Lesson 18.2: Map Scales and Real-World Distance Calculation
Applied concepts and practical problem solving for Map Scales and Real-World Distance Calculation.
⏱️ Reading Time: 20 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Maps, Locations, and Directions
City Urban Planning: Measuring park boundaries and cycling routes on municipal blueprints.
💡 Core Mathematical Concepts: Map Scales and Real-World Distance Calculation
Focus areas: Using map scale ratios (e.g., 1 cm = 50 m) to find real distances..
| Concept / Term | Mathematical Meaning | Real-Life Application |
|---|---|---|
| Map Scale | The ratio between distance on the map and real-world distance | 1 cm on map represents 50 metres in reality |
| Calculating Real Distance | Map measurement (cm) × Scale factor | 6 cm on map with 1 cm = 50 m -> 6 × 50 = 300 m |
| Map Route Planning | Measuring multiple straight segments to find total path length | Adding distances on trail maps |
📝 Step-by-Step Worked Examples
Worked Example 1: Convert map distance
Scale is 1 cm = 2 km. Road measures 7.5 cm on map -> Real length = 7.5 × 2 = 15 km.
Worked Example 2: Scale conversion
If real distance is 400 m and scale is 1 cm = 50 m -> Map distance = 400 ÷ 50 = 8 cm.
⚠️ Common Misconceptions to Avoid
Common Misconception: Mixing centimetres with kilometres in scale multiplication
Correction: Keep track of units: if scale is 1 cm = 100 m, multiplying 4 cm gives 400 m, NOT 400 cm.
Common Misconception: Using wrong scale key
Correction: Always verify which map legend scale applies to the current map sheet.
🎯
Self-Check Challenge
On a hiking map, the scale is 1 cm = 250 metres. A mountain trail measures 8 cm on the map. What is the real trail length in kilometres?
Answer & Explanation:
8 cm × 250 m = 2,000 metres. 2,000 m ÷ 1,000 = 2 kilometres.
🎯 Key Learning Takeaways
Extend understanding of Map Scales and Real-World Distance Calculation.
Solve multi-step real-world problems systematically.
Verify solutions through mathematical reasoning.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G5-M-CH18-WS05
A4 • 15 Qs
Maps, Locations, and Directions: Worksheet 5
Practice Assessment 5 • Central Botanical Gardens Context
G5-M-CH18-WS04
A4 • 15 Qs
Maps, Locations, and Directions: Worksheet 4
Practice Assessment 4 • Eco-Friendly Solar Park Context
G5-M-CH18-WS03
A4 • 15 Qs
Maps, Locations, and Directions: Worksheet 3
Practice Assessment 3 • Harbor Marine Terminal Context
G5-M-CH18-WS02
A4 • 15 Qs
Maps, Locations, and Directions: Worksheet 2
Practice Assessment 2 • Science & Discovery Museum Context
G5-M-CH18-WS01
A4 • 15 Qs
Maps, Locations, and Directions: Worksheet 1
Practice Assessment 1 • City Regional Airport Context
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
Three emergency response stations are located at A(2, 2), B(2, 8), and C(10, 2). If these three stations are connected by straight boundary fences, what is the area of the triangular zone enclosed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24 square units
Step-by-Step Explanation:
Base (AC) = 10 - 2 = 8 units. Height (AB) = 8 - 2 = 6 units. Area of right triangle = 1/2 × base × height = 1/2 × 8 × 6 = 24 square units.
2
Short Answer
Hard
2 Marks
On a topographical map, the scale is 1:50,000 (1 cm on the map = 50,000 cm in reality). How many kilometers does a 12 cm trail on the map represent on the ground?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 km
Step-by-Step Explanation:
12 cm × 50,000 = 600,000 cm. 600,000 cm ÷ 100 = 6,000 m. 6,000 m ÷ 1,000 = 6 km.
3
Short Answer
Hard
2 Marks
Why is an 8-point compass rose more precise for navigation than a 4-point cardinal compass?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An 8-point compass adds intercardinal bearings (NE, SE, SW, NW), dividing the 360° circle into 45° sectors rather than 90° sectors, doubling directional precision.
