Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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.

Performance objectives

• Use scales to calculate actual distances on maps and plans.
• Calculate map distances from real-world distances.
• Use maps to determine directions and orientation.
• Determine the area of irregular shapes using scale maps.
• Apply scale to solve real-life problems.

Lesson summary

This week, we delve into the practical application of measurement focusing on scales, maps, and plans. This is an incredibly important skill in Mathematical Literacy because it empowers you to understand and interpret representations of the world around you, from building plans for a new shack in your community to understanding the distances involved in a road trip across South Africa. Whether you’re planning a taxi route, calculating the amount of fencing needed for a garden, or interpreting floor plans for a potential new home, a solid understanding of scale, maps, and plans is essential. It allows you to make informed decisions and solve everyday problems effectively.

Lesson notes

What is Scale? Scale is the ratio that represents the relationship between a distance on a map, plan, or model and the corresponding distance in the real world. It tells us how much the real world has been reduced or enlarged to fit onto a smaller surface.

There are three main types of scales: Ratio Scale: This is expressed as a ratio, such as 1:100, 1:5000, or 1:

1

0

0

0

0

0. It means that one unit on the map or plan represents 100, 5000, or 100,000 units in reality, respectively. For example, a scale of 1:100 means 1 cm on the plan represents 100 cm (or 1 meter) in the real world.

Statement Scale: This describes the relationship in words, such as "1 cm represents 1 km" or "1 inch equals 5 miles". This is often found below the map or plan.

Bar Scale (or Graphical Scale): This is a visual representation of the scale using a line divided into segments, each representing a specific distance on the ground. You can directly measure distances on the map and compare them to the bar scale to find the corresponding real-world distance.

Understanding and Using Scale Ratios: The ratio scale is the most versatile. Let's break down how to use it.

Example 1: A map has a scale of 1:50,

0

0

0. The distance between two towns on the map is 8 cm. What is the actual distance between the towns?

Explanation: The scale 1:50,000 means 1 cm on the map represents 50,000 cm in reality.

Calculation: Actual distance = Map distance x Scale factor Actual distance = 8 cm x 50,000 Actual distance = 400,000 cm Convert cm to km: 400,000 cm / 100 cm/m / 1000 m/km = 4 km Answer: The actual distance between the towns is 4 km.

Example 2: The distance between Johannesburg and Pretoria is approximately 60 km. On a map, this distance is represented by 6 cm. What is the scale of the map?

Explanation: We need to find the ratio between the map distance and the real-world distance.

Calculation: First, convert both distances to the same unit, preferably cm: Real distance: 60 km x 1000 m/km x 100 cm/m = 6,000,000 cm Scale = Map distance : Real distance Scale = 6 cm : 6,000,000 cm Simplify the ratio by dividing both sides by 6: Scale = 1 : 1,000,000 Answer: The scale of the map is 1:1,000,

0

0

0. Using Bar Scales: Bar scales are straightforward. Simply measure the distance on the map and then compare it to the bar scale to read off the corresponding real-world distance.

Example 3: A map has a bar scale where 1 cm on the bar represents 5 km. The distance between two points on the map measures 3.5 cm when you use a ruler. What is the real-world distance?

Explanation: Each centimeter on the map represents 5 km, as depicted by the bar scale.

Calculation: Real distance = Map distance x Distance represented by 1 cm on the bar scale. Real distance = 3.5 cm 5 km/cm Real distance = 17.5 km Answer: The actual distance between the two points is 17.5 km.

Direction and Orientation: Maps are usually oriented with North at the top. A compass rose (or north arrow) is often included to indicate the direction of North. You can use this to determine the direction from one location to another.

Remember the cardinal directions: North, South, East, and West. You can also use intermediate directions like Northeast, Southeast, Northwest, and Southwest.

Area Calculation using Scale Maps: If you need to find the area of a region on a map, you need to account for the scale. First, find the area on the map. Then, square the scale factor and multiply it by the area on the map.

Example 4: A farmer owns a piece of land represented on a map with a scale of 1:10,

0

0

0. The area of the land on the map is 50 cm². What is the actual area of the land in hectares?

Explanation: The scale is 1:10,000, meaning the scale factor is 10,

0

0

0. We need to square this to find the area scale factor.

Calculation: Area scale factor = (10,000)² = 100,000,000 Actual area in cm² = Map area x Area scale factor Actual area in cm² = 50 cm² x 100,000,000 Actual area in cm² = 5,000,000,000 cm² Convert cm² to m²: 5,000,000,000 cm² / (100 cm/m)² = 500,000 m² Convert m² to hectares: 500,000 m² / 10,000 m²/hectare = 50 hectares Answer: The actual area of the land is 50 hectares. Guided Practice (With Solutions)

Question 1: A building plan uses a scale of 1:

5

0. The length of a wall on the plan is 12 cm. What is the actual length of the wall in meters?

Solution: Scale: 1:50 (1 cm on plan = 50 cm in reality)

Plan length: 12 cm Actual length in cm: 12 cm x 50 = 600 cm Actual length in meters: 600 cm / 100 cm/m = 6 meters Answer: The actual length of the wall is 6 meters.

Question 2: On a map with a scale of 1:250,000, two cities are 15 cm apart. What is the actual distance between the cities in kilometers?

Solution: Scale: 1:250,000 (1 cm on map = 250,000 cm in reality)

Map distance: 15 cm Actual distance in cm: 15 cm x 250,000 = 3,750,000 cm Actual distance in km: 3,750,000 cm / 100 cm/m / 1000 m/km = 37.5 km Answer: The actual distance between the cities is 37.5 kilometers.