NCV 2 Mathematical Literacy Hands-On Training Module 3

Space, Shape and Orientation

Mathematical Literacy 2Future Managers 1


• Space, shapes and time

• Calculations to solve space and shape problems

• Maps, Grids and Routes

• Diagrams and instructions


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


Frequently used shapes

Mathematical Literacy 2

Circle

Polygons

Future Managers 4

• 3D Objects


Prism Cube

Triangular Prism

Cylinder Cone

Sphere

Pyramid

Future Managers 5

Shape Terminology


PerpendicularPerimeterParallelLength

length

breadth

Breadth height

HeightVolume

Future Managers 6

Shape Terminology


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 pg 95

Future Managers 8

Space, Shape and Orientation• Space, shapes and time





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


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


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


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


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’



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


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


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


Circles• Circumference

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

Circumference = 2r

= 2 x (22/7) x 10cm

= 62.86cm


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


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


Orthographic Drawing


Maps, Grids and Routes


Space, Shape and Orientation• Space, shapes and time





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


Types of Maps• City Maps

• National Maps

• Bus Route Maps

• Train Route Maps

• Hiking Maps

• Survey Maps


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


Legends


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


Finding an address



Future Managers 29

Table of distances


Diagram and instructions



• Space, shapes and time





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


Diagram• A diagram is a visual representation of a concept


Flowchart


NCV 2 Mathematical Literacy Hands-On Training Module 3

Education

Transcript of NCV 2 Mathematical Literacy Hands-On Training Module 3