Maps, Plans & Representations

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A B 0 200 m

Maps, plans and other representations is about reading everyday documents — street maps, floor plans, seating charts, national road maps — and using scale to work out real distances and sizes.

In this lesson you will learn to:

• recognise the different types of maps and plans;
• read and use number scales and bar scales;
• calculate a real distance from a map;
• work with floor and elevation plans;
• use compass directions to give and follow routes;
• read a distance table; and
• plan a route and estimate travelling time.

1. Types of Maps & Plans

Bedroom Kitchen Bath Scale 1 : 100

Bedroom Kitchen Bath Scale 1 : 100

• A plan is drawn to scale — every real measurement is shrunk by the same factor.
• A key or legend explains the symbols (doors, windows, taps).
• North is usually marked so you can orient the plan.

\[ \text{map} = \text{a scaled picture of something real} \]

Key idea: a map or plan is a real place shrunk down evenly. The amount it is shrunk by is the scale — the next topic.

2. Scale

0 100 200 300 400 Distance in metres

There are two ways to show a scale:

\[ 1:50 \;\Rightarrow\; 1\text{ cm on the plan} = 50\text{ cm in real life} \]

The scale \(1:50\) tells you the drawing is 50 times smaller than reality.

0 100 200 300 400 Distance in metres

A bar scale is used by measuring, then multiplying.

\[ \text{real} = \text{map measurement} \times \text{scale} \]

Key idea: number scale — multiply by the scale factor. Bar scale — measure against the bar. Keep your units consistent throughout.

3. Distance on a Map

\[ \text{real distance} = \text{map distance} \times \text{scale} \]

Worked Example 1. A map has a scale of \(1:50\,000\). Two towns are 6 cm apart on the map. How far apart are they in real life?

To go from To Do this cm m \(\div 100\) m km \(\div 1\,000\) cm km \(\div 100\,000\) km m \(\times 1\,000\) m cm \(\times 100\)

\[ \text{map distance} = \frac{\text{real distance}}{\text{scale}} \]

Worked Example 2. On the same \(1:50\,000\) map, how far apart would two towns 4 km apart in real life be on the map?

\[ \text{map} \xrightarrow{\times \text{scale}} \text{real} \qquad \text{real} \xrightarrow{\div \text{scale}} \text{map} \]

Key idea: multiply to go from map to real; divide to go from real to map. Convert units at the end.

4. Floor Plans

Bedroom Kitchen Bath Scale 1 : 100

Worked Example 3. A floor plan is drawn to scale \(1:100\). A kitchen wall measures 8,5 cm on the plan. How long is the real wall?

\[ \text{plan length} = \frac{\text{real length}}{\text{scale}} \]

To DRAW a plan, divide each real measurement by the scale.

\[ \text{scale} \rightarrow \text{real size} \rightarrow \text{quantity} \rightarrow \text{cost} \]

Floor-plan questions usually go one step further — once you have the real size you can find:

• the perimeter, for skirting board or fencing;
• the area, for tiles, carpet or paint;
• the cost, by multiplying the quantity by a price per unit.

\[ 1:100 \Rightarrow 1\text{ cm} = 1\text{ m} \]

Key idea: plans use small scales like \(1:50\) or \(1:100\). Multiply plan measurements up to real size, then answer the question asked.

5. Compass Directions

N NE E SE S SW W NW

Directions are given using the compass.

N NE E SE S SW W NW

To describe a route, combine directions with landmarks and turns.

• “Left” and “right” depend on which way you are FACING.
• Compass directions (N, S, E, W) do NOT — they are always the same.

\[ \text{N} \to \text{E} \to \text{S} \to \text{W} \text{ (clockwise)} \]

Key idea: compass directions are fixed; left and right are not. Use compass directions for maps and left/right only from the traveller's point of view.

6. Distance Tables

km JHB Bloem Durban CT JHB — 398 568 1 402 Bloem 398 — 634 1 004 Durban 568 634 — 1 634 CT 1 402 1 004 1 634 —

A distance table gives the road distance between towns. To read it, find one town in a row and the other in a column.

km JHB Bloem Durban CT JHB — 398 568 1 402 Bloem 398 — 634 1 004 Durban 568 634 — 1 634 CT 1 402 1 004 1 634 —

Worked Example 4. A driver goes from Durban to Johannesburg and then to Cape Town. How far do they travel in total?

\[ \text{row} \; \cap \; \text{column} = \text{distance} \]

Key idea: the table gives direct distances. For a journey with stops, ADD the legs together.

7. Route Planning

\[ \text{time} = \frac{\text{distance}}{\text{speed}} \]

Route planning combines distance with the speed-distance-time relationship.

\[ \text{time} = \frac{398}{100} = 3{,}98\text{ hours} \]

A driver travels the 398 km from Johannesburg to Bloemfontein at an average speed of 100 km/h. How long does the trip take?

\[ \text{total time} = \text{driving time} + \text{stops} \]

A realistic journey includes rest breaks and fuel stops.

• Add every stop to the driving time for the total journey time.
• To find an arrival time, add the total time to the departure time (watch AM/PM).

\[ \text{distance} \div \text{speed} = \text{driving time} \]

Key idea: plan a route by finding the distance from the table, dividing by the speed for driving time, then adding stops. Convert decimal hours to minutes properly.

A B 0 200 m

You can now:

• recognise maps, floor plans, elevation and layout plans;
• use a number scale (multiply) and a bar scale (measure);
• calculate real distances from a map and convert units carefully;
• size rooms from a floor plan and work out perimeter, area and cost;
• give and follow compass directions;
• read a distance table and add the legs of a journey; and
• plan a route using distance, speed and time.