Gr 11 Math Lit: Ch 4 Sum Maps, Plans and other Representations

Maps, Plans, and Representations

National Road Maps

• Show major routes, roads, and distances between major cities and towns in South Africa
• Skills:
  • Decide on the most appropriate route between destinations
  • Estimate traveling costs and times
  • Plan stopping points for accommodation, breaks, or refueling
  • Use distance tables to determine distances

Strip Charts

• Show locations of towns, other roads, and points of interest on a specific route
• Skills:
  • Determine more accurate traveling distances on specific sections of a route
  • Decide on appropriate stopping points for refueling or breaks
  • Estimate traveling costs and times
  • Use distance markers and indicators on the chart

Street Maps

• Show positions and names of streets and other locations within a city
• Skills:
  • Identify locations using symbols
  • Follow and provide directions using street names and directional indicators (e.g., left, right)
  • Use a grid reference system with the street index to find specific streets

Housing Complex Maps

• Show positions of houses within a small housing complex
• Skills:
  • Work with a map that shows a small area with limited detail
  • Follow and describe directions to a specific location within the complex

Using Scales

• Use the given scale to estimate traveling distances when a distance table or distance markers are not provided
• Two types of scale calculations:
  • Type 1: Map Measurement to Actual Distance
    • Measure a distance on a map
    • Use the given scale to convert this measurement to the actual distance
    • Formula: Actual Distance = Map Measurement × Scale Factor
  • Type 2: Actual Distance to Map Measurement
    • Start with a known actual distance
    • Use the given scale to convert this actual distance to the map measurement
    • Formula: Map Measurement = Actual Distance ÷ Scale Factor

Types of Scales

Number Scale

• Expressed in the format 1:50,000
• Conversion is straightforward: enlarge or reduce by the scale factor
• A number scale shows a specific relationship between the size of the area on the map and the actual size of that area

Bar Scale

• Shows the relationship between measured length and actual distance
• Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
• Different from a number scale in that it does not state how many times smaller the map is from the actual size, but rather how many measured units are equal to a specific number of actual units

Building Plans

Key Concepts

• Floor Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
  • Purpose: To see the design and dimensions of the inside of a building or structure
  • Visible Features: Dimensions and layout of the inside of the building, including lengths and widths of the building, windows, and doors
• Elevation Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from the side
  • Purpose: To see the design and dimensions of the outside of a building or structure
  • Visible Features: Dimensions and layout of the outside of the building, including the design of the roof, walls, windows, and doors
• Design Drawing:
  • Function: Shows the design, layout, and components of an item to be constructed or manufactured
  • Purpose: To see what a completed item will look like and the dimensions of its parts
  • Visible Features: The design plan shows the different component parts, dimensions of these parts, and specific instructions on how they should look

Key Concepts for Working with Plans

• Describe features of a building/structure
• Match features between plans
• Understand compass directions
• Use scale to determine dimensions

Design Drawings

• Describe the item/object shown on the design plan
• Identify the dimensions of the item/object
• Describe the different component parts required to make the item/object
• Identify a cutting list of parts needed to make the item/object

Key Concepts for Design Drawings

• Describe the item/object
• Identify dimensions
• Describe component parts
• Cutting list

Drawing Scaled Plans

• Calculate plan measure from actual dimension
• Formula: Plan Measure = Actual Dimension ÷ Scale Factor
• Use the given scale to reduce the actual measurement proportionately

Models

Key Skills and Objectives

• Build 3D models from 2D plans/nets
• Draw 2D plans/nets of 3D models
• Use models to investigate various problems

Purpose

• Facilitate the movement between 2D and 3D representations of objects

Process

• Understanding 2D plans/nets
• Building 3D models
• Drawing 2D plans/nets

Assembling

Key Concepts and Skills

• Understand instructions
• Gather materials and tools
• Measure and cut
• Estimate quantities and costs
• Calculate time
• Follow steps in sequence
• Check and adjust
• Use mathematical tools and techniques

Steps to Assemble Components

• Interpret instructions
• Prepare materials and tools
• Measure accurately
• Cut materials as needed
• Estimate quantities and costs
• Estimate time
• Follow the sequence
• Check and adjust
• Complete the assembly

