Mathematical Literacy Level 2 Module 6

Mathematical Literacy NQF 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Two-dimensional shapes and three-dimensional objects Module 6 Downloaded from hlayiso.com Maths Lit NQF Level 2

Overview 6.1 Names and properties of two-dimensional shapes 6.2 Calculating length, perimeter and area 6.3 Three-dimensional (3-D) objects 6.4 Calculating the volume of 3-D objects Downloaded from hlayiso.com Maths Lit NQF Level 2

Names and properties of two- dimensional shapes Unit 6.1 • Two-dimensional shapes are flat shapes. They have no 'thickness'. Can you describe the properties of • squares • rectangles • triangles • circles in terms of their sides and angles? Downloaded from hlayiso.com Maths Lit NQF Level 2

Number of straight and curved sides Unit 6.1 Rectangles and squares have 4 straight sides. Downloaded from hlayiso.com Maths Lit NQF Level 2

Number of straight and curved sides Unit 6.1 Triangles have 3 straight sides. Downloaded from hlayiso.com Maths Lit NQF Level 2

Number of straight and curved sides Unit 6.1 Circles have only one curved edge. Downloaded from hlayiso.com Maths Lit NQF Level 2

Number of straight and curved sides Unit 6.1 P Q R Triangle PQR has three vertices. Downloaded from hlayiso.com Maths Lit NQF Level 2

Number of straight and curved sides Unit 6.1 L M N O Rectangle LMNO has four vertices. Downloaded from hlayiso.com Maths Lit NQF Level 2

Number of straight and curved sides Unit 6.1 What is a vertex? Definition The corner or point where two straight sides of a shape meet. Plural of vertex is vertices. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Equal sides Unit 6.1 • All four sides of a square are equal in length. AB = BD = DC = CA • Opposite sides of a rectangle are equal in length. EF = HG and FG = EH • The equal sides are marked to show they are equal. A B E F H G C D Downloaded from hlayiso.com Maths Lit NQF Level 2

Angles Unit 6.1 Definition An angle is the amount of turn between two lines with a common vertex. • Right angles • The sides of squares and rectangles form right angles at large angle with more turn the corners (vertices). small angle with less turn • A right angle measures 90°. P Q S T • Square symbols show the right angles. V U R Downloaded from hlayiso.com Maths Lit NQF Level 2

Parallel and perpendicular lines Unit 6.1 P Q 90˚ PQ perpendicular to QR R If two line segments are at right angles to each other, then they are perpendicular. Downloaded from hlayiso.com Maths Lit NQF Level 2

Parallel and perpendicular lines Unit 6.1 A B D C Parallel lines are always exactly the same distance apart and they never touch each other. We use arrows on lines to show that they are parallel. In rectangle ABCD, AB is parallel to CD and BC is parallel to DA. Downloaded from hlayiso.com Maths Lit NQF Level 2

Describing shapes by their properties Unit 6.1 J K P Q S R M L Squares Rectangles • 2-D shape with four straight • 2-D shape with four straight sides. sides. • All sides are equal in length. • Both pairs of opposite sides are • All angles are right angles. equal in length. • All angles are right angles. Downloaded from hlayiso.com Maths Lit NQF Level 2

Describing shapes by their properties Unit 6.1 A B D C • A straight line from one vertex of a shape to the opposite vertex is called a diagonal. • The two diagonals of a square or a rectangle are equal in length. • The diagonals of rectangle ABCD are AC and BD. Downloaded from hlayiso.com Maths Lit NQF Level 2

Describing shapes by their properties Unit 6.1 A B A hypotenuse B C D C • The diagonals divide the rectangle into four large triangles. • A closed shape with three straight sides is a triangle. • A right-angled triangle has the longest side, the hypotenuse, opposite the right angle. Downloaded from hlayiso.com Maths Lit NQF Level 2

