BOOK 1 – Construction, Building, Resources, Mining, Infrastructure, Primary Industries and Agribusiness, Local Government and Civil, Business, Retail and IT
Workplace Numeracy And Calculations
WORKPLACE
NUMERACY AND
CALCULATIONS
REGIONAL AUSTRALIAN WORKFORCE DEVELOPMENT
“DRIVEN BY LOCAL INDUSTRY & COMMUNITY”
A Commonwealth of Australia project funded by:
Department of Education, Employment and Workplace Relations
Materials produced by:
Regional Skills Training Pty Ltd
1
COPYRIGHT NOTICE
These interactive workbooks were produced by Regional Skills Training and funded by DEEWR (Department of Education,
Employment and Workplace Relations) and are intended for free use to any student, RTO or school. Note the work is copyright
and should not be reproduced or copied for commercial gain.
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CONTENTS
 1.
Introduction and how to use these materials
03
 2.
Learning materials, what are these about?
04
Employability Skills
04
Do you know how to complete basic numeracy calculations
05
3.1
Measuring length
10
3.2
Measuring volume
12
3.3
What about calculating the volume of simple objects
14
3.4
Measuring weight 17
3.5
Measuring time 20
3.6
Measuring temperature
21
 4
Complete numeracy calculations and measurements required in the workplace
22
 5.
Estimate approximate quantities required for different tasks
26
What formula do I use?
27
 6.
What other workplace requirements need to be considered 35
 7.
Being confident about your skill levels
38
 8.
Assessment
39
 9.
Bibliography and source materials
40
2.1
 3.
5.1
Workplace Numeracy And Calculations
1.INTRODUCTION
HOW TO USE THESE MATERIALS
This workbook relates to workplace numeracy and
calculations and is appropriate to people employed in
a range of workplaces in the rural, regional and remote
sectors of Australia.
Skills and knowledge developed will ensure your ability to
apply calculations and numeracy skills appropriate to your
workplace and industry sector. Resources and activities
provided are designed to develop your skills and provide
formative assessments to monitor progress. Completion
of appropriate summative assessments provided by your
Registered Training Organisation (RTO) will enable you to
achieve competency in the unit applicable to your sector.
These student materials apply to the following industry
sectors and units of competence.
Sector
Unit code
What workbook
do you complete
Unit name
Construction, Building
CPCCCM1005A
Book 1
Carry out Measurements and Calculations
Resources, Mining,
RIICCM201A
Infrastructure, Primary Industries
and Agribusiness
Book 1
Carry out Measurements and Calculations
Local Government, Civil
LGAWORK206A
Book 1
Measure and Calculate Civil Materials
Business, Retail and IT
CPCCCM1005A
Book 1
Carry out Measurements and Calculations
3
Workplace Numeracy And Calculations
2.LEARNING MATERIALS
WHAT ARE THEY ABOUT?
This workbook is about the skills required for:
• Taking accurate measurements.
• Performing simple calculations to determine task and material requirements.
• Estimating approximate quantities.
• Planning and preparation for safe work practices.
2.1 EMPLOYABILITY SKILLS
What is numeracy in the workplace?
Numeracy is about using maths to make sense of the world. If you have appropriate numeracy and calculation skills for workplaces
appropriate to these units of competency you will be able to:
• identify the meaning of mathematical information in activities and texts
• problem solve using mathematical processes
• communicate using mathematical symbols and diagrams
• understand and apply mathematical ideas and techniques appropriate to your workplace such as charts, tables, plans and diagrams
• understand metric measurements for distances, quantities, mass, capacity, time and temperature
The learning materials provide opportunities to develop and apply employability skills that are learnt throughout work and life, to your job.
The statements below indicate how these processes are applied in the workplace related to the application of numeracy and
calculations in completing your daily work tasks. Completed activities and summative assessments must be able to demonstrate
competent “employability skills” in the workplace.
Communication
• communicates with clients, colleagues and others using effective and appropriate
communication techniques.
• understands, interprets and applies information as required from relevant: plans and
drawings, specifications, designs
• applies measurements and calculations using appropriate equipment, formulas and
records as required
• calculate basic weights, distances and volumes
Teamwork
• works as part of a team to prioritise and action tasks
• work cooperatively with people of different ages, gender, race, religion or political
persuasion and people with disability
Problem Solving
• measuring and calculating material quantities
Initiative and Enterprise
• identify and assess risks in the workplace
Planning and Organising
• selects and uses appropriate materials, tools and equipment
• identifies requirements, applies relevant resources and sequences tasks using time
management techniques
• manage time and priorities to complete work
• follow procedures and techniques relevant to the equipment and work being done
Self-management
• contributes to workplace responsibilities, such as current work site environmental/
sustainability frameworks or management systems
• take responsibility for planning and organising own work priorities and completing
assigned tasks
Learning
• understand equipment characteristics, technical capabilities, limitations and procedures
Technology
• uses calculators
• uses computers and relevant software
• use communications technology appropriate to the workplace (email, mobile, radio, etc.)
4
Workplace Numeracy And Calculations
3.DO YOU KNOW HOW
TO COMPLETE BASIC NUMERACY CALCULATIONS
Basic numeracy skills are essential in any workplace. A variety of measurements are required to be performed daily and must
be accurate, appropriate to workplace needs and up to workplace standards and accuracy requirements. Measurements
may include length, width, area and volume and are to be taken in metric scale. As you complete this workbook you should
use the same measuring “tools” that you have in the workplace. In most cases this is likely to be a good quality steel tape
measure, a calculator, measuring jugs, calibration equipment etc.