Maps, Plans, and Representations

National Road Maps

• Show major routes, roads, and distances between major cities and towns in South Africa
• Skills:
  • Decide on the most appropriate route between destinations
  • Estimate traveling costs and times
  • Plan stopping points for accommodation, breaks, or refueling
  • Use distance tables to determine distances

Strip Charts

• Show locations of towns, other roads, and points of interest on a specific route
• Skills:
  • Determine more accurate traveling distances on specific sections of a route
  • Decide on appropriate stopping points for refueling or breaks
  • Estimate traveling costs and times
  • Use distance markers and indicators on the chart

Street Maps

• Show positions and names of streets and other locations within a city
• Skills:
  • Identify locations using symbols
  • Follow and provide directions using street names and directional indicators (e.g., left, right)
  • Use a grid reference system with the street index to find specific streets

Housing Complex Maps

• Show positions of houses within a small housing complex
• Skills:
  • Work with a map that shows a small area with limited detail
  • Follow and describe directions to a specific location within the complex

Using Scales

• Use the given scale to estimate traveling distances when a distance table or distance markers are not provided
• Two types of scale calculations:
  • Type 1: Map Measurement to Actual Distance
    • Measure a distance on a map
    • Use the given scale to convert this measurement to the actual distance
    • Formula: Actual Distance = Map Measurement × Scale Factor
  • Type 2: Actual Distance to Map Measurement
    • Start with a known actual distance
    • Use the given scale to convert this actual distance to the map measurement
    • Formula: Map Measurement = Actual Distance ÷ Scale Factor

Types of Scales

Number Scale

• Expressed in the format 1:50,000
• Conversion is straightforward: enlarge or reduce by the scale factor
• A number scale shows a specific relationship between the size of the area on the map and the actual size of that area

Bar Scale

• Shows the relationship between measured length and actual distance
• Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
• Different from a number scale in that it does not state how many times smaller the map is from the actual size, but rather how many measured units are equal to a specific number of actual units

Building Plans

Key Concepts

• Floor Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
  • Purpose: To see the design and dimensions of the inside of a building or structure
  • Visible Features: Dimensions and layout of the inside of the building, including lengths and widths of the building, windows, and doors
• Elevation Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from the side
  • Purpose: To see the design and dimensions of the outside of a building or structure
  • Visible Features: Dimensions and layout of the outside of the building, including the design of the roof, walls, windows, and doors
• Design Drawing:
  • Function: Shows the design, layout, and components of an item to be constructed or manufactured
  • Purpose: To see what a completed item will look like and the dimensions of its parts
  • Visible Features: The design plan shows the different component parts, dimensions of these parts, and specific instructions on how they should look

Key Concepts for Working with Plans

• Describe features of a building/structure
• Match features between plans
• Understand compass directions
• Use scale to determine dimensions

Design Drawings

• Describe the item/object shown on the design plan
• Identify the dimensions of the item/object
• Describe the different component parts required to make the item/object
• Identify a cutting list of parts needed to make the item/object

Key Concepts for Design Drawings

• Describe the item/object
• Identify dimensions
• Describe component parts
• Cutting list

Drawing Scaled Plans

• Calculate plan measure from actual dimension
• Formula: Plan Measure = Actual Dimension ÷ Scale Factor
• Use the given scale to reduce the actual measurement proportionately

Models

Key Skills and Objectives

• Build 3D models from 2D plans/nets
• Draw 2D plans/nets of 3D models
• Use models to investigate various problems

Purpose

• Facilitate the movement between 2D and 3D representations of objects

Process

• Understanding 2D plans/nets
• Building 3D models
• Drawing 2D plans/nets

Assembling

Key Concepts and Skills

• Understand instructions
• Gather materials and tools
• Measure and cut
• Estimate quantities and costs
• Calculate time
• Follow steps in sequence
• Check and adjust
• Use mathematical tools and techniques

Steps to Assemble Components

• Interpret instructions
• Prepare materials and tools
• Measure accurately
• Cut materials as needed
• Estimate quantities and costs
• Estimate time
• Follow the sequence
• Check and adjust
• Complete the assembly