Circles Unit 6.1 • All the points on the circle are exactly the same distance from the centre. • The curved edge of a circle is called the circumference. • The diameter is a straight line diameter drawn through the centre of a circle joining any two points on the circumference. • The radius is half the length of the circumference. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 6.1 Unit 6.1 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 6.1 Unit 6.1 Complete Exercise 6.1 on page 107 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating length, perimeter and area Unit 6.2 • Solving problems with right-angled triangles • Many real-life contexts include right-angled triangles Roof trusses Folded paper A ladder against a wall Downloaded from hlayiso.com Maths Lit NQF Level 2

The Theorem of Pythagoras Unit 6.2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 6.2 Unit 6.2 Complete Exercise 6.2 on page 111 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 6.2 Unit 6.2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Perimeter Unit 6.2 Definition Perimeter is the distance all the way around a shape. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Perimeter Unit 6.2 S S S • Perimeter of the square = side + side + side + side S = 4s Downloaded from hlayiso.com Maths Lit NQF Level 2

Perimeter Unit 6.2 c a b • Perimeter of the triangle = side a + side b + side c Downloaded from hlayiso.com Maths Lit NQF Level 2

Perimeter Unit 6.2 b l l • Perimeter of the rectangle = length + length + breadth + breadth b = 2l + 2b Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 6.3 a) iii) page 112 Unit 6.2 9cm a) iii) Find the perimeter of this triangle. 40cm • We need to find the length of the hypotenuse first. (hypotenuse)2 = 92 + 402 (hypotenuse)2 = 81 + 1 600 hypotenuse = 1681 = 41 cm • Perimeter = 9 + 40 + 41 = 90 cm Downloaded from hlayiso.com Maths Lit NQF Level 2

Circumference of a circle Unit 6.2 • Circumference of a circle = 2 × π × radius. = 2πr The symbol π is a number close to 3,14. We call it pi. Example: Radius = 3 cm The radius of a circle is 3 cm. Calculate the circumference. C = 2πr C = 2 × 3,14 × 3 C = 25,12 cm Downloaded from hlayiso.com Maths Lit NQF Level 2

Area Unit 6.2 Definition Area is a measurement of how much surface a shape covers. We calculate area by multiplying two dimensions of the shape. The units of area are always square units. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Area Unit 6.2 S S S S • Area of a square = side × side = s2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Area Unit 6.2 b l l b • Area of a rectangle = length × breadth = l× b Downloaded from hlayiso.com Maths Lit NQF Level 2

Area Unit 6.2 a c h b • For the area of a triangle, we know need to know the length of its base and its perpendicular height. A=½×b×h Downloaded from hlayiso.com Maths Lit NQF Level 2

Area Unit 6.2 r • Area of a circle = πr2 Use 3,14 for π Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 6.5 c) page 115 Unit 6.2 A round hut has a diameter of 8 m. What is the area of its floor? • Use formula for area of a circle. • Radius is half of diameter, so it is 4 m. • A = πr2 • A = 3,14 × (4)2 = 3,14 × 16 = 49,824 m2 • Round off to one decimal place. Area = 49,8 m2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 6.3 Unit 6.2 Complete Exercise 6.3 on page 116 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Three-dimensional (3-D) objects Unit 6.3 face vertex face edge A 3-D object has faces, edges and vertices: • A face is a surface of the object. • An edge is a line where two faces meet. • A vertex is the point where edges meet - the corner. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 6.4 Unit 6.3 Complete Exercise 6.4 on page 120 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the volume of 3-D objects Unit 6.4 • 3-D objects have height, width and depth. • We can calculate the volume of any 3-D object. Definition Volume is a measure of how much space things take up. The object can be open or closed, full or empty. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the volume of 3-D objects Unit 6.4 s s s • Volume of a cube = side × side × side = s3 We multiply three dimensions, so the units are cubic units. Downloaded from hlayiso.com Maths Lit NQF Level 2

Calculating the volume of 3-D objects Unit 6.4 h b l • Volume of a rectangular prism = length × breadth × height = l×b×h Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 6.5 and 6.6 Unit 6.4 Complete Exercise 6.5 and 6.6 on pages 123 and 124 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Module assessment Module 6 Complete Module assessment on page 125 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

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