This section of the workbook will discuss all of the most commonly used measurements in the workplace. In a later section of
the workbook the same measurements will be looked at using workplace examples.
The first decision you must make is to select the appropriate calculation method for achieving the required result.
The metric system was devised during the French Revolution (1789-1799) in order to standardise the different systems of
measurement which were then being used. The metric system has standard units of measurement for problems involving
length, area, volume, mass, temperature, electricity and time. Larger or smaller units of measurement in the metric system
are obtained by multiplying and dividing by powers of 10.
Metric rulers and tape measures
The simplest metric measuring device is the metric ruler. A metric ruler is a narrow straight length of wood, plastic or
metal marked along its length with millimetre and centimetre units. Long metric rulers might also have a metre unit. Rulers
measure distance or length.
Metric scales measure weight
• Metric balance scales have two plates attached to a lever. On one side are placed known gram weights. The unknown
sample is placed on the other. When the plates balance, the unknown weight is equal to the known weights.
• Metric spring scales have the unknown weight attached to a spring of known properties. The spring stretching moves a
pointer to the gram or kilogram weight.
• Digital metric scales use electronic circuits to determine the weight of an unknown sample in grams or kilograms.
• Hydraulic and pneumatic metric scales are used for measuring very heavy objects. They use fluid pressure changes to
determine weights in kilograms.
Metric graduated cylinders are used to measure volumes
They are essentially tall cylinders of glass or plastic with marks up their sides. The marks are in units of fractions of a litre,
most often millilitres. The cylinder is partially filled with water and the volume of the water is read. An object of unknown
volume is placed in the water and a new reading is taken. The first reading is subtracted from the second. This gives the
volume of the object.
Celsius Thermometers
The Celsius temperature scale is the scale used by the metric system. It is based on the freezing and boiling points of water.
Thermometers marked in degrees Celsius are metric temperature measuring tools.
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Workplace Numeracy And Calculations
Watches and Clocks
The second is the basic metric unit of time. Watches and clocks are metric time-measuring tools.
Decimals in measurement
We use decimals to specify units of measurement when we need more precision about length, volume, mass, or time.
For example, when specifying the height of a person we can be quite specific e.g. 1.63 meters tall. To say that person is
“about” 1 or 2 metres tall doesn’t give us a very good idea of how tall that person really is.
The prefixes for the different units of length, volume, and mass in the metric system obey the following rules:
Prefix
Multiply by
milli-
0.001
centi-
0.01
deci-
0.1
deka-
10
hecto-
100
kilo-
1000
So for example:
1 hectometre = 100 metres
1 centigram = 0.01 gram
3 millilitres = 3 × (0.001 litres) = 0.003 litres
0.9 kilometres = 0.9 × (1000 metres) = 900 metres
6
Workplace Numeracy And Calculations
 ACTIVITY 1
Think about all of the different measurements you may be required to use and understand in your workplace.
Complete the table below. Make sure you include a variety of tasks that include:
•
•
•
•
•
Length
Weight
Volume
Temperature
Time
What is the task requiring you to
use numeracy calculations/skills
What tools are used
for this task
What is
the unit
used
Why is this task completed in your
workplace
e.g. Measure window glass
Steel tape measure
Millimetres
Glass needs replacing as it is broken
7
Workplace Numeracy And Calculations
Now that you have thought about the actual numeracy calculations that are required in your workplace and the units and
tools used, we will look at individual types of calculations in depth. First you need to understand the symbols used in
numeracy calculations. The following symbols are the most likely that you will find used in your workplace. All math symbols
are shorthand marks that represent mathematical concepts.
Symbol
Name
Symbol
Name
+
addition sign, plus sign
√
square root
-
subtraction sign, minus sign
±
plus or minus
x or *
multiplication sign
∠
angle
÷ or /
division sign
°
degree
=
equal
⊥
perpendicular
≠
not equal
||
parallel
<
less than
∼
is similar to
>
greater than
∅
null or empty set
≤
less than or equal to
∈
is a member of
≥
greater than or equal to
∉
is not a member of
#
number sign
⊂
is a subset of
()
parentheses
∴
therefore
and
Σ
sum
ellipsis (and so on)
infinity
&
percent
...
π
Pi
∞
|x|
absolute value of x
%
8
Workplace Numeracy And Calculations
 ACTIVITY 2
Now let’s look at a few of these symbols used in a very simple way to illustrate different basic maths concepts.
Numeracy
calculation
What does it mean
What math function
are you performing
1+3=4
One plus three equals four
Addition
10 – 4 = 6
Ten minus four equals six
Subtraction
3x3=9
Three multiplied by three equals nine
Multiplication
9÷3=3
Nine divided by three equals three
Division
< 12 kilograms
Less than twelve kilograms
Less than
>12 kilograms
Greater than 12 kilograms
Greater than
Where could you use this
calculation in your workplace
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Workplace Numeracy And Calculations
3.1 MEASURING LENGTH
The standard unit of length in the metric system is the metre. Other units of length and their equivalents in metres are as follows:
1 millimetre = 0.001 metre
1 centimetre = 0.01 metre or 10 millimetres
1 decimetre = 0.1 metre or 10 centimetres
1 kilometre = 1000 metres
We symbolise these lengths as follows:
1 millimetre = 1 mm
1 centimetre = 1 cm
1 metre = 1 m
1 decimetre = 1 dm
1 kilometre = 1 km
The first step you need to determine is: WHAT IS THE CORRECT UNIT OF LENGTH TO USE WHEN TAKING A MEASUREMENT?
