Lesson Notes By Weeks and Term v5 - Grade 10
Maps, plans and other representations of the physical world – Week 2 focus
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Maps, plans and other representations of the physical world – Week 2 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: 2
Theme: General lesson support
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This week, we continue our exploration of maps, plans, and other representations of the physical world. Last week, we focused on basic map reading and scale. This week, we will delve deeper into understanding different types of maps, interpreting more complex plans (like house plans), and most importantly, calculating distances and areas using map scales. This is a crucial skill for everyday life in South Africa. Whether you're planning a road trip from Johannesburg to Durban, understanding the layout of a new shopping mall in Cape Town, or helping your family build an extension to your home in a rural area, understanding maps and plans is essential.
2.1 Types of Maps and Plans Street Maps: These are designed for navigation within cities and towns. They show roads, streets, landmarks, and points of interest. Examples include Google Maps or printed maps provided by tourism agencies. Think of the maps of Johannesburg, Durban or Cape Town with roads and landmarks.
Topographic Maps: These maps represent the Earth's surface in three dimensions, showing elevation using contour lines. They are useful for hiking, engineering projects, and understanding the terrain of a region. They can be used for planning routes through mountainous regions of the Drakensberg.
Thematic Maps: These maps focus on specific themes or topics, such as population density, rainfall distribution, or economic activities. They visually represent statistical data across geographical areas. For example, a thematic map could show the unemployment rate in different provinces of South Africa.
House Plans: These detailed drawings show the layout of a house, including the location of walls, doors, windows, rooms, and fixtures. They are essential for building and renovating homes. A house plan will have dimensions for each room.
Site Plans: These plans show the layout of a property, including the location of the house, garage, driveway, garden, and other features. They provide a broader context than house plans. A site plan shows where the house sits on the property and relationships to other structures. 2.2 Map Scales A map scale is the ratio between a distance on a map and the corresponding distance on the ground. It is crucial for determining actual distances from a map.
Ratio Scale: Expressed as a ratio, such as 1:50,
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0. This means that 1 unit of measurement on the map represents 50,000 of the same units on the ground. For example, 1 cm on the map represents 50,000 cm (or 500 meters or 0.5 km) on the ground.
Bar Scale (Graphical Scale): A line or bar on the map divided into segments that represent specific distances on the ground. This is useful because it remains accurate even if the map is enlarged or reduced.
Word Scale: Expressed in words, such as "1 cm represents 1 km." 2.3 Calculating Actual Distances Example 1: Using a Ratio Scale A map has a scale of 1:25,
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0. The distance between two schools, Masedi High School and Thuto Primary School, measures 8 cm on the map. What is the actual distance between the schools?
Solution: Understand the scale: 1 cm on the map = 25,000 cm on the ground. Calculate the distance on the ground in cm: 8 cm (map) * 25,000 cm/cm (scale) = 200,000 cm Convert to a more useful unit (e.g., meters or kilometers): 200,000 cm / 100 cm/m = 2000 meters 2000 meters / 1000 meters/km = 2 km Therefore, the actual distance between the two schools is 2 km.
Example 2: Using a Bar Scale You have a map with a bar scale where 1 cm represents 5 km. You measure the distance between your house and the nearest clinic as 3.5 cm on the map. What is the actual distance?
Solution: Understand the bar scale: 1 cm on the map = 5 km on the ground.
Calculate the actual distance: 3.5 cm (map) * 5 km/cm (scale) = 17.5 km Therefore, the actual distance between your house and the clinic is 17.5 km. 2.4 Calculating Areas from Scaled Drawings Example 3: Calculating the Area of a Rectangular Garden from a Plan A rectangular garden is drawn on a plan with a scale of 1:
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0. On the plan, the garden measures 5 cm in length and 3 cm in width. What is the actual area of the garden in square meters?
Solution: Convert plan dimensions to actual dimensions: Actual length: 5 cm 100 = 500 cm = 5 meters Actual width: 3 cm 100 = 300 cm = 3 meters Calculate the actual area: Area = Length Width = 5 meters * 3 meters = 15 square meters Therefore, the actual area of the garden is 15 square meters.
Example 4: Estimating the Area of an Irregular Shape Imagine a dam shown on a map. It has an irregular shape. To estimate its area, you can overlay a grid (squares) on the map. Count the number of whole squares completely inside the dam's outline. Then, estimate the fraction of each partial square inside the dam. Sum the whole squares and estimated fractions to get the total number of squares covered. Then multiply by the area represented by each square (determined by the map scale) to estimate the total area of the dam. For example, if each square on the grid represents 100 square meters, and you counted approximately 50.5 squares inside the dam, the estimated area of the dam would be 50.5 * 100 = 5050 square meters. Guided Practice (With Solutions)
Question 1: A map has a scale of 1:50,
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0. Two towns, Springbok and Pofadder, are 6 cm apart on the map. What is the actual distance between the towns in kilometers?
Solution: Understand the scale: 1 cm on the map = 50,000 cm on the ground. Calculate the distance on the ground in cm: 6 cm * 50,000 cm/cm = 300,000 cm Convert to kilometers: 300,000 cm / 100 cm/m / 1000 m/km = 3 km Answer: The actual distance between Springbok and Pofadder is 3 km.