Step-by-Step Explanation:
Finer 45° angular resolution reduces trajectory drift in navigation.
4
Short Answer
Hard
2 Marks
Explain why maps include a scale bar and a North arrow (compass rose) to be practically useful for navigation.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A scale bar allows users to convert paper measurements into real-world distances, while the North arrow provides directional orientation relative to the physical landscape.
Step-by-Step Explanation:
Scale provides proportional distance quantification; the orientation rose anchors spatial bearings.
5
Short Answer
Medium
1 Mark
A scout claims: 'Facing East and making a 180° turn will leave me facing North.' Correct the scout's direction.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
West
Step-by-Step Explanation:
A 180° turn faces the exact opposite direction. Opposite of East is West.
6
Short Answer
Medium
1 Mark
A student plots the point (4, 7) by counting 7 units along the horizontal x-axis and 4 units up the vertical y-axis. What error was made?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reversed the x and y coordinates (should be 4 horizontal and 7 vertical)
Step-by-Step Explanation:
The first number is x (horizontal), the second is y (vertical). The student plotted (7, 4).
7
Fill in the Blanks
Medium
1 Mark
Map Scale Puzzle: Map distance = 4 cm, Real distance = 20 km. Scale: 1 cm = [ ? ] km.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
20 ÷ 4 = 5 km.
8
Fill in the Blanks
Medium
1 Mark
Identify the direction: Directly opposite to South-West on an 8-point compass is [ ? ].
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
North-East
Step-by-Step Explanation:
Opposite to South is North, opposite to West is East -> North-East.
9
Short Answer
Medium
1 Mark
A treasure hunter walks 50 meters North, turns 90° clockwise and walks 50 meters, turns 90° clockwise and walks 50 meters, and finally turns 90° clockwise and walks 50 meters. Where is the hunter relative to the start?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
At the starting point
Step-by-Step Explanation:
The path traces a closed 50 m square (North, East, South, West), returning to the exact starting point.
10
Short Answer
Medium
1 Mark
On a town map, a scale bar shows 1 cm = 250 meters. A delivery van travels along Main Street which measures 8 cm on the map. What is the real-world distance in kilometers?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 km
Step-by-Step Explanation:
8 cm × 250 m = 2,000 meters. 2,000 m = 2 km.
11
Short Answer
Medium
1 Mark
At the Central Botanical Gardens, an aerial drone survey uses a grid map. The drone launches from Base at (1, 2) and flies to Station Alpha at (7, 10). What is the horizontal distance in grid units between Base and Station Alpha?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 units
Step-by-Step Explanation:
Horizontal distance = 7 - 1 = 6 units.
12
Multiple Choice
Easy
1 Mark
A hiker starts at (2, 3) and moves 4 units East and 3 units North. What are the new coordinates?
A
(6, 6)
B
(6, 3)
C
(2, 6)
D
(5, 7)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(6, 6)
Step-by-Step Explanation:
East increases x: 2 + 4 = 6. North increases y: 3 + 3 = 6. New position is (6, 6).
13
Multiple Choice
Easy
1 Mark
Which compass direction lies exactly halfway between North and East?
A
North-East (NE)
B
North-West (NW)
C
South-East (SE)
D
East-North (EN)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
North-East (NE)
Step-by-Step Explanation:
The 8-point compass intercardinal direction between North and East is North-East.
14
Multiple Choice
Easy
1 Mark
If a map scale indicates 1 cm = 5 km, what actual distance on the ground is represented by 6 cm on the map?
A
30 km
B
25 km
C
11 km
D
35 km
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30 km
Step-by-Step Explanation:
6 cm × 5 km/cm = 30 km.
15
Multiple Choice
Easy
1 Mark
On a standard grid map, which coordinate is traditionally written first?
A
The horizontal coordinate (X-axis)
B
The vertical coordinate (Y-axis)
C
The altitude coordinate
D
The compass bearing
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The horizontal coordinate (X-axis)
Step-by-Step Explanation:
Coordinates are written (x, y) with horizontal along the corridor first, then vertical up the stairs.
