Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate real-world distances using map scales.
• Interpret map symbols and keys.
• Determine the actual area of features on maps.
• Use grid references to locate places.
• Calculate ratios of map distance to actual distance.

Lesson summary

This week, we'll delve deeper into maps, plans, and other representations of the physical world, building upon the foundational knowledge you've already acquired. This is a crucial skill, especially in South Africa, where navigating diverse landscapes, understanding urban development plans, and interpreting building layouts are essential for daily life and future career opportunities. Imagine trying to give directions to a taxi driver in a rural area, understanding the layout of a shopping mall in Sandton, or interpreting the architectural plans for a new RDP house - all of these rely on your ability to work with maps and plans.

Lesson notes

Scale: Scale is the ratio between a distance on a map or plan and the corresponding distance on the ground. It's crucial for converting measurements between the map and reality.

There are three main types of scales: Numerical Scale (Representative Fraction - RF): Expressed as a ratio, e.g., 1:50,

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0. This means 1 unit on the map represents 50,000 of the same units on the ground. It's unitless, so it works with any unit of measurement (cm, mm, inches, etc.) as long as both sides of the ratio use the same unit.

Statement Scale (Verbal Scale): Expressed in words, e.g., "1 cm represents 1 kilometer." This is straightforward and easy to understand.

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

Distance Calculation: Using Numerical Scale: If the scale is 1:100,000 and you measure a distance of 5 cm on the map, the actual distance is 5 cm 100,000 = 500,000 cm. To convert to kilometers, divide by 100,000 (since 1 km = 100,000 cm): 500,000 cm / 100,000 = 5 km.

Using Statement Scale: If the scale is "1 cm represents 2 km" and the distance on the map is 3.5 cm, the actual distance is 3.5 cm 2 km/cm = 7 km.

Using Bar Scale: Measure the distance on the map using a ruler. Then, compare this distance to the bar scale to determine the corresponding ground distance.

Area Calculation: To calculate the actual area represented on a map, you need to square the scale factor.

If the scale is 1:500, the scale factor is

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0. If you measure an area of 10 cm² on the map, the actual area is 10 cm² (500)² = 10 cm² * 250,000 = 2,500,000 cm². To convert to m², divide by (100)² = 10,000 (since 1 m = 100 cm and we are dealing with area, so we square the conversion factor): 2,500,000 cm² / 10,000 = 250 m². To convert to hectares, divide by 10,000 again (since 1 hectare = 10,000 m²): 250 m² / 10,000 = 0.025 hectares.

Map Symbols and Keys: Maps use symbols to represent real-world features like roads, buildings, rivers, mountains, and vegetation. A map key (or legend) explains what each symbol represents.

Grid References (Coordinates): Maps often use a grid system to locate specific points. This can be alphanumeric (e.g., A1, B3) or numerical (e.g., latitude and longitude).

Alphanumeric Grids: Look for the letter and number corresponding to the point you want to locate. Be careful to read them in the correct order (e.g., letter first, then number).

Latitude and Longitude: Latitude lines run horizontally (east-west) and measure distance north or south of the equator. Longitude lines run vertically (north-south) and measure distance east or west of the Prime Meridian.

Examples: Example 1: Distance Calculation (Numerical Scale) A map of Kruger National Park has a scale of 1:250,

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0. The distance between Skukuza and Satara on the map measures 12 cm. What is the actual distance between these two camps?

Solution: Actual distance = Map distance Scale factor = 12 cm * 250,000 = 3,000,000 cm.

Converting to kilometers: 3,000,000 cm / 100,000 cm/km = 30 km.

Example 2: Area Calculation A farmer wants to determine the size of his rectangular field.

On a plan with a scale of 1:1000, the field measures 8 cm long and 5 cm wide. What is the actual area of the field in square meters?

Solution:* Map length = 8 cm, Map width = 5 cm Actual length = 8 cm 1000 = 8000 cm = 80 m Actual width = 5 cm 1000 = 5000 cm = 50 m Area = length width = 80 m * 50 m = 4000 m² Example 3: Interpreting Map Symbols A map of Cape Town shows a blue line with the label "Liesbeek River". According to the map key, a blue line represents a river.

Therefore, you know that the Liesbeek River flows through Cape Town.

Example 4: Grid References A map uses an alphanumeric grid. The location of the Union Buildings in Pretoria is marked as D

5. This means the Union Buildings are located in the square where grid line D intersects with grid line

5. Guided Practice (With Solutions)

Question 1: A map has a scale of 1 cm = 5 km. Two towns are 7.5 cm apart on the map. What is the actual distance between the towns?

Solution: Actual distance = 7.5 cm 5 km/cm = 37.5 km.

Commentary: This is a straightforward application of the statement scale. Make sure to include the units in your answer.

Question 2: On a plan with a scale of 1:200, a rectangular swimming pool measures 4 cm by 2.5 cm. Calculate the actual area of the swimming pool in square meters.

Solution:* Map length = 4 cm, Map width = 2.5 cm Actual length = 4 cm 200 = 800 cm = 8 m Actual width = 2.5 cm 200 = 500 cm = 5 m Area = length width = 8 m * 5 m = 40 m²

Commentary: Remember to convert the measurements from centimeters to meters before calculating the area.

Question 3: A map of Johannesburg uses the following symbols: a filled circle for schools, a star for hospitals, and a small house icon for residential areas. You see a star symbol near Parktown.