BUDGETING, ODDS & PROBABILITY - VCAL - NUMERACY - Victorian Responsible ...
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VCAL – NUMERACY BUDGETING, ODDS & PROBABILITY
Acknowledgements
Project sponsor: Shane Lucas, Chief Executive Officer, Victorian Responsible
Gambling Foundation
Resource authors: Justine Sakurai, Multifangled Pty Ltd
Resource editors: Mark Riddiford, Senior Prevention Advisor (Education) and
Carl Nilsson-Polias, Senior Communication Advisor, Victorian
Responsible Gambling Foundation
Designer: Ben Galpin
First published 2016
Reprinted with amendments 2021
© The Victorian Responsible Gambling Foundation and licensed for re-use under the
Creative Commons Attribution 3.0 Australia licence.
responsiblegambling.vic.gov.au/copyright
Victorian Responsible Gambling Foundation
Address: Level 6, 14–20 Blackwood Street, North Melbourne, Victoria 3051
Mail: PO Box 2156, Royal Melbourne Hospital, Victoria 3050
Ph: (03) 9452 2600
Website: responsiblegambling.vic.gov.au
Email: contact@responsiblegambling.vic.gov.au
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 2
beaheadofthegame.com.au
The Victorian Responsible Gambling Foundation is working towards reducing harm from
gambling in our community by building greater awareness and understanding of the risks
involved. We work with young people, educators, coaches and parents, to provide balanced
information and practical resources to prepare young people before they reach the legal
gambling age.
The gambling environment has changed. Never before has gambling been so heavily promoted
and accessible, especially through sport, making it feel like a normal part of the game. As a result,
it is harder for students to recognise the potential harms of gambling. We want young people to
love the game, not the odds.
Our Be Ahead of the Game school education program is one of a suite of Love the Game
community programs that raise awareness about the way young people are being increasingly
exposed to gambling. Drawing on the latest research, this free program supports your secondary
school community to help students develop informed attitudes to gambling.
This program offers:
• face-to-face information sessions for teachers, parents and students
• resources, including this one, containing activities to incorporate in your curriculum plans
across a variety of subject areas
• useful resources for parents.
You can select these and other strategies for preventing gambling harm in the program’s School
Gambling Policy template, which can be adapted to suit your school’s needs. Access the policy
template at lovethegame.vic.gov.au/schools
If, when teaching this unit, you become concerned that gambling is affecting a student
or someone they know, you can refer them to our free and confidential Gambler’s Help
Youthline support service on 1800 262 376 or at gamblershelp.com.au/youthline.
Concerned teachers and parents can also contact this service for advice or visit
gamblershelp.com.au for more information.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 3
beaheadofthegame.com.au
Resources for the VCAL
The Victorian Responsible Gambling Foundation has produced a number of resources to support
the delivery of the Victorian Certificate of Applied Learning (VCAL).
VCAL is accredited at three levels: Foundation, Intermediate and Senior. The three qualification
levels cater for a range of students with different abilities and interests. They also provide a
progression in the development of personal, workplace and subject specific skills, knowledge
and attributes which help students make informed choices about employment and education
pathways.
The VCAL Curriculum covers the following strands:
• Literacy and Numeracy Skills
• Industry Specific Skills
• Work Related Skills
• Personal Development Skills.
The Victorian Responsible Gambling Foundation’s VCAL resources cover:
• Literacy and Numeracy Skills
• Personal Development Skills (PDS).
The table below lists the resources and the main VCAL curriculum areas covered by each
resource. Each resource may cover learning outcomes from areas other than those noted.
Detailed curriculum alignment can be found in each resource.
PDS Literacy: Literacy: Oral Numeracy
Reading and Communication
Unit 1 Unit 2 Writing Unit 1 Unit 2
Knowing the
score
Knowing when
it’s a concern
Love the game
Potential
influences
What are the
odds?
