Mathematical Literacy Level 4 Module 4

Mathematical Literacy NQF 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Read, interpret and use representations Module 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 4.1 Working with scale 4.2 Working with layout, room and building plans 4.3 Using road, street and route maps 4.4 Sequencing activities to complete a task Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with scale Unit 4.1 • Accurate maps are drawn to scale. The distances shown on the map are in proportion to the actual distances. Map / Plan A map or plan represents an area that is much larger than the image on paper. Scale is written • as a ratio length of a line in image : actual length of line or • as a fraction: length of line in image actual length of line Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with scale Unit 4.1 • Bar scales make it easy to estimate the distance between two points on a map. • This is a bar scale: Each rectangle represents 10 km. • The total length of the bar shows the distance on the map and represents 40 km on the ground. Downloaded from hlayiso.com Maths Lit NQF Level 4

Scale: Bar scales Unit 4.1 • A bar scale could also look like this: • On this scale, 1 rectangle represents 100 km; the length of the scale represents 400 km. • On this scale, 1 rectangle represents 10 km; the length of the scale represents 40 km. Note: If the drawing is scaled up or down, the bar scale increases or decreases in the same proportion. Downloaded from hlayiso.com Maths Lit NQF Level 4

Calculating the scale of a map, plan or model Unit 4.1 We can calculate the scale of a map, plan or model if we know the real distance and the distance on the map. • Write the plan or map unit first in the ratio: 1 : 50 plan actual • Convert both of the units to centimetres. • Simplify by dividing by common factors to get the first number to 1. • Write the ratio without units. The units cancel each other out. Downloaded from hlayiso.com Maths Lit NQF Level 4

Calculating the scale of a map, plan or model Unit 4.1 > Example 4.1 page 93 no 1 1. If a door on a model house is 4 cm high and it is 2 m in reality, what is the scale of the model? 1. Convert both measurements to cm. 2 m = 200 cm, so ratio is 4 : 200 = 1 : 50 Downloaded from hlayiso.com Maths Lit NQF Level 4

Using scale to calculate actual distances Unit 4.1 To work out the approximate real lengths and distances, measure the lengths on maps, plans and models. • Calculate what 1 cm on the map is equal to as a real-life distance. • Example: If a map has a scale of 1 : 50 000, then 1 cm on the map is 50 000 cm in real life. 50 000 cm = 500 m = 0,5 km. So every 1 cm on the map represents 0,5 km in real life. • Steps: 1. Multiply distance on plan or map by scale factor. Keep the units in cm. 2. Convert the cm measurement to the unit that is asked for, or the most appropriate unit. Downloaded from hlayiso.com Maths Lit NQF Level 4

Using scale to calculate actual distances Unit 4.1 > Example 4.2 page 94 no 1 A map has a scale of 1 : 100 000. Devesh measures a distance as 182 mm on the map. How far is this in real life? To work out the distance in real life, multiply this length by 100 000: 182 mm × 100 000 = 18 200 000 mm = 1 820 000 cm = 18 200 m = 18,2 km. Downloaded from hlayiso.com Maths Lit NQF Level 4

Calculating measurements on a map Unit 4.1 from actual distances We can also use an actual distance to calculate a length on a map, if we know what the scale of the map is. 1 Convert the actual measurement on the map or plan to cms. 2 Divide by the scale factor. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.3 page 94 no 1. Unit 4.1 > Example 4.3 page 94 no 1. A map has a scale of 1 : 50 000. Anele walks a distance of 3 km. Calculate the length of her route on the map. • Convert the measurement to cm: 3 km = 3 000 m = 300 000 cm. • Divide by the scale factor: 300 000 cm ÷ 50 000 = 6 cm • 3 km of her route is 6 cm on the map. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 4.1 Unit 4.1 Complete Exercise 4.1 on page 95 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 4.2 Unit 4.1 Complete Exercise 4.2 on page 96 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with layout, room and building Unit 4.2 plans To calculate costs, use the plans to calculate areas and to check the numbers of 1 each fitting, then use the costs per unit area or per item to calculate the 2 total cost. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.4 page 99 Unit 4.2 Complete the table of building cost estimates. Item needed Cost per item Quantity Total cost required Floors & R550 per m2 60 m2 foundations of floor area Walls and R3 620 per m2 200 m2 brickwork of wall area Roofing R2 100 per m2 60 m2 floor area Double doors R2 000 each 2 sets Single doors R760 each 3 Double windows R1 500 each 2 Single windows R670 each 6 Total costs Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.4 page 99 Unit 4.2 Item needed Cost per item Quantity Total cost required Floors & R550 per m2 of floor 60 m2 R3 3000 foundations area Walls and R3 620 per m2 of 200 m2 R724 000 brickwork wall area Roofing R2 100 per m2 floor 60 m2 R126 000 area Double doors R2 000 each 2 sets R4 000 Single doors R760 each 3 R2 280 Double windows R1 500 each 2 R3 000 Single windows R670 each 6 R4 020 Total costs R896 300 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 4.3 Unit 4.2 Complete Exercise 4.3 on page 100 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Using road, street and route maps Unit 4.3 If you need to find bus or train routes and times, you usually need: 1 A map or 2 to know the area 3 and have a timetable Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.5 page 102 Unit 4.3 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 4.4 Unit 4.3 Complete Exercise 4.4 on page 103 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Road and street maps Unit 4.3 • Different maps are appropriate for different purposes. • If you are planning a long-distance journey, use a large scale map. When you get to your destination, you need a smaller scale map showing more detail of smaller areas. Strip maps • Strip maps show a route as a straight line, with all the major towns and landmarks, and the distances marked. • They are not drawn to scale. • They are convenient to use because you don’t need to understand your spatial orientation. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.6 page 108 Unit 4.3 Nozulu has the following directions to drive from Harare to Bulawayo in Zimbabwe. In central Harare: • From Simon Mazorodze Rd/A4: 1,4 km • Turn right on to Willowvale Rd: 6,3 km • Turn right onto High Glen Rd: 8,8 km • Slight left to the A5 • Drive to Chegutu on A5 for 15,4 km • Cross Kwekwe River • Continue on A5 for 202 km to enter the Matabeleland North province • Pass Joshua Nkomo Airport on the right • Turn left at Woodville Drive, drive for 74,0 km • Drive to Harare Rd/A5 in Bulawayo: 67,0 km Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.6 page 108 Unit 4.3 It is simplified in a strip map. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 4.5 Unit 4.3 Complete Exercise 4.5 on page 109 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Sequencing activities to complete Unit 4.4 a task Flow chart A flow chart is a visual representation of a process that needs to be followed. • It is useful when there are different choices to make (shown by branches in the flow chart) and these lead on to different outcomes. • In a flow chart, boxes of different shapes have different functions. Start or end of the Actions Decisions process Downloaded from hlayiso.com Maths Lit NQF Level 4

Sequencing activities to complete Unit 4.4 a task • Flow diagrams show the timing of actions, from top to bottom (vertically), or from left to right (horizontally). • Flow diagrams can show where some actions happen at the same time. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 4.7 page 112 Unit 4.4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 4.6 Unit 4.4 Complete Exercise 4.6 on page 113 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 4 Complete Module assessment on page 116 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

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