This is sometimes determined by the industry e.g. Building and Construction primarily use millimetres to assure the greatest
accuracy. Otherwise it is entirely dictated by the length of the object being measured e.g.
•
•
•
•
Measure the thickness of glass for a window in millimetres.
Measure the diagonal of a television screen in centimetres.
Measure the width of a road in metres.
Measure the distance between two airports in kilometres.
Various instruments are used to measure length. For example:
• Rulers and tape measures are marked in millimetres or centimetres to measure shorter lengths accurately.
They may also measure smaller distances of metres i.e. less than 50 metres.
• A trundle wheel is used to measure length to the nearest metre. Note that a counter may be attached to the trundle
wheel to count metres. You will often see a trundle wheel being used by roadside engineers.
• A car’s odometer measures distance in tenths of a kilometre.
It is clear from the visual comparison of the lengths that a centimetre is a larger unit than a millimetre or conversely that a
millimetre is a smaller unit than a centimetre. You should always convert your measurements to the unit appropriate to the
length or the unit that is expected to be used in the workplace.
10
Workplace Numeracy And Calculations
So how do we convert any length from a large unit into a small unit so that we talk about that measurement in the most
appropriate term? It is simply a matter of multiplying by the relevant power of 10.
The same process works in reverse to convert length from a small unit into a large unit, divide by the relevant power of 10.
Let’s look at the following simple conversions:
•
•
•
•
•
How do we convert 5 cm to mm? Remember from above that 1cm = 10 mm then 5cm x 10mm = 50mm
How do we convert 4.43 cm to mm? Remember from above that 1cm = 10mm then 4.43cm x 10mm = 44.30mm
How do we convert 9 metres to cm? Remember from above that 1metre = 100 cm then 9m x 100cm = 900cm
How do we convert 7.9 metres to cm? Remember from above that 1metre = 100 cm then 7.9m x 100cm = 790cm
How do we convert 3 kilometres to metres? Remember that 1km = 1000 metres then 3km x 1000mtrs = 3000metres
11
Workplace Numeracy And Calculations
 ACTIVITY 3
Complete the following table converting measurements as requested for each calculation.
The measurement is:
Convert the measurement to:
1600 millimetres
centimetres
1400 metres
kilometres
5 metres
decimetres
5 kilometres
metres
263.4 millimetres
centimetres
863.25 metres
kilometres
4345 millimetres
decimetres
487.65 centimetres
metres
59.6 kilometres
metres
Answer
3.2 MEASURING VOLUME
The standard unit of volume in the metric system is the litre. One litre is equal to 1000 cubic centimetres in volume.
Other units of volume and their equivalents in litres are as follows:
1 millilitre = 0.001 litre
1 centilitre = 0.01 litre
1 decilitre = 0.1 litre
1 kilolitre = 1000 litres
From these units, we see that 1000 millilitres equal 1 litre: so 1 millilitre equals 1 cubic centimetre in volume.
We symbolise these volumes as follows:
1 millilitre = 1 ml
1 centilitre = 1 cl
1 decilitre= 1 dl
1 litre = 1 l
1 kilolitre = 1 kl
Have a look at the website Wisc-Online. If you click through the slideshow it will give you a pictorial demonstration of using
graduated cylinders to measure the volume of a liquid. This is the most common method used when small amounts of
liquid are measured.
12
Workplace Numeracy And Calculations
 ACTIVITY 4
Complete the activities on the final 2 pages of the Wisc-Online slide show by clicking on the arrow in the bottom
corner of the screen to advance to slide 10.
www.wisc-online.com/objects/ViewObject.aspx?ID=gch302
Did you get the answers correct? If not have another look at the units used to measure volume above and then
complete the slide show activity again.
Think about when you might measure small amounts of liquid in your workplace using graduated measuring
jugs or cylinders. List examples from your workplace below.
What is the workplace activity
What liquid is measured
e.g. Spraying crops for pests
Pesticide Chemicals to mix with water in boom spray
13
Workplace Numeracy And Calculations
3.3 WHAT ABOUT CALCULATING THE VOLUME OF SIMPLE OBJECTS
In the previous exercise you calculated the volume of a liquid. What about the volume of an object? In these cases volume is
measured in cubes (or cubic units).
How many cubes are in this rectangular shape? To give you an easy demonstration
the shape has been divided into cubic centimetres. If you count each cubic
centimetre you will see that it has a volume of 48 cubic units. This is all good if
a shape is visibly divided into cubic units but this is very unlikely. So you need to
know the formulae to calculate the volume of an object. For the purposes of this
workbook you will start with a simple rectangle shape like a box.
The volume of a rectangular box is = length x width x height
You need to do two multiplications to work out the volume. You calculate the area of one face (or side) and multiply that by its
height. The examples below show how there are three ways of doing this.
Area = 6 x 4 = 24
Volume = Area x 2
Volume = 24 x 2 = 48 cubic units
Area = 6 x 2 = 12
Volume = Area x 4
Volume = 12 x 4 = 48 cubic units
Area = 4 x 2 = 8
Volume = Area x 6
Volume = 8 x 6 = 48 cubic units. Cubic units is written as unit3
Notice how you get the same answer no matter what side you use to find an area.
