Mathematical Literacy Level 3 Module 5

Mathematical Literacy NQF 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Revise and acquire the correct vocabulary for space, shape and orientation Module 5 Downloaded from hlayiso.com Maths Lit NQF Level 3

Overview 5.1 Recognise and identify shapes and objects and their attributes 5.2 The Theorem of Pythagoras 5.3 Use given formulae to calculate area, perimeter, volume and surface area Downloaded from hlayiso.com Maths Lit NQF Level 3

Recognise and identify shapes and Unit 5.1 objects and their attributes Two-dimensional (2-D) shapes Rectangles Rectangles are four-sided shapes with these two properties: • both pairs of opposite sides are equal • the corners are all right angles The longer side is the length and the shorter side is the breadth. Downloaded from hlayiso.com Maths Lit NQF Level 3

How do we know if a shape is a rectangle? Unit 5.1 A shape is a rectangle: • if a 4-sided shape has all its angles equal to 90° • if the opposite sides are equal, and at least one of the angles is 90° The sides of a shape are marked with lines to show they are equal. The diagonals of a rectangle each divide it into two identical triangles. A B A B E D C D C Downloaded from hlayiso.com Maths Lit NQF Level 3

Squares Unit 5.1 A square is a 2-D shape with • four straight sides, all equal in length • four right angles U X V W Downloaded from hlayiso.com Maths Lit NQF Level 3

Triangles Unit 5.1 A triangle is a 2-D shape • Any closed shape with three straight sides is a triangle. • A right-angled triangle has one of the angles equal to 90°. • The side opposite the right angle is always the longest side and it is called the hypotenuse. Downloaded from hlayiso.com Maths Lit NQF Level 3

Circles and semi-circles Unit 5.1 • All the points on the outside of the circle are exactly the same distance from the centre. radius centre • Semi-circles are half circles. • The straight edge is formed by the diameter of the circle. r Downloaded from hlayiso.com Maths Lit NQF Level 3

Three-dimensional (3-D) objects Unit 5.1 Remember the parts of a 3-D object: vertex face • Rectangular prisms are box shapes. All the faces are rectangles and opposite faces are exactly the same. • Cubes are a kind of rectangular prism. All six faces of a cube are identical squares. Downloaded from hlayiso.com Maths Lit NQF Level 3

Three-dimensional (3-D) objects Unit 5.1 Cylinders • They have top and base circles that are the same. • The side face is formed by one rectangle, which curves all the way around. Downloaded from hlayiso.com Maths Lit NQF Level 3

Three-dimensional (3-D) objects Unit 5.1 Spheres • They are perfectly round 3-D objects. • Every point on the surface is the same distance from the centre. • Examples: Soccer balls, tennis balls, globes, ball bearings • The sphere is the 3-D object with the smallest surface enclosing a given volume. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 5.1 Unit 5.1 Complete Exercise 5.1 on page 81 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

The Theorem of Pythagoras Unit 5.2 The Theorem of Pythagoras states that: • the square of the length of the A hypotenuse is equal to • the squares of the other two sides added together. r y In triangle ABC, we can write this as B C x AB2 + BC2 = AC2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.1 page 82 Unit 5.2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 5.2 Unit 5.2 Complete Exercise 5.2 on page 83 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

More right-angled triangles Unit 5.2 • If we know the length of the hypotenuse, we can use the Theorem of Pythagoras A to calculate the lengths of the other sides of a right-angled triangle. r y In triangle ABC, we can write this as: BC2 = AC2 - AB2 or B C x AB2 = AC2 - BC2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.2 page 85 Unit 5.2 Calculate the lengths of QR, PS and SR in the diagram. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.2 page 85 Unit 5.2 Step 1: Write down the formula and change it so that the length QR2 = PR2 − PQ2 we are looking for is on the left- hand side. Step 2: Substitute the known QR2 = (14,86) 2 − 102 values into the formula and QR2 = 221 – 100 calculate. QR2 = 121 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.2 page 85 Unit 5.2 QR = 121 Step 3: Find the square root. = 11 units QR = 11 units PS = QR (opposite sides of a Step 4: Write down the answer. rectangle are equal) so PS = 11, SR = PQ, so SR = 10 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 5.3 Unit 5.2 Complete Exercise 5.3 on page 86 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Use given formulae to calculate area, perimeter, surface area and volume Unit 5.3 Area Area is the amount of space that a 2-D shape covers. Perimeter ” Perimeter is the length all the way around a shape. If you add the lengths of the sides together, you get the perimeter. Circumference ” The perimeter of a circle is called a circumference. Downloaded from hlayiso.com ” Maths Lit NQF Level 3

