Mathematical Literacy Level 4 Module 3

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

Solving space, shape and orientation problems Module 3 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 3.1 Solve problems using the Theorem of Pythagoras 3.2 Solving area and perimeter problems 3.3 Solve volume and surface area problems Downloaded from hlayiso.com Maths Lit NQF Level 4

Solve problems using the Theorem Unit 3.1 of Pythagoras • You are not always told which angles are right angles, but you can often work this out from the context. • For example, the angle between a horizontal structure and a vertical structure is always a right angle. Downloaded from hlayiso.com Maths Lit NQF Level 4

Solve problems using the Theorem Unit 3.1 of Pythagoras • But don’t assume an angle is right angled unless you have facts about it. • Wherever you see a right angle, you can use a right-angled triangle to help you solve the problem. • The triangle can be in different positions and facing different ways. Downloaded from hlayiso.com Maths Lit NQF Level 4

The Theorem of Pythagoras Unit 3.1 A B A A C B C C B The Theorem of Pythagoras states that: The square of the length of the hypotenuse is equal to the squares of the other two sides added together. In triangle ABC, we can write this as AB2 + BC2 = AC2 Downloaded from hlayiso.com Maths Lit NQF Level 4

The Theorem of Pythagoras Unit 3.1 A B A A C B C C B • So if we are given the lengths of the other two sides, we can calculate the length of the hypotenuse. • We can also calculate any other side by manipulating the formula. Important! This theorem does not apply to triangles that do not have a right angle. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.1 page 75 question 1 Unit 3.1 Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.1 page 75 question 3 Unit 3.1 3. A metal bracket on a wall supports a pot plant. Calculate x. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 3.1 Unit 3.1 Complete Exercise 3.1 on page 76 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Solving area and perimeter problems Unit 3.2 Perimeter • Perimeter is the total length all the way around a shape • Add the lengths of all the sides to get the perimeter. • The perimeter of a circle is called the circumference. • Perimeter is measured in units of length, not square units. Downloaded from hlayiso.com Maths Lit NQF Level 4 ”

Solving area and perimeter problems Unit 3.2 Area • Amount of space that a closed shape covers • The units of area are always square units Downloaded from hlayiso.com ” Maths Lit NQF Level 4

Solving area and perimeter problems Unit 3.2 Remember: • A = lb means A = l × b • A = ½ πr2 means A = ½ × π × r × r • 3,14 is an approximate value of π. • If you have a scientific calculator, use the π key to be more accurate. Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with formulae Unit 3.2 S Cube S S • Perimeter = 4s S • Area = s2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with formulae Unit 3.2 c a Triangle h b Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with formulae Unit 3.2 b Rectangle l l • Perimeter = 2l + 2b • Area = l × b b Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with formulae Unit 3.2 r Circle Downloaded from hlayiso.com Maths Lit NQF Level 4

Working with formulae Unit 3.2 Semi-Circle r Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.2 page 78 Unit 3.2 • Calculate the area and the perimeter of this shape. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.2 page 78 Unit 3.2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.3 page 79 Unit 3.2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Changing the subject of a formula Unit 3.2 We can change a formula around to calculate a different quantity, without changing the facts in the formula. 1 Write down the formula and any information you are given. Change the formula so that the unknown value is on its own on the 2 left-hand side. 3 Put the known values into the formula and do the calculation. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 80 Unit 3.2 • In this triangle, calculate the length of the base. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 80 Unit 3.2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Calculating costs Unit 3.2 • Area and perimeter calculations are important in practical situations such as creating objects, building, gardening, developing plans, decorating. • To calculate the costs, we need to calculate the quantities needed first and then multiply by the cost rate of the materials. ? A quantity surveyor is someone who works in the construction industry. Their main job is to calculate and manage the costs of a whole project. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 81 Unit 3.2 1. A landscaper wants to fence parts of a garden as shown in the diagram here. a) Work out the total quantity of fencing needed. b) If fencing costs R75 per metre, what will the total cost be? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 81 Unit 3.2 a) Circumference of herb garden = 2πr = 2π (2,5) = 15,7 m Circumference of rose garden = 2πr = 2π (3) = 18,85 m Perimeter of ornamental trees and lawn = 2(4 + 3) = 14 m Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 81 Unit 3.2 Total quantity of fencing = 15,7 m + 18,85 m + 14 m = 48,55 m b) 48,55 m × R75/m = R3 641,25 Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 81 Unit 3.2 2. The landscaper wants to apply lawn dressing to the trees and lawn area and compost to the herb and rose gardens. He needs 5 kg of compost or lawn dressing to each square metre of garden. He has the following prices: Product 20 kg 50 kg 100 kg Compost R200 R420 R800 Lawn dressing R250 R650 R1 695 Which bags should he buy for this season, and how much will it cost in total? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 3.4 page 81 Unit 3.2 2. Area of herb garden = πr2 = 19,63 m2 Area of rose garden = πr2 = 28,27 m2 Area of lawn and trees garden = 3 × 4 = 12 m2 5 kg of compost or lawn dressing per m2 Amount of compost needed = (19,63 + 28,27) × 5 = 239,5 kg Amount of lawn dressing needed = 12 × 5 = 60 kg He needs to buy the 50 kg bag of compost and the 20 kg bag of lawn dressing: Cost = R250 + R420 = R670 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 3.2 Unit 3.2 Complete Exercise 3.2 on page 82 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Solve volume and surface area problems Unit 3.3 height length width • All objects have 3 dimensions: length, width and height. • We use volume to measure and compare how much space things take up. • Liquids (water, milk, cool drink, etc) are measured in units such as litres and millilitres. Downloaded from hlayiso.com Maths Lit NQF Level 4

Solve volume and surface area problems Unit 3.3 height length width • We can measure the volume of solid objects in cubic units. • We can convert between liquid volume and solid units. (see Topic 1). • Volume is calculated by multiplying 3 dimensions together, so it is measured in cubic units • Example: Volume of a box = length × breadth × height (in cubic units) Downloaded from hlayiso.com Maths Lit NQF Level 4

Formulae for surface area and volume Unit 3.3 s s Cube s Surface area = 6 × side2 = 6s2 Volume = s3 Downloaded from hlayiso.com Maths Lit NQF Level 4

Formulae for surface area and volume Unit 3.3 h b l Rectangle Surface area = 2(lb + lb + bh) Volume = l × b × h Downloaded from hlayiso.com Maths Lit NQF Level 4

Formulae for surface area and volume Unit 3.3 r h Cylinder Surface area = area of 2 circles + area of rectangle = 2πr2 + 2πrh Volume = πr2h Downloaded from hlayiso.com Maths Lit NQF Level 4

Formulae for surface area and volume Unit 3.3 r r r Sphere Surface area = 4πr2 Volume = πr3 Downloaded from hlayiso.com Maths Lit NQF Level 4

Formulae for surface area and volume Unit 3.3 Cone Downloaded from hlayiso.com Maths Lit NQF Level 4

Volume and surface area Unit 5.3 Triangular prism Downloaded from hlayiso.com Maths Lit NQF Level 4

Nets of 3-D objects Unit 5.3 • To find the surface area of 3-D objects, it helps to imagine or sketch their nets (when they are ‘opened up’ and laid flat). • The total surface area is the sum of the areas of the flat shapes. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 3.3 Unit 3.3 Complete Exercise 3.3 on page 86 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Assignment 1 Unit 3.3 Complete Assignment 1 on page 87 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Assignment 2 Unit 3.3 Complete Assignment 2 on page 89 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

VIDEO: Application in the Workplace Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 3 Complete Module assessment on page 91 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

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