16
Short Answer
Hard
2 Marks
Three emergency response stations are located at A(2, 2), B(2, 8), and C(10, 2). If these three stations are connected by straight boundary fences, what is the area of the triangular zone enclosed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24 square units
Step-by-Step Explanation:
Base (AC) = 10 - 2 = 8 units. Height (AB) = 8 - 2 = 6 units. Area of right triangle = 1/2 × base × height = 1/2 × 8 × 6 = 24 square units.
17
Short Answer
Hard
2 Marks
On a topographical map, the scale is 1:50,000 (1 cm on the map = 50,000 cm in reality). How many kilometers does a 12 cm trail on the map represent on the ground?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 km
Step-by-Step Explanation:
12 cm × 50,000 = 600,000 cm. 600,000 cm ÷ 100 = 6,000 m. 6,000 m ÷ 1,000 = 6 km.
18
Short Answer
Hard
2 Marks
Why is an 8-point compass rose more precise for navigation than a 4-point cardinal compass?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An 8-point compass adds intercardinal bearings (NE, SE, SW, NW), dividing the 360° circle into 45° sectors rather than 90° sectors, doubling directional precision.
Step-by-Step Explanation:
Finer 45° angular resolution reduces trajectory drift in navigation.
19
Short Answer
Hard
2 Marks
Explain why maps include a scale bar and a North arrow (compass rose) to be practically useful for navigation.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A scale bar allows users to convert paper measurements into real-world distances, while the North arrow provides directional orientation relative to the physical landscape.
Step-by-Step Explanation:
Scale provides proportional distance quantification; the orientation rose anchors spatial bearings.
20
Short Answer
Medium
1 Mark
A scout claims: 'Facing East and making a 180° turn will leave me facing North.' Correct the scout's direction.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
West
Step-by-Step Explanation:
A 180° turn faces the exact opposite direction. Opposite of East is West.
21
Short Answer
Medium
1 Mark
A student plots the point (4, 7) by counting 7 units along the horizontal x-axis and 4 units up the vertical y-axis. What error was made?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reversed the x and y coordinates (should be 4 horizontal and 7 vertical)
Step-by-Step Explanation:
The first number is x (horizontal), the second is y (vertical). The student plotted (7, 4).
22
Fill in the Blanks
Medium
1 Mark
Map Scale Puzzle: Map distance = 4 cm, Real distance = 20 km. Scale: 1 cm = [ ? ] km.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
20 ÷ 4 = 5 km.
23
Fill in the Blanks
Medium
1 Mark
Identify the direction: Directly opposite to South-West on an 8-point compass is [ ? ].
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
North-East
Step-by-Step Explanation:
Opposite to South is North, opposite to West is East -> North-East.
24
Short Answer
Medium
1 Mark
A treasure hunter walks 50 meters North, turns 90° clockwise and walks 50 meters, turns 90° clockwise and walks 50 meters, and finally turns 90° clockwise and walks 50 meters. Where is the hunter relative to the start?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
At the starting point
Step-by-Step Explanation:
The path traces a closed 50 m square (North, East, South, West), returning to the exact starting point.
25
Short Answer
Medium
1 Mark
On a town map, a scale bar shows 1 cm = 250 meters. A delivery van travels along Main Street which measures 8 cm on the map. What is the real-world distance in kilometers?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 km
Step-by-Step Explanation:
8 cm × 250 m = 2,000 meters. 2,000 m = 2 km.
26
Short Answer
Medium
1 Mark
At the Eco-Friendly Solar Park, an aerial drone survey uses a grid map. The drone launches from Base at (1, 2) and flies to Station Alpha at (7, 10). What is the horizontal distance in grid units between Base and Station Alpha?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 units
Step-by-Step Explanation:
Horizontal distance = 7 - 1 = 6 units.
27
Multiple Choice
Easy
1 Mark
A hiker starts at (2, 3) and moves 4 units East and 3 units North. What are the new coordinates?
A
(6, 6)
B
(6, 3)
C
(2, 6)
D
(5, 7)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(6, 6)
Step-by-Step Explanation:
East increases x: 2 + 4 = 6. North increases y: 3 + 3 = 6. New position is (6, 6).
