MATHEMATICAL LITERACY GRADE 12 CAPS TOPIC 3 Maps

*MATHEMATICAL LITERACY GRADE 12 CAPS TOPIC 3: Maps, plans and other representations of the physical world Section 3. 4: Plans (floor, elevation and design plans)

*Topic 3: Maps, plans and other representations of the physical world. The following sections will be covered: 3. 1. Scale 3. 2. 1 Map Work(1) 3. 2. 2 Map Work(2) 3. 3 Compass Directions 3. 4. Plans (floor, elevation and design plans) 3. 5. Models

*Section 3. 4: Plans *In section 3. 4, learners will be able to: ØInterpret elevation of buildings that include the words ‘North Elevation’, ‘South Elevation’, ‘East Elevation’ and ‘West Elevation’ and match features on the plan. ØWork with floor plans and assembly diagrams. ØWork with the scale on a plan and to find actual lengths. ØDraw scaled elevation plans and use them to calculate measurements and costs ØWork out the quantities of materials needed based on a plan.

*Interpreting Plans 1. A Floor Plan: shows a top view of a building, without the roof. It gives the layout of the inside of the building and the position of rooms, windows, doors and other features inside the building. Dimensions of the lengths and widths, but not heights, of various features are visible. Figure 1 on the next slide shows the floor plan of an RDP house.

*Interpreting Plans(RDP house design).

*Interpreting Plans 2. Elevation Plans: show a side view of a building as seen from the outside. They show the design of the outside walls, the position of windows and doors in those walls, and the design of the roof. Dimensions of the lengths and heights, but not widths, of various features are also visible. The labels ‘North’, ‘South’, ‘East’ and ‘West’ elevation show the compass direction that the side of the building faces. This is important for determining the position of different sides of the house in relation to the sun at different times of the day. This concept was covered in section 3. 3 of this topic.

*Elevation Plans(RDP House) *Consider the different elevations of the RDP House on the next two slides.

*Elevation Plans(RDP House)

*Activity: 1 Use the floor plan and the elevation plans of the RDP House on the previous slides to answer the following questions. 1. How many bedrooms are there in this house? 2. Are the bedrooms the same size? 3. The units of the dimensions are not given. Give a reason why they cannot be in cm. 4. Write down the dimensions (length and breadth) of the outside of the house with the correct units. 5. How many external doors are there? An external door leads to the outside of the house.

*Activity: 1 6. How many windows does this house have? 7. Are there going to be any windows in the south elevation? Give a reason for your answer. 8. Why is the elevation that is not shown called the south elevation? Refer to the compass on the floor plan in your answer. 9. How many doors will the south elevation have? Give a reason for your answer. 10. Will the south elevation have a wall with a point on top or will it be a wall with a flat top? Give a reason for your answer.

*Activity: 1 11. Looking at the west elevation, it seems as if there is a piece of the roof missing. Explain the shape of the roof using the plans and pictures of the house. 12. Does this house have a flat roof? Where can we see this in the plans? 13. Are the floor plan and the elevation plans drawn to the same scale? Give a reason for your answer.

* Solutions : Activity 1 1. 2 bedrooms 2. No. 3. If they were in cm, the measurements would all be too small to a real sized house. 4. Length = 700 cm (7 m), breadth = 620 cm (6, 2 m) 5. Two (2) 6. Five (5) 7. No. There are no windows indicated on the plan. 8. This will be the view you will see when you are facing a southerly direction.

* Solutions : Activity 1 9. One(1). There is only one door indicated on the plan. 10. It will be a pointed wall because the opposite wall(north elevation) has a pointed wall for the pitched roof. 11. The front portion does not have a roof on it because there is no room to cover. The one side of the building is longer than the other and so there is no room to cover on the shorter side. 12. No. We can see from the north elevation that the roof is a pitched roof and not a flat roof. 13. No. If we measure the width of the building in the north elevation and the front of the building in the floor plan, we can see that they are different. If they were in the same scale they would have the same measurement.

*Determining the scale in which a plan has been drawn. Scale determines how many times smaller or bigger an object shown on a plan is than its actual size. It does not matter which measurement we use to determine the scale as they will all have been shrunken or enlarged by exactly the same ratio. NB: Scale was dealt with in section 3. 1.

*Example: 1 Below is the north elevation of the RDP House. Determine the scale that was used to draw the elevation plan.