Maps, Plans, and Representations

National Road Maps

• Show major routes, roads, and distances between major cities and towns in South Africa
• Skills:
  • Decide on the most appropriate route between destinations
  • Estimate traveling costs and times
  • Plan stopping points for accommodation, breaks, or refueling
  • Use distance tables to determine distances

Strip Charts

• Show locations of towns, other roads, and points of interest on a specific route
• Skills:
  • Determine more accurate traveling distances on specific sections of a route
  • Decide on appropriate stopping points for refueling or breaks
  • Estimate traveling costs and times
  • Use distance markers and indicators on the chart

Street Maps

• Show positions and names of streets and other locations within a city
• Skills:
  • Identify locations using symbols
  • Follow and provide directions using street names and directional indicators (e.g., left, right)
  • Use a grid reference system with the street index to find specific streets

Housing Complex Maps

• Show positions of houses within a small housing complex
• Skills:
  • Work with a map that shows a small area with limited detail
  • Follow and describe directions to a specific location within the complex

Using Scales

• Use the given scale to estimate traveling distances when a distance table or distance markers are not provided
• Two types of scale calculations:
  • Type 1: Map Measurement to Actual Distance
    • Measure a distance on a map
    • Use the given scale to convert this measurement to the actual distance
    • Formula: Actual Distance = Map Measurement × Scale Factor
  • Type 2: Actual Distance to Map Measurement
    • Start with a known actual distance
    • Use the given scale to convert this actual distance to the map measurement
    • Formula: Map Measurement = Actual Distance ÷ Scale Factor

Types of Scales

Number Scale

• Expressed in the format 1:50,000
• Conversion is straightforward: enlarge or reduce by the scale factor
• A number scale shows a specific relationship between the size of the area on the map and the actual size of that area

Bar Scale

• Shows the relationship between measured length and actual distance
• Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
• Different from a number scale in that it does not state how many times smaller the map is from the actual size, but rather how many measured units are equal to a specific number of actual units

Building Plans

Key Concepts

• Floor Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
  • Purpose: To see the design and dimensions of the inside of a building or structure
  • Visible Features: Dimensions and layout of the inside of the building, including lengths and widths of the building, windows, and doors
• Elevation Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from the side
  • Purpose: To see the design and dimensions of the outside of a building or structure
  • Visible Features: Dimensions and layout of the outside of the building, including the design of the roof, walls, windows, and doors
• Design Drawing:
  • Function: Shows the design, layout, and components of an item to be constructed or manufactured
  • Purpose: To see what a completed item will look like and the dimensions of its parts
  • Visible Features: The design plan shows the different component parts, dimensions of these parts, and specific instructions on how they should look

Key Concepts for Working with Plans

• Describe features of a building/structure
• Match features between plans
• Understand compass directions
• Use scale to determine dimensions

Design Drawings

• Describe the item/object shown on the design plan
• Identify the dimensions of the item/object
• Describe the different component parts required to make the item/object
• Identify a cutting list of parts needed to make the item/object

Key Concepts for Design Drawings

• Describe the item/object
• Identify dimensions
• Describe component parts
• Cutting list

Drawing Scaled Plans

• Calculate plan measure from actual dimension
• Formula: Plan Measure = Actual Dimension ÷ Scale Factor
• Use the given scale to reduce the actual measurement proportionately

Models

Key Skills and Objectives

• Build 3D models from 2D plans/nets
• Draw 2D plans/nets of 3D models
• Use models to investigate various problems

Purpose

• Facilitate the movement between 2D and 3D representations of objects

Process

• Understanding 2D plans/nets
• Building 3D models
• Drawing 2D plans/nets

Assembling

Key Concepts and Skills

• Understand instructions
• Gather materials and tools
• Measure and cut
• Estimate quantities and costs
• Calculate time
• Follow steps in sequence
• Check and adjust
• Use mathematical tools and techniques

Steps to Assemble Components

• Interpret instructions
• Prepare materials and tools
• Measure accurately
• Cut materials as needed
• Estimate quantities and costs
• Estimate time
• Follow the sequence
• Check and adjust
• Complete the assembly