14
Workplace Numeracy And Calculations
Units for measuring volume
There are very big differences between units of measure for volume. For example, there are 100 centimetres in 1 metre but
there are 1,000,000 (yes, 1 million) cubic centimetres in a cubic metre.
Why the big difference? Because in volume we have not just length; we have length, width, and height.
Look at the following examples of calculating the volume of a rectangular object.
Volume = Length x Width x Height so volume =
12 cm x 8 cm x 6 cm = 576 cm3
 ACTIVITY 5
Look at the following 2 diagrams. Calculate the volume of both and write you answer in the space provided.
Volume = Length x Width x Height so volume =
Volume = Length x Width x Height so volume =
15
Workplace Numeracy And Calculations
 ACTIVITY 6
Can you think of examples when you will need to calculate volumes? Complete the table below with examples
applicable to your workplace.
Workplace example
Why do you need to make the calculation
Loading a ute to take tool boxes to the mines
How many tool boxes can I fit
 ACTIVITY 7
The following links have been provided to more worksheets related to calculating volumes. Click into each link and print the
worksheet. Now you need to complete each worksheet using a calculator and the correct formula. Once you have done the
calculations go back to the on line worksheet and click on the box to show the answers. If you get any wrong, go back to your
calculation to see where you have made a mistake. Don’t look at the answer first as it doesn’t help. This is just like workplace
skills… you need to practice properly to get it right! Remember to ask your supervisor or lecturer if you are not able to work out
the answers correctly.
Click here to complete Volumes of Rectangular Prisms
OR if you are using the printed resource, enter the address below into your web browser.
www.helpingwithmath.com/printables/worksheets/geo0601volume01.htm
Click here to complete Volumes of Rectangular Prisms
OR if you are using the printed resource, enter the address below into your web browser.
www.helpingwithmath.com/printables/worksheets/geo0601volume02.htm
Click here to complete Volumes of “Real-world” objects e.g. of cereal boxes
OR if you are using the printed resource, enter the address below into your web browser.
www.helpingwithmath.com/printables/worksheets/geo0601volume03.htm
Click here to complete Calculating Volumes e.g. of triangular prisms and cylinders
OR if you are using the printed resource, enter the address below into your web browser.
www.helpingwithmath.com/printables/worksheets/geo0701volume01.htm
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Workplace Numeracy And Calculations
3.4 MEASURING WEIGHT
Metric Scales measure weight in either grams or kilograms.
The standard unit of mass in the metric system is the gram. Other units of mass and their equivalents in grams are as follows:
1 milligram = 0.001 gram
1 centigram = 0.01 gram
1 decigram = 0.1 gram
1 kilogram = 1000 grams
We symbolise these masses as follows:
1 milligram = 1 mg
1 centigram = 1 cg
1 decigram = 1 dg
1 gram = 1 g
1 kilogram = 1 kg
For reference, 1 gram is about the mass of a paper clip. One kilogram is about the mass of a litre of water.
Weight and Mass
Before we go any further, let’s be clear about the difference between weight and mass. Most of the time, when we’re talking
about weight, we actually mean mass. Kilograms, centigrams, decigrams, grams, milligrams are all measurements of mass.
• Mass is the amount of matter something is made from. Big things are generally more massive than small ones.
• Weight is a measurement of how much the force of gravity acts on a mass of a given size. The force of gravity varies
slightly all over earth so, while an object has the same mass, its weight varies. For the extreme example think about the
moon? Gravity is about one sixth the strength on the moon, as it is on earth. So things weigh only one sixth as much on
the moon as they do on earth, even though their mass is exactly the same in both places.
However in our daily lives it is unlikely that you will refer to mass and weight. Most of the time, it’s acceptable to refer to
weights in mass units (such as kilograms) because any mass on earth converts to a weight in pretty much the same way. It is
certainly far more common to hear someone say “This parcel weighs 1 kilogram” than to hear it referred to by its mass. So now
you know the difference between mass and weight we will just concentrate on the way “weight” is used in the workplace.
17
Workplace Numeracy And Calculations
How can you measure weight?
Using a steelyard to measure the weight of letters. You put the letters on the pan, move the sliding weight until the arm is
horizontal, and then read the weight off the scale.
An electronic balance like this measures accurately and shows the result on a digital display. You can see that this apple
weighs 73.5 grams. Photos by Joshua Adam Nuzzo courtesy of US Navy
Large things (such as trucks) are obviously much too big to weigh with ordinary scales or balances, but it’s still important
to know accurate weights. For instance they must comply with weight limits for loads and also restrictions on weights that
may also exist, depending on the road type they are on. Trucks are weighed by driving them onto weighbridges, which are
supported by hydraulic rams. The heavier the truck, the greater the force on the rams and the harder they have to push
upward to balance the truck’s weight exactly.
18
Workplace Numeracy And Calculations
 ACTIVITY 8
How many times do you weigh things in the course of a day? Think about when you might measure weight in
your workplace. List examples from your workplace below.
What is the workplace activity
What weight is measured
Sending parcels by post for goods ordered
The total weight of the parcel to determine postage costs
19
Workplace Numeracy And Calculations
3.5 MEASURING TIME
The following conversions are useful when working with time:
1 minute = 60 seconds
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours
1 week = 7 days
1 year = 365 1/4 days (for the Earth to travel once around the sun)
In practice, every three calendar years will have 365 days, and every fourth year is a “leap year”, which has 366 days, to
make up for the extra quarter day over four years. The years 1992, 1996, 2000, and 2004 are all leap years. This gives us a
total of 52 complete 7 day weeks in each calendar year, with 1 day left over (or 2 in a leap year).