Budgeting, losses
and probability
Note: Not all learning outcomes from a VCAL unit are covered in each resource.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 4
beaheadofthegame.com.auResource overview Resource focus This resource has been developed to address learning outcomes from Unit 1 Numeracy Skills (NUM) for students working at Foundation, Intermediate and Senior levels. These resources may also be adapted to suit the Victorian Curriculum Mathematics requirements. Developing numerical skills by using the worksheets and activities, students will develop awareness of the mathematics associated with gambling and risk. Students learn to recognise the costs of living and start to develop personal budgeting skills, including an understanding of the responsibilities of paying common bills. Resource structure This resource consists of: • information for teachers about how to deliver the activities • worksheets, templates and resources for students There are 14 activities in this resource: 1. Budget task 8. Odds 2. Creating a budget (part one) 9. Odds at the racetrack 3. Creating a budget (part two) 10. Lottery odds (Senior) 4. Understanding bills 11. Odds with pokies 5. How much are people spending (part one) 12. An experiment with odds 6. How much are people spending (part two) 13. Understanding gambling in Victoria 7. Coin experiment 14. Calculating risk. Resource requirements For the learning activities described in this resource, teachers will need to ensure that students have access to: • an internet-connected device • a calculator or a device with calculation software • a spreadsheet and/or graphing software • a class set of dice for the experiment with odds activity. BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 5 beaheadofthegame.com.au
Assessment
The following can be used to assess students’ competence in the Numeracy Skills Unit 1 learning
outcomes:
• class discussions
• worksheets and related documents
• results of spreadsheets and graphing tasks
• research findings
• feedback on the activity (Senior)
In addition, you might observe students’ participation in working in a team and in conducting the
activity.
Students may work individually, in groups or as a class to complete the activities presented here.
The teacher is encouraged to use these worksheets in a pedagogical manner that best suits their
students.
Summary of activities
Activities Activity overview Resource requirements
1. Budget task Students brainstorm individually, in • Access to a calculator or software
pairs or with the class the expenses with calculation capability
covered in a weekly personal budget • Worksheet
that is familiar to them. They make
• Teacher whiteboard or screen
calculations from weekly to monthly
sharing on device
to yearly and find totals. They read
a graph to find average wages for
generalised industry areas and make
decisions about their budgets.
2. C
reating a Students work through three scenarios • Access to a calculator or software
budget (part of different budgets and make with calculation capability
one) calculations from a short text. • Worksheet
• Teacher whiteboard or screen
sharing on device
3. C
reating a Students consider their priorities when • Worksheet
budget (part making a budget. They make decisions • Teacher whiteboard or screen
two) relating to the importance of budget sharing on device
items.
4. U
nderstanding To prepare for budgeting, students • Access to a calculator or software
bills study a water bill and a gas bill and with calculation capability
determine key facts from these bills • Worksheet
and perform simple calculations. By
• Teacher whiteboard or screen
examining bills, they learn to look
sharing on device
for key features of a bill and become
familiar with the numerical language • Projection software
used on these documents.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 6
beaheadofthegame.com.auActivities Activity overview Resource requirements
5. H
ow much A mix and match activity looking at • Access to a calculator or software
are people numbers related to gambling harm with calculation capability
spending (part in the Victorian community from • Worksheet
one) the VRGF. Students will make some
• Teacher whiteboard or screen
calculations either individually or
sharing on device
in a group to complete the activity.
Students complete multiplication • An internet-connected device
algorithms. responsiblegambling.vic.gov.au/
resources/gambling-victoria/
expenditure-on-gambling-victoria-and-
australia/
6. H
ow much Students will use spreadsheet • Access to a calculator or software
are people or graphing software to create a with calculation capability
spending (part spreadsheet and graph of data • Worksheet
two) obtained from the VRGF website.
• Teacher whiteboard or screen
They will answer a series of questions
sharing on device
about the data they have selected. It
is recommended that students submit • An internet-connected device
their work electronically for this activity. • Spreadsheet and/or graphing
software
responsiblegambling.vic.gov.au/
resources/gambling-victoria/pokies-
across-victoria/
7. C
oin Students look at the concept of odds • Class set of dice
experiment and answer a series of questions • Access to a calculator or software
relating to the understanding of odds. with calculation capability
• Worksheet
• Teacher whiteboard or screen
sharing on device
8. Odds Students learn how odds can be • Access to a calculator or software
expressed as a ratio. They consider with calculation capability
what the ratio means and how the ratio • Worksheet
can be expressed as a percentage.