Maps, Plans, and Representations

National Road Maps

• Show major routes, roads, and distances between major cities and towns in South Africa
• Skills:
  • Decide on the most appropriate route between destinations
  • Estimate traveling costs and times
  • Plan stopping points for accommodation, breaks, or refueling
  • Use distance tables to determine distances

Strip Charts

• Show locations of towns, other roads, and points of interest on a specific route
• Skills:
  • Determine more accurate traveling distances on specific sections of a route
  • Decide on appropriate stopping points for refueling or breaks
  • Estimate traveling costs and times
  • Use distance markers and indicators on the chart

Street Maps

• Show positions and names of streets and other locations within a city
• Skills:
  • Identify locations using symbols
  • Follow and provide directions using street names and directional indicators (e.g., left, right)
  • Use a grid reference system with the street index to find specific streets

Housing Complex Maps

• Show positions of houses within a small housing complex
• Skills:
  • Work with a map that shows a small area with limited detail
  • Follow and describe directions to a specific location within the complex

Using Scales

• Use the given scale to estimate traveling distances when a distance table or distance markers are not provided
• Two types of scale calculations:
  • Type 1: Map Measurement to Actual Distance
    • Measure a distance on a map
    • Use the given scale to convert this measurement to the actual distance
    • Formula: Actual Distance = Map Measurement × Scale Factor
  • Type 2: Actual Distance to Map Measurement
    • Start with a known actual distance
    • Use the given scale to convert this actual distance to the map measurement
    • Formula: Map Measurement = Actual Distance ÷ Scale Factor

Types of Scales

Number Scale

• Expressed in the format 1:50,000
• Conversion is straightforward: enlarge or reduce by the scale factor
• A number scale shows a specific relationship between the size of the area on the map and the actual size of that area

Bar Scale

• Shows the relationship between measured length and actual distance
• Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
• Different from a number scale in that it does not state how many times smaller the map is from the actual size, but rather how many measured units are equal to a specific number of actual units

Building Plans

Key Concepts

• Floor Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
  • Purpose: To see the design and dimensions of the inside of a building or structure
  • Visible Features: Dimensions and layout of the inside of the building, including lengths and widths of the building, windows, and doors
• Elevation Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from the side
  • Purpose: To see the design and dimensions of the outside of a building or structure
  • Visible Features: Dimensions and layout of the outside of the building, including the design of the roof, walls, windows, and doors
• Design Drawing:
  • Function: Shows the design, layout, and components of an item to be constructed or manufactured
  • Purpose: To see what a completed item will look like and the dimensions of its parts
  • Visible Features: The design plan shows the different component parts, dimensions of these parts, and specific instructions on how they should look

Key Concepts for Working with Plans

• Describe features of a building/structure
• Match features between plans
• Understand compass directions
• Use scale to determine dimensions

Design Drawings

• Describe the item/object shown on the design plan
• Identify the dimensions of the item/object
• Describe the different component parts required to make the item/object
• Identify a cutting list of parts needed to make the item/object

Key Concepts for Design Drawings

• Describe the item/object
• Identify dimensions
• Describe component parts
• Cutting list

Drawing Scaled Plans

• Calculate plan measure from actual dimension
• Formula: Plan Measure = Actual Dimension ÷ Scale Factor
• Use the given scale to reduce the actual measurement proportionately

Models

Key Skills and Objectives

• Build 3D models from 2D plans/nets
• Draw 2D plans/nets of 3D models
• Use models to investigate various problems

Purpose

• Facilitate the movement between 2D and 3D representations of objects

Process

• Understanding 2D plans/nets
• Building 3D models
• Drawing 2D plans/nets

Assembling

Key Concepts and Skills

• Understand instructions
• Gather materials and tools
• Measure and cut
• Estimate quantities and costs
• Calculate time
• Follow steps in sequence
• Check and adjust
• Use mathematical tools and techniques

Steps to Assemble Components

• Interpret instructions
• Prepare materials and tools
• Measure accurately
• Cut materials as needed
• Estimate quantities and costs
• Estimate time
• Follow the sequence
• Check and adjust
• Complete the assembly

Maps, Plans, and Representations

National Road Maps

• Show major routes, roads, and distances between major cities and towns in South Africa
• Skills:
  • Decide on the most appropriate route between destinations
  • Estimate traveling costs and times
  • Plan stopping points for accommodation, breaks, or refueling
  • Use distance tables to determine distances