The year is divided into 12 months, each of which has 30 or 31 days, except for February, which has 28 days (or 29 days in a leap year).
So why do you need to understand measuring time in the workplace? Think about how time is important in the workplace.
1. You are probably required to fill in a time sheet that records the time you start and finish work each day. This is an
important document as it is used to validate how many hours you have worked and therefore what you should be paid
and when you are due for time off or holidays.
2. You are probably expected to complete tasks within an allotted time frame.
3. You might be asked to keep an appointment at a specific time.
While most workplaces and work vehicles are likely to have clocks, many people will use their mobile phone for alarms,
times and reminders.
20
Workplace Numeracy And Calculations
 ACTIVITY 9
Write below a list of examples regarding how you rely on using “time” in your workplace. Think of at least 5 examples
Example
1.
2.
3.
4.
5.
3.6 MEASURING TEMPERATURE
Temperature is expressed in degrees Celsius in the metric system. The boiling point of water (at sea level) is 100° Celsius, or
100° C. The freezing point of water (at sea level) is 0° Celsius. A hot day is about 35° Celsius. There are many circumstances
where temperature is important in the workplace.
1. The workplace must recognise extreme temperature risks to workers. This may relate to cold or heat. Each state has
laws that apply to safe work conditions and risk hazards related to temperature. Look at the following web sites related
to safe work conditions in extreme temperatures.
ACT www.legislation.act.gov.au/sl/2009-45/current/pdf/2009-45.pdf
NSW www.legislation.nsw.gov.au/fragview/inforce/subordleg+648+2001+ch.4-pt.4.3-div.3+0+N?SRTITLE
NTwww.worksafe.nt.gov.au/corporate/legislation.shtml
QLD www.deir.qld.gov.au/workplace/subjects/sunsafety/index.htm
SAwww.safework.sa.gov.au/show_page.jsp?id=2474
VICwww.worksafe.vic.gov.au/wps/wcm/connect/wsinternet/WorkSafe/Home/Laws+and+Regulations/
Occupational+Health+and+Safety/
WA www.slp.wa.gov.au/pco/prod/filestore.nsf/Documents/MRDocument:20289P/$FILE/
OccupSftyAndHealthRegs1996_07-j0-00.pdf?OpenElement
TAS www.wst.tas.gov.au/safety_comply/legislation
2. Temperature is often an integral part of a production process. This could apply to meeting specific temperature
requirements for smelting, for food processing and pasteurisation or for sowing of a crop or harvesting.
The following video illustrates both points we have discussed about how temperature is important in the workplace. It
shows the harvest of Pinot Noir grapes at night because the cool night temperature is beneficial for the quality of the
grapes as well as the health and safety of the workers, as they are not exposed to hot working conditions.
Click here view video “Harvesting the Amber Ridge Pinot at Night ”
OR if you are using the printed resource, enter the address below into your web browser.
www.clicker.com/web/in-the-vineyard/Harvesting-the-Amber-Ridge-Pinot-at-Night-281921/
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Workplace Numeracy And Calculations
22
4.COMPLETE NUMERACY
CALCULATIONS AND MEASUREMENTS REQUIRED IN THE WORKPLACE
As you have seen there are many different measurements that may be used in the workplace and also many different ways
that the required measurement may be obtained.
Think about the array of different measuring and calculating tools that are used in the workplace. Some examples may include:
•
•
•
•
•
•
•
•
calculators
laser equipment
rulers
tape measures
trundle wheels
scales, weighbridges
thermometers
timers, clocks
As an efficient worker you must be able to competently use any of these tools as required to correctly complete processes or
procedures related to workplace numeracy calculations. For industry sectors applicable to this workbook, typical workplace
numeracy situations may relate to:
•
•
•
•
•
•
understanding building plans e.g. in constructing structures
understanding engineering drawings e.g. in building a road
following process specifications correctly e.g. in correctly following a production process
following manufacturer specifications and instructions e.g. in using a product correctly
reading maps e.g. to find specific work locations
following instructions on material safety data sheets (MSDS) e.g. in correctly calculating chemical mixes
Workplace Numeracy And Calculations
 ACTIVITY 10
Complete all of the following calculations. For each calculation you are required to provide an example that
illustrates how the same calculation is used in your workplace.
What is the calculation
Hints to help with the
answer
Length
A roll of cable is 1000 metres.
You use 46 metres for a job.
How many metres are left on the roll?
You need to use
subtraction for this
calculation
Perimeter
A fence needs to be erected to create a
safe work area. The fenced area needs to
be 40 mtrs x 60 mtrs.
What is the length of fencing required?
You need to use
addition for this
calculation
Area
You need to cement a pad for a fuel tank
area to refill trucks and prevent seepage
into the ground from any spill. The pad is
15 mtrs x 6 mtrs.
What is the area of cement required?
You need to use
multiplication for this
calculation
Using volume
What is the total volume capacity needed
for a tank if you need to empty the
following containers into the 1 tank?
10 containers each containing 40 litres
4 containers each containing 5 litres
15 containers each containing 25 litres
You need to use
multiplication and
addition for this
calculation
You need to use
Using Numbers
Diesel costs $1.92 per litre. The capacity multiplication for this
of the tank on the truck is 200 litres. How calculation
much does it cost per tank of fuel?
