Lesson Notes By Weeks and Term v5 - Grade 10
Maps, plans and other representations of the physical world – Week 1 focus
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Maps, plans and other representations of the physical world – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 10
Term: Term 4
Week: 1
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
This week, we embark on a journey into the world of maps, plans, and other representations of the physical world. This isn’t just about drawing pretty pictures; it’s about developing crucial life skills that empower you to navigate your surroundings, understand spatial relationships, and make informed decisions.
Think about it: from finding your way to a friend's house in your township to understanding the layout of a new shopping mall, or even planning your own small garden, these skills are constantly used in daily life.
What are Maps and Plans? Maps and plans are visual representations of physical spaces, reduced in size to fit on a manageable surface (like paper or a screen). They provide essential information about locations, distances, and features of an area. A map generally represents a larger area, such as a city, region, or country. A plan often depicts a smaller area in more detail, such as a building layout (floor plan) or a small plot of land (site plan).
Map Symbols and Conventions: Maps use symbols and conventions to represent real-world features. It is crucial to understand these to read and interpret maps accurately.
Legend (Key): This is the dictionary of the map. It explains what each symbol represents (e.g., a blue line for a river, a red cross for a hospital). Always refer to the legend when reading a map.
North Arrow: This indicates the direction of North. Once you know North, you can easily determine the other cardinal directions (South, East, West).
Scale: The scale shows the relationship between distances on the map and the corresponding distances in the real world.
It can be represented in three main ways: Verbal Scale: A statement like "1 cm represents 1 kilometer".
Ratio Scale (Representative Fraction): A ratio like 1:100,000 (meaning 1 unit on the map represents 100,000 units in the real world).
Linear Scale (Bar Scale): A visual representation of the scale using a line divided into segments that represent specific distances.
Grid References: Many maps use a grid system (e.g., alphanumeric grid) to help locate specific points.
Understanding Directions and Bearings: Compass Directions: The four cardinal directions are North (N), South (S), East (E), and West (W). There are also intermediate directions like North-East (NE), South-East (SE), South-West (SW), and North-West (NW).
Bearings: Bearings are angles measured clockwise from North. They are usually expressed in degrees (e.g., 0° for North, 90° for East, 180° for South, 270° for West).
Using Scale to Calculate Distances: The scale is the key to converting distances on a map to real-world distances.
Example 1 (Verbal Scale): A map has a scale of 1 cm represents 5 km. Two towns are 8 cm apart on the map. What is the actual distance between the towns?
Solution: Since 1 cm represents 5 km, then 8 cm represents 8 5 km = 40 km.
Answer: The actual distance between the towns is 40 km.
Example 2 (Ratio Scale): A map has a scale of 1:50,
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0. Two points are 3 cm apart on the map. What is the actual distance between the points in meters?
Solution: 1 cm on the map represents 50,000 cm in reality.
Therefore, 3 cm on the map represents 3 * 50,000 cm = 150,000 cm. To convert cm to meters, divide by 100: 150,000 cm / 100 = 1500 meters.
Answer: The actual distance between the points is 1500 meters.
Example 3 (Linear Scale): Imagine a map with a bar scale where a 2 cm segment represents 10 km. You measure the distance between your home and the nearest clinic on the map as 5 cm. What is the real-world distance?
Solution: First determine the value represented by 1 cm on the bar scale: 10km / 2cm = 5km/cm. Then, multiply the measured distance on the map (5 cm) by the value of 1 cm: 5 cm 5 km/cm = 25 km.
Answer: The real-world distance between your home and the nearest clinic is 25 km.
Types of Maps and Plans: Street Maps: Show roads, streets, and landmarks within a city or town. Useful for navigation.
Topographic Maps: Show the shape of the land using contour lines (lines connecting points of equal elevation). Useful for hiking and understanding terrain.
Floor Plans: Show the layout of a building, including rooms, doors, and windows. Useful for interior design and construction.
Site Plans: Show the layout of a property, including buildings, landscaping, and other features. Useful for property development and landscaping.
Thematic Maps: Focus on a specific theme or topic, such as population density, rainfall, or economic activity.
Grid References: Grid references use a combination of letters and numbers to pinpoint specific locations on a map. Find the vertical grid line (e.g., a letter) and the horizontal grid line (e.g., a number) that intersect closest to the location you want to find. Then, state the letter first followed by the number (e.g. A5). Sometimes, 4-figure and 6-figure grid references are used to provide more detail. Guided Practice (With Solutions)
Question 1: A map of Durban has a scale of 1:25,
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0. The distance between the Moses Mabhida Stadium and uShaka Marine World is 6 cm on the map. What is the actual distance between them in kilometers?
Solution: Understand the scale: 1 cm on the map represents 25,000 cm in reality.
Calculate the real-world distance in cm: 6 cm * 25,000 cm/cm = 150,000 cm Convert cm to km: There are 100 cm in a meter and 1000 meters in a kilometer, so there are 100,000 cm in a kilometer.
Therefore, 150,000 cm / 100,000 cm/km = 1.5 km.