28
Multiple Choice
Easy
1 Mark
Which compass direction lies exactly halfway between North and East?
A
North-East (NE)
B
North-West (NW)
C
South-East (SE)
D
East-North (EN)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
North-East (NE)
Step-by-Step Explanation:
The 8-point compass intercardinal direction between North and East is North-East.
29
Multiple Choice
Easy
1 Mark
If a map scale indicates 1 cm = 5 km, what actual distance on the ground is represented by 6 cm on the map?
A
30 km
B
25 km
C
11 km
D
35 km
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30 km
Step-by-Step Explanation:
6 cm × 5 km/cm = 30 km.
30
Multiple Choice
Easy
1 Mark
On a standard grid map, which coordinate is traditionally written first?
A
The horizontal coordinate (X-axis)
B
The vertical coordinate (Y-axis)
C
The altitude coordinate
D
The compass bearing
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The horizontal coordinate (X-axis)
Step-by-Step Explanation:
Coordinates are written (x, y) with horizontal along the corridor first, then vertical up the stairs.
31
Short Answer
Hard
2 Marks
Three emergency response stations are located at A(2, 2), B(2, 8), and C(10, 2). If these three stations are connected by straight boundary fences, what is the area of the triangular zone enclosed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24 square units
Step-by-Step Explanation:
Base (AC) = 10 - 2 = 8 units. Height (AB) = 8 - 2 = 6 units. Area of right triangle = 1/2 × base × height = 1/2 × 8 × 6 = 24 square units.
32
Short Answer
Hard
2 Marks
On a topographical map, the scale is 1:50,000 (1 cm on the map = 50,000 cm in reality). How many kilometers does a 12 cm trail on the map represent on the ground?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 km
Step-by-Step Explanation:
12 cm × 50,000 = 600,000 cm. 600,000 cm ÷ 100 = 6,000 m. 6,000 m ÷ 1,000 = 6 km.
33
Short Answer
Hard
2 Marks
Why is an 8-point compass rose more precise for navigation than a 4-point cardinal compass?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An 8-point compass adds intercardinal bearings (NE, SE, SW, NW), dividing the 360° circle into 45° sectors rather than 90° sectors, doubling directional precision.
Step-by-Step Explanation:
Finer 45° angular resolution reduces trajectory drift in navigation.
34
Short Answer
Hard
2 Marks
Explain why maps include a scale bar and a North arrow (compass rose) to be practically useful for navigation.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A scale bar allows users to convert paper measurements into real-world distances, while the North arrow provides directional orientation relative to the physical landscape.
Step-by-Step Explanation:
Scale provides proportional distance quantification; the orientation rose anchors spatial bearings.
35
Short Answer
Medium
1 Mark
A scout claims: 'Facing East and making a 180° turn will leave me facing North.' Correct the scout's direction.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
West
Step-by-Step Explanation:
A 180° turn faces the exact opposite direction. Opposite of East is West.
36
Short Answer
Medium
1 Mark
A student plots the point (4, 7) by counting 7 units along the horizontal x-axis and 4 units up the vertical y-axis. What error was made?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reversed the x and y coordinates (should be 4 horizontal and 7 vertical)
Step-by-Step Explanation:
The first number is x (horizontal), the second is y (vertical). The student plotted (7, 4).
37
Fill in the Blanks
Medium
1 Mark
Map Scale Puzzle: Map distance = 4 cm, Real distance = 20 km. Scale: 1 cm = [ ? ] km.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
20 ÷ 4 = 5 km.
38
Fill in the Blanks
Medium
1 Mark
Identify the direction: Directly opposite to South-West on an 8-point compass is [ ? ].
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
North-East
Step-by-Step Explanation:
Opposite to South is North, opposite to West is East -> North-East.
39
Short Answer
Medium
1 Mark
A treasure hunter walks 50 meters North, turns 90° clockwise and walks 50 meters, turns 90° clockwise and walks 50 meters, and finally turns 90° clockwise and walks 50 meters. Where is the hunter relative to the start?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
At the starting point
Step-by-Step Explanation:
The path traces a closed 50 m square (North, East, South, West), returning to the exact starting point.