• Teacher whiteboard or screen
Students consider the advantages and
sharing on device
disadvantages associated with odds.
9. O
dds at the Students learn the different ways which • Access to a calculator or software
racetrack odds may be written or presented with calculation capability
at the racetrack. They consider the • Worksheet
scenario of a day at a racetrack and
• Teacher whiteboard or screen
calculate payouts and losses. They also
sharing on device
learn about commission fees.
10. Lottery odds Students consider a complex • Access to a calculator or software
(Senior) combination formula and follow step- with calculation capability
by-step instructions to undertake • Worksheet
an unfamiliar algebraic substitution.
• Teacher whiteboard or screen
They learn how odds are calculated
sharing on device
with lotto scenarios and consider the
extreme odds presented.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 7
beaheadofthegame.com.auActivities Activity overview Resource requirements
11. O
dds with By conducting a small experiment using • Random number generator
pokies a random number generator, students software
develop a sense of creating low odds. • Access to a calculator or software
They learn how pokies machines use with calculation capability
maths to make a profit for the owner of
• Worksheet
the machine.
• Teacher whiteboard or screen
sharing on device
12. A
n experiment Students study a graph to deduce • Class set of dice
with odds odds and answer a series of questions. • Access to a calculator or software
Students conduct an experiment using with calculation capability
dice to consolidate their knowledge.
• Worksheet
• Teacher whiteboard or screen
sharing on device
13. Understanding Students examine a graph of Australian • Access to a calculator or software
gambling in gambling statistics and answer a with calculation capability
Victoria series of questions demonstrating • Worksheet
their knowledge of the conventions
• Teacher whiteboard or screen
of graphs and their ability to make
sharing on device
assumptions based on available data.
14. C
alculating This activity is designed to promote • Set of risk cards
risk discussion about the concept of risk • Access to a calculator or software
using odds. Students order cards from with calculation capability
least to most risky using the scenarios
presented. Students are to understand
that gambling is the riskiest activity.
The most up-to-date version of this resource is available at
beaheadofthegame.com.au
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 8
beaheadofthegame.com.auCurriculum links
The Numeracy (NUM) units are designed to support students to develop mathematical skills in
order to carry out processes and functions in everyday life. These numerical skills should allow
for practical application of mathematics in life, work and the community. These skills include
numerical calculation skills and financial literacy.
The activities in this resource support the development of the learning outcomes in NUM Unit 1
and, as such, the focus is on Learning Outcome 1 Numerical Information and Learning Outcome 2
Financial Literacy.
Reference to links between the activities and specific elements and learning outcomes is noted in
the table below and the following pages. However, the activities are broad and can be undertaken
in different ways. The alignment shows what is possible. It is up to teachers to check the students
work against the curriculum.
The information about the NUM units has been adapted from the VCAL Planning Guide – Literacy
and Numeracy Skills Strand, available at vcaa.vic.edu.au/curriculum/vcal/vcal-curriculum
For assessment guidelines and practices, see also vcaa.vic.edu.au/assessment/vcal-assessment
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
At the Foundation level, At the Intermediate level, At the Senior level,
students should students should students should
• be able to perform simple • develop everyday numeracy • explore mathematics beyond
and familiar numeracy tasks skills to make sense of their its familiar and everyday use
• develop the ability to make daily personal and public to its application in wider,
sense of mathematics in their lives less personal contexts
daily personal lives. • understand the use of • be able to interpret and
software tools and devices analyse how mathematics is
applied to tasks such as represented and used.
those in the workplace and • recognise and use some
the community. of the conventions and
symbolism of formal
mathematics.
Activity alignment to VCAL unit learning outcomes
The activities in this resource support the development of the learning outcomes in NUM Unit 1.
Assessment tools for units other than NUM Unit 1 are not provided. Note, the activities in this
resource are broad and can be undertaken in different ways. Teachers should check what students
have produced against the curriculum.
Activities may be mapped against different levels depending on the level of teacher support
and scaffolding.
To modify activities for different levels, teacher judgement is encouraged to use part or all of each
worksheet.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 9
beaheadofthegame.com.auActivities 1, 2 and 3: Budgeting
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
Learning outcome 1 Learning outcome 1 Learning outcome 1
• Add, subtract, multiply and • Perform a range of • Estimate and demonstrate an
divide simple numbers, calculations of whole approximation for a detailed
fractions and decimals. numbers, fractions and budget involving a group
• Perform simple calculations. decimals with the four activity.
operations.
