with Dave, embedded from YouTube.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Reading a real map critically

2The elements of a map

3Scale

Reading a real map critically

The elements of a map

Scale