40
Short Answer
Medium
1 Mark
On a town map, a scale bar shows 1 cm = 250 meters. A delivery van travels along Main Street which measures 8 cm on the map. What is the real-world distance in kilometers?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 km
Step-by-Step Explanation:
8 cm × 250 m = 2,000 meters. 2,000 m = 2 km.
41
Short Answer
Medium
1 Mark
At the Harbor Marine Terminal, an aerial drone survey uses a grid map. The drone launches from Base at (1, 2) and flies to Station Alpha at (7, 10). What is the horizontal distance in grid units between Base and Station Alpha?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 units
Step-by-Step Explanation:
Horizontal distance = 7 - 1 = 6 units.
42
Multiple Choice
Easy
1 Mark
A hiker starts at (2, 3) and moves 4 units East and 3 units North. What are the new coordinates?
A
(6, 6)
B
(6, 3)
C
(2, 6)
D
(5, 7)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(6, 6)
Step-by-Step Explanation:
East increases x: 2 + 4 = 6. North increases y: 3 + 3 = 6. New position is (6, 6).
43
Multiple Choice
Easy
1 Mark
Which compass direction lies exactly halfway between North and East?
A
North-East (NE)
B
North-West (NW)
C
South-East (SE)
D
East-North (EN)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
North-East (NE)
Step-by-Step Explanation:
The 8-point compass intercardinal direction between North and East is North-East.
44
Multiple Choice
Easy
1 Mark
If a map scale indicates 1 cm = 5 km, what actual distance on the ground is represented by 6 cm on the map?
A
30 km
B
25 km
C
11 km
D
35 km
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30 km
Step-by-Step Explanation:
6 cm × 5 km/cm = 30 km.
45
Multiple Choice
Easy
1 Mark
On a standard grid map, which coordinate is traditionally written first?
A
The horizontal coordinate (X-axis)
B
The vertical coordinate (Y-axis)
C
The altitude coordinate
D
The compass bearing
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The horizontal coordinate (X-axis)
Step-by-Step Explanation:
Coordinates are written (x, y) with horizontal along the corridor first, then vertical up the stairs.
46
Short Answer
Hard
2 Marks
Three emergency response stations are located at A(2, 2), B(2, 8), and C(10, 2). If these three stations are connected by straight boundary fences, what is the area of the triangular zone enclosed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24 square units
Step-by-Step Explanation:
Base (AC) = 10 - 2 = 8 units. Height (AB) = 8 - 2 = 6 units. Area of right triangle = 1/2 × base × height = 1/2 × 8 × 6 = 24 square units.
47
Short Answer
Hard
2 Marks
On a topographical map, the scale is 1:50,000 (1 cm on the map = 50,000 cm in reality). How many kilometers does a 12 cm trail on the map represent on the ground?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 km
Step-by-Step Explanation:
12 cm × 50,000 = 600,000 cm. 600,000 cm ÷ 100 = 6,000 m. 6,000 m ÷ 1,000 = 6 km.
48
Short Answer
Hard
2 Marks
Why is an 8-point compass rose more precise for navigation than a 4-point cardinal compass?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An 8-point compass adds intercardinal bearings (NE, SE, SW, NW), dividing the 360° circle into 45° sectors rather than 90° sectors, doubling directional precision.
Step-by-Step Explanation:
Finer 45° angular resolution reduces trajectory drift in navigation.
49
Short Answer
Hard
2 Marks
Explain why maps include a scale bar and a North arrow (compass rose) to be practically useful for navigation.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A scale bar allows users to convert paper measurements into real-world distances, while the North arrow provides directional orientation relative to the physical landscape.
Step-by-Step Explanation:
Scale provides proportional distance quantification; the orientation rose anchors spatial bearings.
50
Short Answer
Medium
1 Mark
A scout claims: 'Facing East and making a 180° turn will leave me facing North.' Correct the scout's direction.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
West
Step-by-Step Explanation:
A 180° turn faces the exact opposite direction. Opposite of East is West.