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