What
is your
answer
Example of how this calculation is
used in your workplace
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Workplace Numeracy And Calculations
What is the calculation
Hints to help with the
answer
Using Weight
The towing capacity of your vehicle is one
tonne. You have a load of 1214 kg. Can
you use your vehicle to tow this load?
You need to understand
the different metric
weights for this answer
Using Numbers
The air pressure on a tyre measures
83 psi. It should have 90 psi.
How many psi should be added?
You need to use addition
or subtraction for this
calculation
Using Percentage
A company has 32 lost time injuries
in a year. The target for next year is to
reduce this number by 20%. What is the
maximum number of injuries that could
occur and meet the target?
You need to use
both multiplication
and division to
calculate percentage.
Alternatively use the %
key on your calculator
You need to use addition
Measuring Time
as well as multiplication
It takes 18 minutes to fill the tipper and
13 minutes to complete the circuit to the to calculate this answer
processing heap. You need to make sure
that there are 10 loads in the heap by the
end of the shift.
How long will this take with two trucks
on the go?
Measuring Time
A plane is scheduled to leave at 21.50.
The service is running an hour and
a quarter late. What time will the
plane leave?
You need to use the 24
hour clock to answer
this question
Measuring Length
Your house plan requires you to cut a
length of wood to 1.56 mtrs. How long is
this in millimetres?
You need to use
multiplication for this
calculation
What
is your
answer
Example of how this calculation is
used in your workplace
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Workplace Numeracy And Calculations
The following building skills toolbox is a great resource. It has been constructed for the building industry so examples do
relate to that sector. However, it is still a useful toolbox for any industry, as the principles of numeracy calculations are the
same for every workplace.
On the left hand side of the page are some sections you can click on. When each section opens have a look at the
right hand side of the page. Each of the calculations you have looked at in this workbook are described again in this toolkit.
This provides you with another look at the method required for each measurement with clear working diagrams.
Click here to open the tool box on the topic
OR if you are using the printed resource, enter the address below into your web browser.
http://toolboxes.flexiblelearning.net.au/demosites/series5/517/_competencies/measurecalc/fset.htm
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Workplace Numeracy And Calculations
5.ESTIMATE
APPROXIMATE QUANTITIES REQUIRED FOR DIFFERENT TASKS
Everything you have done so far relates to basic calculations in the workplace. Sometimes calculations may be more
complex. This could be for a variety of reasons but probably the most common are:
1. The volume, area or length that you need to calculate is not simple because the object is irregular.
2. The materials that need to be used for a job are often in loose states e.g. builders sand, gravel, bulk seed in a silo.
You have looked at the simple calculations for area and volume. These generally relate to rectangles, squares and cubes.
Irregular area and volume calculations could apply to more difficult shapes such as:
•
•
•
•
•
•
circles
triangles
trapezoides
cones
pyramids
cylinders
Let’s look at some calculations that are common in the workplace. For each of the calculations you need to use the correct
formula and make the calculation with a calculator. Alternatively you could use the excellent hyperlinks below that will take
you to a simple effective calculation website called Online Calculators. Although the web site is a UK link, the calculators
provide metric options for all of the different examples and calculator tools so it is completely relevant to your exercises.
www.online-calculators.co.uk/diy/
www.online-calculators.co.uk/area/
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Workplace Numeracy And Calculations
5.1 WHAT FORMULA DO I USE?
What is the formula for calculating area where the shapes are defined by the opposite sides being straight, parallel,
and of equal length?
Formula: Area = L (length) x W (width)
The area of all 3 shapes is found by multiplying the length (L) times the width (W). For example if:
L = 75 cm and W = 25 cm, then the Area = 75 x 25 =1875 cm2.
The area of a circle is found by multiplying the constant pi (π) (= 3.14) times the square of the radius (r).
The radius is half of the diameter.
Formula: Area = π x r2
π (pi) = 3.14
r2 (radius squared) = r x r
For example: If the radius is 6 metres:
Then Area = π x r2
= 3.14 x (6 x 6)
= 3.14 x 36
= 113 metres2
The area of a triangle is found by multiplying the length of the base times the length of the height, then dividing this result by 2.
Formula: Area = (b x h) ÷ 2
b = length of base
h = length of height
For example if b = 10 metres and h = 5 metres
Area = (10 x 5) ÷ 2
= (10 x 5) ÷ 2
= 50 ÷ 2
= 25 metres2
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Workplace Numeracy And Calculations
The area of a trapezoid is found by first finding the average length of the parallel sides (A + B) ÷ 2,
then multiplying the result times the height (h).
Formula: Area = [(A + B) ÷ 2] x h
For example if A = 20 metres, B + 10 metres, h = 5 metres
Area = [(A + B) ÷ 2] x h
= [(20 + 10) ÷ 2] x 5
= [30 ÷ 2] x 5
= 15 x 5
= 75 metres2
The area of an oval is found by multiplying the width (W) times the length (L), then multiplying the result by 0.8
Formula: Area = (Width x Length) x 0.8 Example
For example if W = 100 metres, L = 200 meters
= (100 x 200) x 0.8
= 20,000 x 0.8
= 16,000 metres2
Compound Simple Shapes
Many workplace measurements can be divided into multiple simple shapes. These areas are then easily
calculated by using the formulas for the simple shapes and adding the results for the total square area.