*Example: 1 Step 1: measure with ruler a dimension whose actual size is known. The height of the side of the house measures 2, 25 cm. Step 2: equate the measured length and the actual length by writing them as a ratio. Write the measured length first: 2, 25 cm : 2, 7 m. Step 3: convert both measurements to the same units: 2, 25 cm: 270 cm Step 4: to obtain the required scale in the form 1 : n, you divide both sides of the ratio by 2, 25 cm. Therefore, the accurate and appropriate number scale for this elevation is 1 : 120.

*Work with floor plans and assembly diagrams: Activity: 2

*Activity 2 1. The following questions refer to the floor plan of the flat on the previous slide. a) What does the plan show? b) Estimate the total floor area of the flat. c) How many windows are there in the flat? d) Does the floor door open inwards or outwards? e) What furniture and fittings are shown on the plan? f) When walk into this flat, what will you see?

*Solutions: Activity 2 a) The floor plan of a single bedroom flat. b) Answers will differ. c) Two windows. d) Inwards. e) Bath, toilet, sink and fittings, kitchen sink, oven, fridge. f) When you enter the flat, you will see the kitchen on the left, the living room straight ahead, with the bedroom to the right of the living room. The bathroom is on the right.

*Activity: 3

* Activity: 3 The diagram on the previous slide shows the layout of office space in a small company. 1. The office is 12 m long and 6 m wide. Use those dimensions and a scale of 1 : 80 to draw a flat floor plan showing the shape of the office and the position of the doors and windows. 2. The office spaces are open plan and they are separated from each other by moveable partitions. Estimate the length of these partitions and draw them on your plan.

* Activity: 3 3. Estimate the dimensions of the L-shaped desks , single and double filing cabinets and the space occupied by a chair. Show all your working. 4. Add the furniture and partitions to your plan. 5. A work space consists of an L-shaped desk, a single filing cabinet and a chair. Could you fit another work space into the office? Suggest how you would do this and draw a rough plan to show you would reorganise the space and where you would put the additional work space.

*Solutions: Activity 3

*Solutions: Activity 3 3. Filing cabinet Length: 6 mm ÷ 90 mm x 12 000 mm = 800 mm long. Width: 3, 5 mm ÷ 90 mm x 12 000 mm = 467 mm wide. L-shaped desk Length: 12 mm ÷ 90 mm x 12 000 mm = 1 600 mm long. Width: 3, 5 mm ÷ 90 mm x 12 000 mm = 1 067 mm wide. Chair 5 mm ÷ 90 mm x 12 000 mm = 667 mm A chair occupies a space of 667 mm x 667 mm.

*Solutions: Activity 3

*Solutions: Activity 3 5. Answers will differ. See example below:

*Drawing scaled elevation plans. You already know how to draw an accurate , scaled drawing. To draw an elevation plan, you work in the same way, but you have to think about the view that you are drawing, what shape it will be and which features you will show on the elevation. EXAMPLE 2: Patrice drew a sketch of his north-facing garden shed. He marked the dimensions on the sketch as shown on the diagram on the next slide. Use this sketch to draw the north and west elevations of the shed using a scale of 1: 100.

*Example: 2 Sketch of a garden shed.

*Solution: Example: 2 Start by converting all measurements to the same units. For a scale of 1: 100, it is easiest to use cm. Length of building: 360 cm Width of building: 220 cm Height to start of roof: 300 cm Height to top of roof: 420 cm Width of door: 90 cm Height of door: 210 cm Width of window: 75 cm

*Solution: Example 2 Draw a rough sketch to show each elevation and mark the dimensions on them.

*Solution: Example 2 NB: if is the front of the building (like in this diagram), then west must be to the right. *Divide the dimensions by 100 to find the exact lengths for the scale diagram. *Draw an accurate diagram using the scaled dimensions. See the accurate draw on the next slide.

*Solution: Example 2

*Formal Assessment Questions

*Formal Assessment Questions

*Formal Assessment Questions

*Formal Assessment Questions 1. Use the information from the floor plan and the photographs to draw a north, south, west and east elevation of an RDP if the front of the house faces north. 2. Use your elevation plans to estimate the surface area to be painted on an RDP house. 3. Calculate the cost of painting a house, given a rate of R 9, 50 per square metre for base coat and surface preparation and a rate of R 12, 60 per square metre for painting with exterior paint.

*Solutions Formal Assessment Questions

*Solutions Formal Assessment Questions

*Solutions Formal Assessment Questions

*Solutions Formal Assessment Questions

* Solutions Formal Assessment Questions *

* Solutions Formal Assessment Questions *

*Solutions Formal Assessment Questions *