Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Interpret and use different types of scales.
• Calculate actual distances using a scale factor.
• Estimate distances and sizes from maps and plans.
• Determine appropriate scales for creating maps.
• Solve practical problems involving scale.

Lesson summary

This week, we delve into the crucial topic of scale, maps, and plans. Understanding scale is essential for interpreting maps, architectural plans, and even models. In South Africa, this knowledge is vital for navigating our diverse landscapes, understanding urban planning initiatives, and making informed decisions about property and construction. Imagine planning a road trip from Cape Town to Johannesburg using a map – without understanding the scale, you could significantly miscalculate the travel time and distance! Similarly, understanding building plans is crucial if you're thinking of renovating your house or starting a small construction project.

Lesson notes

What is Scale? Scale is the ratio between the distance on a map, plan, or model and the corresponding distance on the ground or the real object. It allows us to represent large areas or objects on a smaller, manageable surface.

There are three main types of scales: Numerical Scale (Ratio Scale): This is expressed as a ratio, like 1:

5

0

0

0

0. This means that 1 unit of measurement on the map (e.g., 1 cm) represents 50000 of the same units on the ground (e.g., 50000 cm). Always ensure that you convert the units to the same measurement.

Word Scale (Verbal Scale): This is expressed in words, like "1 centimetre represents 5 kilometres". This clearly states the relationship between map distance and real-world distance.

Bar Scale (Graphic Scale): This is 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. Understanding the Numerical Scale (Ratio Scale): The numerical scale (e.g., 1:100) can be interpreted as follows: 1: This represents the distance on the map/plan. 100: This represents the corresponding distance in reality. The units must be the same. If the "1" represents 1 cm on the map, then the "100" represents 100 cm in reality.

Converting Units: It's crucial to be able to convert between different units of measurement: 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm Calculations with Scale: Finding the Actual Distance: Actual Distance = Map Distance x Scale Factor The scale factor is the second number in the ratio scale (e.g., in 1:50000, the scale factor is 50000).

Finding the Map Distance: Map Distance = Actual Distance / Scale Factor Finding the Scale: Scale = Map Distance : Actual Distance (Simplify this ratio to have "1" on the map side, e.g., 1:X). Ensure both distances are in the same unit.

Worked example

Example 1: Using a Numerical Scale

A map has a scale of 1:

2

5

0

0

0

0. Two towns are 8 cm apart on the map. What is the actual distance between the towns in kilometers?

Step 1: Identify the scale and map distance.

Scale: 1:250000

Map Distance: 8 cm

Step 2: Calculate the actual distance in centimeters.

Actual Distance (cm) = Map Distance x Scale Factor

Actual Distance (cm) = 8 cm x 250000 = 2000000 cm

Step 3: Convert centimeters to kilometers.

Actual Distance (km) = 2000000 cm / 100 cm/m / 1000 m/km = 20 km

Answer: The actual distance between the towns is 20 km.

Example 2: Using a Word Scale

A plan of a house has a scale of "1 cm represents 2 meters". A room is 4.5 cm long on the plan. What is the actual length of the room?

Step 1: Identify the scale and plan distance.

Scale: 1 cm represents 2 meters

Plan Distance: 4.5 cm

Step 2: Calculate the actual length.

Actual Length (m) = Plan Distance x Scale Factor (which is 2 in this case)

Actual Length (m) = 4.5 cm x 2 m/cm = 9 meters

Answer: The actual length of the room is 9 meters.