The formula used below would be:
For 2 rectangles use: Area of a rectangle + Area of a rectangle
For 2 triangles and 1 rectangle use: Area of a triangle + Area of a triangle + Area of a rectangle
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Workplace Numeracy And Calculations
Odd Shapes
The method used for irregular shaped areas is called the “offset method”. First measure the length of the longest axis of the
area (line AB). This is called the length line. Next, divide the length line into equal sections, for example 10 metres. At each
of these points, measure the distance across the area in a line perpendicular to the length line at each point (lines C through
G). These lines are called offset lines. Finally, add the lengths of all offset lines and multiply the result times the distance that
separates these lines (10 metres in this example).
For example: Length line (AB) = 60 metres and the distance between offset lines is 10 metres apart
Length of each offset line
C = 15 mtrs, D = 10 mtrs, E = 15 mtrs, F = 25 mtrs, G = 20 mtrs
Total length of offset lines = C + D + E + F + G
= 15 + 10 + 15 + 25 + 20
= 85 mtrs
Area = Distance between offset lines x sum of the length of the offset lines
= 10 mtrs x 85 mtrs
= 850 metres2
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Workplace Numeracy And Calculations
Volume
All of the previous examples relate to calculating area. What about calculating volume? There are many containers where
you may need to know the volume. How much water does a cylindrical tank hold? What if it is hollow in the centre?
What about a prism, cone or pyramid shaped object? Each calculation is also made with a formula, so once you know what
calculation to make and can measure an object accurately, it is easy to make the calculation to get the correct answer.
Volume of Cylinder
A cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder.
The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases.
The volume of a cylinder is given by the formula:
Volume = Area of base × height
V = πr2h where r = radius of cylinder and h is the height or length of cylinder.
Volume of Hollow Cylinder
Sometimes you may be required to calculate the volume of a hollow cylinder or tube.
where R is the radius of the outer surface and r is the radius of the inner surface.
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Workplace Numeracy And Calculations
Volume of Prism
A prism is a solid that has two parallel faces which are congruent polygons at both ends.
These faces form the bases of the prism. A prism is named after the shape of its base.
The other faces are in the shape of rectangles. They are called lateral faces.
When we cut a prism parallel to the base, we get a cross section of a prism.
The cross section has the same size and shape as the base.
The volume of a right prism is given by the formula:
Volume of prism = Area of base × length
V = Al where A is the area of the base and l is the length or height of the prism.
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Workplace Numeracy And Calculations
Volume of Cone
A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top.
The height of the cone is the perpendicular distance from the base to the vertex.
The volume of a cone is given by the formula:
Volume of cone = ⅓ x Area of base × height
V=
where r is the radius of the base and h is the height of the prism.
Volume of Pyramid
A pyramid is a solid with a polygonal base and several triangular lateral faces.
The pyramid is named after the shape of its base. For example, rectangular pyramid, triangular pyramid.
The lateral faces meet at a common vertex.
The height of the pyramid is the perpendicular distance from the base to the vertex.
The volume of a pyramid is given by the formula:
Volume of pyramid = ⅓ x Area of base × height
V=
where A is the area of the base and h is the height of the pyramid.
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Workplace Numeracy And Calculations
Volume of Sphere
A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the centre of the
sphere. The distance from the centre to the surface is the radius.
Volume of sphere =
where r is the radius.
Volume of hemisphere
A hemisphere is half a sphere, with one flat circular face and one bowl-shaped face.
Volume of hemisphere
where r is the radius.
Obviously all of the calculations can be made using the formula given plus a calculator. In addition there are useful websites
that have built in calculators for different calculations. Have a look at the link below. You are then required to use the given
formula, a calculator or the web links and complete the following activity.
www.online-calculators.co.uk/volumetric/
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Workplace Numeracy And Calculations
 ACTIVITY 11
Complete all examples in the table.
Your workplace task is:
Calculate the area of a football oval that
requires spraying for weeds. The oval is
150mtrs long x 85 mtrs wide.
Calculate the volume of a water tank. The tank is
a cylindrical shape. The base has a radius of
3 metres and it is 3 metres high.
You need to transport 7 crates in a trailer.
The crates are 150cm long x 80cm wide x 40cm high.
What is the total area they will take in a trailer?
You need to calculate the volume required
to backfill an area of soil. The area is a prism
shape with a base of 10 square metres and a
height of 2 metres.
You have been contracted to paint the 4 external
walls of a shed. You need to calculate the surface
area to be painted so you buy the correct amount
of paint.
Each wall is 5 metres x 4 metres.
What is the total volume needed for a tank if you need
to empty the following containers into the 1 tank.
20 containers each containing 60 litres.
4 containers each containing 50 litres.
15 containers each containing 35 litres.
You need to calculate the length of an area that
requires barrier fencing to improve pedestrian
safety where civil works are occurring. The area
is a compound shape comprising a triangle and
a rectangle. The triangle has 3 equal sides of 10
metres and the rectangle has 2 sides of 10 metres
and 2 sides of 20 metres.
What formula do
you need to use
What shapes/
volumes are you
working with
What is your
answer
34
Workplace Numeracy And Calculations
35
6. WHAT OTHER
WORKPLACE REQUIREMENTS NEED TO BE CONSIDERED WHEN COMPLETING NUMERACY AND CALCULATION TASKS
In any workplace there are many instructions, forms and signs that will require a reasonable level of numeracy skills.
Have a think about the numeracy calculations you have worked through in this book so far. All of the calculations have also
required you to be following some type of instruction as well.
