NCV 2 Mathematical Literacy Hands-On Training Module 3

Space, Shape and Orientation

Mathematical Literacy 2Future Managers 1

Space, Shape and Orientation

• Space, shapes and time

• Calculations to solve space and shape problems

• Maps, Grids and Routes

• Diagrams and instructions

Mathematical Literacy 2Future Managers 2

Space, shapes and time

• At the end of this outcome, you will be able to:– Identify various shapes and objects

– Use the correct terminology identified with the various shapes and objects

– Apply the vocabulary of space, shape and orientation when you deal with everyday problems

– Differentiate between 12 and 24 hours to explain how time elapses

Mathematical Literacy 2Future Managers 3

Frequently used shapes

Mathematical Literacy 2

Circle

Polygons

Future Managers 4

• 3D Objects

Mathematical Literacy 2

Prism Cube

Triangular Prism

Cylinder Cone

Sphere

Pyramid

Future Managers 5

Shape Terminology

Mathematical Literacy 2

PerpendicularPerimeterParallelLength

length

breadth

Breadth height

HeightVolume

Future Managers 6

Shape Terminology

Mathematical Literacy 2

Area

diameter

Diameter

radius

Radius

circumference

Circumference

Future Managers 7

Time

• Clocks can either be analogue or digital

• From 12 noon to 11:59 at night PM is used

• From 12 at night to 11:59 in the morning AM is used

• At 24 hour clock doesn’t use AM or PM, rather for PM add 12 hours to the time

• i.e. 4pm = 16:00; 6pm = 18:00

Mathematical Literacy 2

Mathematical Literacy pg 95

Future Managers 8

Space, Shape and Orientation• Space, shapes and time

• Calculations to solve space and shape problems

• Maps, Grids and Routes

• Diagrams and instructions

Mathematical Literacy 2Future Managers 9

Calculations to solve space and shape problems

• At the end of this outcome, you will be able to:– Calculate areas, volumes and lengths– Do conversions using a scale– Conversions between units of weight– Read dimensions from a plan– Determine elapsed time– Use formulae to solve real world challenges

Mathematical Literacy 2Future Managers 10

Calculations• Dimensions

– Words that can be used for a single dimension:• Length

• Breadth

• Height

• Depth

• Thickness

– A two dimensional shape can be described by two dimensions e.g. length and breadth

– Measurements of two dimensions is called area

Mathematical Literacy 2Future Managers 11

Dimensions• A three dimensional shape has three dimensions

– Three dimensional measurement is called volume or capacity

• The perimeter of a shape is the total distance around its edges.– A perimeter is one dimensional

– A perimeter is always given as a length

– The perimeter of a circle is its circumference

Mathematical Literacy 2Future Managers 12

Area• Area gives us the size of a flat surface

• It is measured in square meters or m2

• Area of a rectangle– Measured by length x breadth

Mathematical Literacy 2

6 cm

3 cmArea = base x height

= 6cm x 3cm

=18cm2

18cm2

Future Managers 13

External Surfaces• Total external surface areas is calculated by

adding the surface area of all sides

• All sides can lie flat, forming a ‘net’

Mathematical Literacy 2

Mathematical Literacy pg 104

Future Managers 14

Triangle• Perimeter– The perimeter of a triangle is calculated by adding the three

sides together

• Area– Is calculated by ½ base x perpendicular height– E.g.. The base of a triangle is 10cm and its height is 12 cm– Area = ½ base x height

= 5cm x 12cm= 60 cm2

Mathematical Literacy 2Future Managers 15

Triangle

• Triangular Prism– Has five surfaces that need to be

calculated– 3 rectangles (length x breadth)– Base Triangle– Top triangle has the same area as

base– Add all sides together

Mathematical Literacy 2Future Managers 16

Circle• Area

– Calculated by r2

– E.g.. Radius of a circle is 10 cm. What is its area?

Area = r2

= (22/7)x(10cm)x(10cm)

=314cm2

Mathematical Literacy 2Future Managers 17

Circles• Circumference

– Calculated by 2r– E.g. What is the circle’s circumference

Circumference = 2r

= 2 x (22/7) x 10cm

= 62.86cm

Mathematical Literacy 2Future Managers 18

Scale• A scale is a way of representing an object by using a

picture or model that is smaller• The scale model has exactly the same proportions as the

real object, but is much smaller• To get from a scale model to the actual size, you need to

multiply every dimension by the same amount. This is called a scale factor

Mathematical Literacy 2Future Managers 19

Plans• There are three main views usually used to show

the features of an object:– The front– The side– The top

• Most architectural drawings are called orthographic drawings

Mathematical Literacy 2Future Managers 20

Orthographic Drawing

Mathematical Literacy 2Future Managers 21

Maps, Grids and Routes

Mathematical Literacy 2Future Managers 22

Space, Shape and Orientation• Space, shapes and time

• Calculations to solve space and shape problems

• Maps, Grids and Routes

• Diagrams and instructions

Mathematical Literacy 2Future Managers 23

Outcomes

• At the end of this outcome, you will be able to:– Locate a position on a map

– Make maps plans according to scale

– Plan route maps for trips

– Locate a starting point and destination point and plan a route between them

– Use maps to communicate information regarding relative positions/routes/lay out

– Plan trips taking into account modes of transport, time available; appointments to be met etc

Mathematical Literacy 2Future Managers 24

Types of Maps• City Maps

• National Maps

• Bus Route Maps

• Train Route Maps

• Hiking Maps

• Survey Maps

Mathematical Literacy 2Future Managers 25

City Maps• A city map will consist of a diagram of all the

streets

• This will be overlaid with a grid

• Any point can be positioned within the a grid square

• The scale will typically be 5cm to 1km or 1:20 000

Mathematical Literacy 2Future Managers 26

Legends

Mathematical Literacy 2Future Managers 27

Finding an address• Go to the map index• Search for the street name• Next to the street name find the following:

– Page number

– Grid number

– Grid letter

• Go to the page number, find the correct grid numbers and search within the block for the street

Mathematical Literacy 2Future Managers 28

Finding an address

Mathematical Literacy 2

Mathematical Literacy pg 111

Future Managers 29

Table of distances

Mathematical Literacy 2Future Managers 30

Diagram and instructions

Mathematical Literacy 2Future Managers 31

Space, Shape and Orientation

• Space, shapes and time

• Calculations to solve space and shape problems

• Maps, Grids and Routes

• Diagrams and instructions

Mathematical Literacy 2Future Managers 32

Diagrams and instructions

• At the end of this outcome, you will be able to:– Identify parts/objects from a diagram– Follow instructions given in manuals and brochures– Use measurements on plan to calculate materials needed– Sequence activities to complete a task– Draw diagrams to use for to support written text / instructions– Use flow diagrams to communicate sequences of events or

decision making processes– Draw rough sketches of objects and/or areas– Make diagrams of objects from different views and according to

scale– Make physical models of objects from plans and/or diagrams

according to scale

Mathematical Literacy 2Future Managers 33

Diagram• A diagram is a visual representation of a concept

Mathematical Literacy 2Future Managers 34

Flowchart

Mathematical Literacy 2Future Managers 35