Strip Charts

• Show locations of towns, other roads, and points of interest on a specific route
• Skills:
  • Determine more accurate traveling distances on specific sections of a route
  • Decide on appropriate stopping points for refueling or breaks
  • Estimate traveling costs and times
  • Use distance markers and indicators on the chart

Street Maps

• Show positions and names of streets and other locations within a city
• Skills:
  • Identify locations using symbols
  • Follow and provide directions using street names and directional indicators (e.g., left, right)
  • Use a grid reference system with the street index to find specific streets

Housing Complex Maps

• Show positions of houses within a small housing complex
• Skills:
  • Work with a map that shows a small area with limited detail
  • Follow and describe directions to a specific location within the complex

Using Scales

• Use the given scale to estimate traveling distances when a distance table or distance markers are not provided
• Two types of scale calculations:
  • Type 1: Map Measurement to Actual Distance
    • Measure a distance on a map
    • Use the given scale to convert this measurement to the actual distance
    • Formula: Actual Distance = Map Measurement × Scale Factor
  • Type 2: Actual Distance to Map Measurement
    • Start with a known actual distance
    • Use the given scale to convert this actual distance to the map measurement
    • Formula: Map Measurement = Actual Distance ÷ Scale Factor

Types of Scales

Number Scale

• Expressed in the format 1:50,000
• Conversion is straightforward: enlarge or reduce by the scale factor
• A number scale shows a specific relationship between the size of the area on the map and the actual size of that area

Bar Scale

• Shows the relationship between measured length and actual distance
• Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
• Different from a number scale in that it does not state how many times smaller the map is from the actual size, but rather how many measured units are equal to a specific number of actual units

Building Plans

Key Concepts

• Floor Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
  • Purpose: To see the design and dimensions of the inside of a building or structure
  • Visible Features: Dimensions and layout of the inside of the building, including lengths and widths of the building, windows, and doors
• Elevation Plan:
  • Function: Shows a 2-dimensional perspective of a building or structure as seen from the side
  • Purpose: To see the design and dimensions of the outside of a building or structure
  • Visible Features: Dimensions and layout of the outside of the building, including the design of the roof, walls, windows, and doors
• Design Drawing:
  • Function: Shows the design, layout, and components of an item to be constructed or manufactured
  • Purpose: To see what a completed item will look like and the dimensions of its parts
  • Visible Features: The design plan shows the different component parts, dimensions of these parts, and specific instructions on how they should look

Key Concepts for Working with Plans

• Describe features of a building/structure
• Match features between plans
• Understand compass directions
• Use scale to determine dimensions

Design Drawings

• Describe the item/object shown on the design plan
• Identify the dimensions of the item/object
• Describe the different component parts required to make the item/object
• Identify a cutting list of parts needed to make the item/object

Key Concepts for Design Drawings

• Describe the item/object
• Identify dimensions
• Describe component parts
• Cutting list

Drawing Scaled Plans

• Calculate plan measure from actual dimension
• Formula: Plan Measure = Actual Dimension ÷ Scale Factor
• Use the given scale to reduce the actual measurement proportionately

Models

Key Skills and Objectives

• Build 3D models from 2D plans/nets
• Draw 2D plans/nets of 3D models
• Use models to investigate various problems

Purpose

• Facilitate the movement between 2D and 3D representations of objects

Process

• Understanding 2D plans/nets
• Building 3D models
• Drawing 2D plans/nets

Assembling

Key Concepts and Skills

• Understand instructions
• Gather materials and tools
• Measure and cut
• Estimate quantities and costs
• Calculate time
• Follow steps in sequence
• Check and adjust
• Use mathematical tools and techniques

Steps to Assemble Components

• Interpret instructions
• Prepare materials and tools
• Measure accurately
• Cut materials as needed
• Estimate quantities and costs
• Estimate time
• Follow the sequence
• Check and adjust
• Complete the assembly

Test your skills in reading and interpreting national road maps and strip charts, including determining routes, estimating travel costs, and planning stops. Learn how to use distance tables and identify locations on a specific route.