Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Determine real-world distances using map scales.
• Calculate real-world areas from plans and maps.
• Interpret map symbols and keys.
• Determine directions and bearings on maps.
• Understand the use of different map types.

Lesson summary

This week, we delve deeper into understanding and interpreting maps, plans, and other representations of the physical world. This is a crucial skill because it allows us to navigate our surroundings, understand spatial relationships, and make informed decisions about locations, distances, and areas. From planning a trip to a new kasi, understanding building layouts during a fire drill, or even budgeting for building materials for an extension to your home, these skills are directly applicable to everyday life in South Africa. Knowing how to interpret these representations empowers you to be more independent and informed citizens.

Lesson notes

2.1 Scale: Scale is the ratio between the distance on a map or plan and the corresponding distance on the ground. It allows us to represent large areas (like cities or countries) on a manageable piece of paper.

There are three main types of scales: Numerical Scale: Expressed as a ratio, e.g., 1:50,

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0. This means that 1 unit on the map represents 50,000 of the same units on the ground. If the unit is cm, then 1 cm on the map represents 50,000 cm (or 500 metres, or 0.5 km) in reality.

Bar Scale (Graphical Scale): A visual representation of the scale, usually a line divided into segments representing specific distances on the ground. This is useful because it remains accurate even if the map is enlarged or reduced.

Statement Scale (Word Scale): A verbal description of the scale, e.g., "1 cm represents 1 kilometre".

Example 1: Using a Numerical Scale A map has a scale of 1:20,

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0. Two points on the map are 5 cm apart. What is the actual distance between these points?

Solution: Scale: 1:20,000 Map Distance: 5 cm Real Distance = Map Distance Scale Factor Real Distance = 5 cm 20,000 = 100,000 cm Convert cm to metres: 100,000 cm / 100 cm/m = 1000 m Convert metres to kilometres: 1000 m / 1000 m/km = 1 km Therefore, the actual distance is 1 km.

Example 2: Using a Bar Scale Imagine a bar scale on a map. The bar is 4 cm long, and it is labelled as representing 2 km. If two locations are 10 cm apart on the map, what is the real-world distance?

Solution: Bar scale: 4 cm = 2 km This means 1cm = 2km/4 = 0.5km Map Distance: 10 cm Real Distance = Map Distance Scale Factor Since 1 cm represents 0.5 km, 10 cm represents 10 0.5 km = 5 km Therefore, the actual distance is 5 km. 2.2 Area Calculations: To calculate areas from maps or plans, we must first convert the dimensions using the map scale. Remember that the area scale is the square of the length scale.

Example 3: Calculating Area from a Plan A plan of a rectangular garden is drawn to a scale of 1:

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0. The length of the garden on the plan is 8 cm, and the width is 5 cm. Calculate the actual area of the garden in square metres.

Solution: Scale: 1:100 Length on plan: 8 cm Width on plan: 5 cm Actual length = 8 cm 100 = 800 cm = 8 m Actual width = 5 cm 100 = 500 cm = 5 m Area of rectangle = Length Width Area = 8 m 5 m = 40 square metres Therefore, the actual area of the garden is 40 m².

Example 4: Calculating Area of a Composite Shape A floor plan of a small house is drawn to a scale of 1:

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0. The house consists of a rectangular section that is 10 cm long and 8 cm wide on the plan, and a square section attached to it that is 4 cm by 4 cm on the plan. What is the total area of the house in square meters?

Solution: Scale: 1:50 Rectangular section length (plan): 10cm, Real length: 10cm 50 = 500 cm = 5m Rectangular section width (plan): 8cm, Real width: 8cm 50 = 400 cm = 4m Square section side (plan): 4cm, Real side: 4cm 50 = 200 cm = 2m Area of rectangular section: 5m 4m = 20 m^2 Area of square section: 2m 2m = 4 m^2 Total area: 20 m^2 + 4 m^2 = 24 m^2 The total area of the house is 24 m^2. 2.3 Map Symbols and Keys: Maps use symbols and keys to represent different features like rivers, roads, buildings, schools, hospitals, and other points of interest. The key or legend explains what each symbol represents. It is crucial to study the key before trying to interpret a map. Symbols can be pictorial (resembling the real-world feature) or abstract (geometric shapes or colors).

Example: A blue line might represent a river, a small red square might represent a building, and a green area might represent a park. 2.4 Directions and Bearings: Cardinal Directions: North (N), South (S), East (E), and West (W).

Ordinal Directions: Northeast (NE), Southeast (SE), Northwest (NW), and Southwest (SW).

Bearings: Angles measured clockwise from North. For example, a bearing of 90° is East, 180° is South, and 270° is West.

Example 5: Determining Direction On a map, a school is located northeast of a stadium. What direction is the stadium from the school?

Solution: If the school is northeast of the stadium, then the stadium is southwest of the school. Guided Practice (With Solutions)

Question 1: A street map has a scale of 1:10,

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0. On the map, the distance between your house and the nearest clinic is 7.5 cm. What is the actual distance in metres?

Solution: Scale: 1:10,000 Map distance: 7.5 cm Real distance = 7.5 cm 10,000 = 75,000 cm Convert to metres: 75,000 cm / 100 cm/m = 750 m Answer: The actual distance is 750 metres.

Question 2: A plan of a rectangular sports field is drawn to a scale of 1 cm = 5 m. The length of the field on the plan is 15 cm, and the width is 8 cm. Calculate the actual area of the sports field in square metres.

Solution: Scale: 1 cm = 5 m Length on plan: 15 cm Width on plan: 8 cm Actual length = 15 cm 5 m/cm = 75 m Actual width = 8 cm 5 m/cm = 40 m Area = Length Width = 75 m * 40 m = 3000 m² Answer: The actual area of the sports field is 3000 square metres.