Area and perimeter Unit 5.3 S Square S S • Perimeter = 4s S • Area = s2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Area and perimeter Unit 5.3 Triangle c h a • Perimeter = a + b + b 1 c 2 • Area = × b × h Downloaded from hlayiso.com Maths Lit NQF Level 3

Area and perimeter Unit 5.3 b Rectangle l l • Perimeter = 2l + 2b • Area = l × b b Downloaded from hlayiso.com Maths Lit NQF Level 3

Area and perimeter Unit 5.3 r Circle Use 3,14 for π • Perimeter = 2πr • Area = πr2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.3 page 88 Unit 5.3 Calculate the perimeter of the inside of the athletics track. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.3 page 88 Unit 5.3 Step 1: The athletics track has the shape of a What basic shapes can you see rectangle with a semi-circle on either side. in the diagram? The circumference of the two semi-circles is equal to the circumference of one circle with Step 2: a diameter of 20 m, which is a radius of 10 m. Calculate the perimeter of the Circumference = 2πr first part. = 2 × 3,14 × 10 m = 62,8 m Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.3 page 88 Unit 5.3 Step 3: The rest of the perimeter is formed by Calculate the perimeter of two straight lines of 100 m each, so the second part. their perimeter is (2 × 100) = 200 m. Step 4: Calculate the total 200 + 62,8 = 262,8 m perimeter. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.4 page 89 Unit 5.3 What is the area of the field in the diagram? Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.4 page 89 Unit 5.3 Step 1: What basic shapes can you see in the diagram? Draw a sketch if you need to. This shape is made of a rectangle (18 m × 16 m) and a triangle. The area will be the sum of these two areas. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.4 page 89 Unit 5.3 Step 2: Calculate the area of the first part. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.4 page 89 Unit 5.3 Step 3: Calculate the area of the second part. Area of rectangle = 18 m × 16 m = 288 m2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.4 page 89 Unit 5.3 Step 4: Calculate the total area. Total area = 72 + 288 = 360 m2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 5.4 Unit 5.3 Complete Exercise 5.4 on page 90 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Volume and surface area Unit 5.3 s s Cube s • Surface area = 6 × side2 = 6s2 • Volume = s3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Volume and surface area Unit 5.3 h b l Rectangular prism • Surface area = 2(lb + lb + bh) • Volume = l × b × h Downloaded from hlayiso.com Maths Lit NQF Level 3

Volume and surface area Unit 5.3 r h Cylinder • Surface area = area of 2 circles + area of rectangle = 2πr2 + 2πrh • Volume = πr2h Downloaded from hlayiso.com Maths Lit NQF Level 3

Volume and surface area Unit 5.3 r r r Sphere • Surface area = 4πr2 • Volume = 4 πr3 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.5 page 91 Unit 5.3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 5.5 Unit 5.3 Complete Exercise 5.5 on page 92 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Changing the subject of a formula Unit 5.3 1 Write down the formula and the information you are given. 2 Change the formula so that the unknown value is on its own on the left-hand side. 3 Put the known values into the formula and do the calculation. Downloaded from hlayiso.com Maths Lit NQF Level 3

Changing the subject of a formula Unit 5.3 Examples: Area of a square A = s2 Area of rectangle A = s 2 A=l×b A l ×b = s= A b b A l = b Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.6 page 95 no 1 Unit 5.3 Give your answers to one decimal place. 1. A rectangle with an area of 30 cm2 can have a breadth of a) 3,5 cm or b) 4,5 cm. What will the length of the other side be in each case? Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.6 page 95 continued ... Unit 5.3 a) A 30 l= = = 8,6 cm b 3,5 A 30 b) l= = = 6,7 cm b 4,5 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.6 page 95 no 2 Unit 5.3 Give your answers to one decimal place. 2. What is the radius of this circle? Area = 15 cm2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.6 page 95 continued ... Unit 5.3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.6 page 95 no 3 Unit 5.3 Give your answers to one decimal place. 3. In the triangle, we are given the area and the perpendicular height. Calculate the length of the base of the triangle. Area = 22 cm2 h = 5 cm b = 7 cm Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 5.6 page 95 continued ... Unit 5.3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 5.6 Unit 5.3 Complete Exercise 5.6 on page 96 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

VIDEO: Applications in the workplace Downloaded from hlayiso.com Maths Lit NQF Level 3

Module assessment Module 5 Complete Module assessment on page 98 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

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