• Read and use simple tables,
maps, diagrams, graphs and • Obtain accurate results
flow charts. for multi-step calculations
involving money.
• Demonstrate the above
mathematical skills and • Estimate and demonstrate a
processes in a hands-on, detailed personal budget.
simple problem-solving • Compare data from familiar
activity. tables and graphs using
software tools and devices.
Learning outcome 2 Learning outcome 2
Describe ways to keep your Estimate and demonstrate a
money safe both manually and detailed personal budget.
electronically.
Activities 4, 5 and 6: Bills and spending
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
Learning outcome 1 Learning outcome 1 Learning outcome 1
• Recognise whole numbers • Perform a range of • Use and apply order of
and simple, familiar fractions calculations of whole arithmetical operations to
and decimals in numeral and numbers, fractions and solve equations with multi-
word form. decimals with the four step calculations, including
• Read and use simple tables, operations. the use of fractions, decimals
maps, diagrams, graphs and • Convert between routine up to thousandths and
flow charts. metric units, demonstrating percentages.
• Recognise whole numbers an understanding of common • Compare data from complex
and simple, familiar fractions prefixes. tables or graphs or schedules
and decimals in numeral and • Compare data from familiar using software tools and
word form. tables and graphs using devices.
software tools and devices.
Learning outcome 2 Learning outcome 2
• Perform calculations based • Compare and contrast the
on monetary notation money notation expressions
expressions within a range within a range of personal
of personal financial and official financial
documents. documents.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 10
beaheadofthegame.com.auActivities 7, 8 and 9: Coin experiment, odds and odds at the racetrack
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
Learning outcome 1 Learning outcome 1 Learning outcome 1
• Recognise whole numbers • Perform a range of • Use and apply order of
and simple, familiar fractions calculations of whole arithmetical operations to
and decimals in numeral and numbers, fractions and solve equations with multi-
word form. decimals with the four step calculations, including
operations. the use of fractions, decimals
• Describe, compare and up to thousandths and
interpret the likelihood of percentages.
everyday chance events • Use knowledge about chance
using qualitative terms. and probability to estimate
and interpret the outcomes
of common chance events
in both numerical and
qualitative terms.
• Use and apply knowledge
about probability to a range
of relevant contexts.
Learning outcome 2
• Perform calculations
involving fractions and
percentages as applied to
money.
Activity 10: Lottery odds
Foundation NUM Unit 1 Intermediate NUM Unit 1 Intermediate NUM Unit 1
Learning outcome 1 Learning outcome 1 Learning outcome 1
• Recognise whole numbers • Perform a range of • Develop, interpret, solve
and simple, familiar fractions calculations of whole and use substitution in
and decimals in numeral and numbers, fractions and routine formulae and
word form. decimals with the four algebraic expressions
operations. as representations and
conventions that describe
relationships between
variables in relevant contexts.
• Calculate theoretical
probabilities and use tree
diagrams to investigate the
probability of outcomes in
simple multiple-event trials.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 11
beaheadofthegame.com.auActivities 11 and 12: Odds with pokies and an experiment with odds
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
Learning outcome 1 Learning outcome 1 Learning outcome 1
• Add, subtract, multiply and • Perform a range of • Use knowledge about chance
divide simple numbers, calculations of whole and probability to estimate
fractions, decimals and numbers, fractions and and interpret the outcomes
decimals. decimals with the four of common chance events
• Order and use whole operations. in both numerical and
numbers and familiar, simple • Describe, compare and qualitative terms.
fractions and decimals in interpret the likelihood of • Use and apply order of
everyday texts or simple everyday chance events arithmetical operations to
tables. using qualitative terms. solve equations with multi-
• Collect and organise familiar • Collect and organise familiar step calculations, including
data. and unfamiliar data and the use of fractions, decimals
construct tables, graphs and up to thousandths and
charts, manually or using percentages.
software tools and devices. • Use and apply knowledge
about probability to a range
of relevant contexts.