Instructions can include:
•
•
•
•
•
•
•
•
•
•
•
•
•
organisation’s work specifications and requirements
plans and specifications
regulatory and legislative requirements
relevant Australian standards
safe work procedures or equivalent
signage
verbal or written and graphical instructions
work bulletins/memos
work schedules
legislative, organisational and site requirements and procedures
code of practice
Employment and Workplace Relations legislation
Equal Employment Opportunity and Disability Discrimination legislation
Workplace Numeracy And Calculations
 ACTIVITY 12
At the most basic level the following signs are commonly seen in the workplace or in your daily life.
To complete the activity please explain:
•
•
What each sign means
What “measurement” is used in the sign
The sign
What does this sign mean
What measurement is used
Your final activity for this workbook asks you to think about numeracy calculations in your workplace again. Now that you
have spent time completing the activities and answering questions, you should be aware of many more situations where
numeracy is important.
36
Workplace Numeracy And Calculations
 ACTIVITY 13
Complete the following providing an example of each situation that applies in your workplace. The blank
sections at the end are for you to add another 4 examples that have not been previously listed but that occur in
your workplace and require numeracy skills to complete.
Workplace document
Plans and specifications
Regulatory and legislative requirements
Australian standards
Safe work procedures or equivalent
Work bulletins/memos/schedules
Verbal or written and graphical instructions
What numeracy
Describe a workplace situation where you
skills are needed participate in this task
37
Workplace Numeracy And Calculations
7. BEING CONFIDENT
ABOUT YOUR SKILL LEVELS IN THE WORKPLACE
After finishing all of the activities in this workbook you should be able to competently complete final summative assessments.
Do you feel that you are confident about your skill levels in the workplace related to workplace numeracy and calculations?
Use the table below to help you check your skills. Before commencing your final assessments it is important to review any
sections in which you feel unsure.
Remember: it is always OK to ask your supervisor or your assessor questions.
In the table below, read the list of skills and knowledge you should have after completing this workbook.
Skills /knowledge you should have
The ability to locate, interpret and apply
relevant information.
The ability to comply with site safety plan, OHS
regulations and state and territory legislation
applicable to workplace operations.
The ability to comply with organisational
policies and procedures, including quality
requirements.
Safely and effectively use tools and equipment.
Communicate and work effectively and safely
with others.
Complete measurements, calculations and
determination of quantities for different
projects of varying complexity in a range of
contexts or occasions over time.
Need practice
1. Put a tick in the column if you can do this now and a brief comment re why you believe you have this skill.
2. Put a tick in the next column if you feel you need more practice and a brief comment as to why.
3. If you require further training, complete the third column listing what training is needed. Show this list to your supervisor
or assessor and ask for more time or training before completing the summative assessments.
Yes
Comment on why
What additional
training do I need
38
Workplace Numeracy And Calculations
8. ASSESSMENT
You have now reached the end of this workbook. All of the information and formative assessments you have covered apply to
the skills related to numeracy and calculations in the workplaces listed at the front of the booklet. Please ask your assessor
for final summative assessment/s for this workbook. Assessments may be provided in a variety of ways and may include:
• written assignments
• short-answer tests
• direct observation of tasks in real or simulated work conditions, with questioning and demonstration to confirm the
ability to consistently and correctly complete tasks
Assessment should confirm that competency is able to be transferred to other circumstances and environments.
 FEEDBACK
This workbook has been developed to guide users to access current information related to gaining skills appropriate to their workplace.
Please complete the following table notifying us of any errors or suggested improvements.
Subject Name
Workplace Numeracy And Calculations
Book Number
Book 1
Page What is the error
10
You tube video is not accurate
Suggested improvement
Better websites / You Tube example
Is there a link to your suggested improvement
Additional comments

Click here to email your completed workbook to your assessor.
39
Workplace Numeracy And Calculations
9. BIBLIOGRAPHY
AND SOURCES FOR CONTENT IN MATERIALS
www.helpingwithmath.com/by_subject/geometry/geo_volume.htm
http://toolboxes.flexiblelearning.net.au/demosites/series5/517/_competencies/measurecalc/fset.htm
www.online-calculators.co.uk/volumetric/
www.online-calculators.co.uk/diy/
www.online-calculators.co.uk/area/
www.legislation.act.gov.au/sl/2009-45/current/pdf/2009-45.pdf
www.legislation.nsw.gov.au/fragview/inforce/subordleg+648+2001+ch.4-pt.4.3-div.3+0+N?SRTITLE
www.worksafe.nt.gov.au/corporate/legislation.shtml
www.deir.qld.gov.au/workplace/subjects/sunsafety/index.htm
www.safework.sa.gov.au/show_page.jsp?id=2474
www.worksafe.vic.gov.au/wps/wcm/connect/wsinternet/WorkSafe/Home/Laws+and+Regulations/
Occupational+Health+and+Safety/
www.slp.wa.gov.au/pco/prod/filestore.nsf/Documents/MRDocument:20289P/$FILE/
OccupSftyAndHealthRegs1996_07-j0-00.pdf?OpenElement
www.wst.tas.gov.au/safety_comply/legislation
www.clicker.com/web/in-the-vineyard/Harvesting-the-Amber-Ridge-Pinot-at-Night-281921/
www.wisc-online.com/objects/ViewObject.aspx?ID=gch302
www.helpingwithmath.com/printables/worksheets/geo0601volume01.htm
www.helpingwithmath.com/printables/worksheets/geo0601volume02.htm
www.helpingwithmath.com/printables/worksheets/geo0601volume03.htm
www.helpingwithmath.com/printables/worksheets/geo0701volume01.htm
40