Activity 13: Understanding gambling in Victoria
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
Learning outcome 1 Learning outcome 1
• Order and use whole • Perform a range of
numbers and familiar, simple calculations of whole
fractions and decimals in numbers, fractions and
everyday texts or simple decimals with the four
tables. operations.
• Collect and organise familiar • Describe, compare and
data. interpret the likelihood of
everyday chance events
using qualitative terms.
• Collect and organise familiar
and unfamiliar data and
construct tables, graphs and
charts, manually or using
software tools and devices.
Learning outcome 3
• Compare data from familiar
tables and graphs using
software tools and devices.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 12
beaheadofthegame.com.auActivity 14: Risk
Foundation NUM Unit 1 Intermediate NUM Unit 1 Senior NUM Unit 1
Learning outcome 1 Learning outcome 1 Learning outcome 1
• Recognise whole numbers • Perform a range of • Use knowledge about chance
and simple, familiar fractions calculations of whole and probability to estimate
and decimals in numeral and numbers, fractions and and interpret the outcomes
word form. decimals with the four of common chance events
operations. in both numerical and
• Describe, compare and qualitative terms.
interpret the likelihood of
everyday chance events
using qualitative terms.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 13
beaheadofthegame.com.auStudent worksheet –
Budget task
This activity covers personal budgets and asks you to look at what you might need to spend
money on (your expenses) and to compare weekly, monthly and yearly figures. This then leads on
to looking at what you might earn (your income) and how it compares with your expenses.
Consider the following scenario: Canberra is an 18-year-old who has just left school and is now
living out of home, sharing a unit with an old schoolmate.
1. What is an essential expense?
2. Brainstorm in pairs or with your class all the essential expenses that Canberra
might have with sharing accommodation. List them in the table below.
Refer to moneysmart.gov.au/budgeting/budget-planner for some ideas of
common expenses
3. Estimate how much each expense might be each week for the two friends.
Expense Cost estimate Explanation
per week for two
people ($)
Electricity
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 14
beaheadofthegame.com.auStudent worksheet – Budget task
Expense Cost estimate Explanation
per week for two
people ($)
4. Work out your estimates for each expense to give yearly and monthly
approximations of living costs. For yearly expenses, multiply the weekly
estimate by 52. For a monthly estimate, divide the yearly expense by 12.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 15
beaheadofthegame.com.auStudent worksheet – Budget task
5. Add up each column to find the weekly, monthly and yearly totals.
Expense Cost estimate × 52 ÷ 12
per week for two for approximate for approximate
people ($) yearly cost ($) monthly cost ($)
Electricity
Totals
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 16
beaheadofthegame.com.auStudent worksheet – Budget task
6. Now consider other non-essential expenses. Some are listed below but add
in other expenses that someone might spend money on. (If some of these
expenses are paid monthly or yearly, consider how you could calculate the
weekly cost.)
Expense Cost estimate × 52 ÷ 12
per week for for approximate for approximate
one person ($) yearly cost ($) monthly cost ($)
Phone
Petrol
Car registration
Car maintenance
Study fees
and costs
Streaming
service fee
Music subscription
Totals
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 17
beaheadofthegame.com.auStudent worksheet – Budget task
7. Now combine all the expenses to get the overall costs – add your totals
together.
Weekly Monthly Yearly
Essential expenses $ $ $
Other expenses $ $ $
Totals $ $ $
8. Consider the following chart from the Australian Bureau of Statistics.
The chart shows the average weekly wage before tax (gross income) by
industries.
Source: ABS.
abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/6302.0Nov%202019?OpenDocument
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 18
beaheadofthegame.com.auStudent worksheet – Budget task
Choosing an industry from the chart above that interests
$
you, what is the average weekly wage?
Approximate monthly wage? $
Approximate yearly wage? $
9. What is the difference between your income, based on the average wage
you chose, and your estimated costs of essential services plus other
expenses?
Weekly Monthly Yearly
Average wage $ $ $
Total expenses
(essential expenses
$ $ $
plus other
expenses)
Difference $ $ $
10. Comment on what your analysis and comparison of your income and
expenses shows?
11. In the light of this, review the budgeting expenses that you listed in the
earlier tables. Are there any changes you would make to your budget based
on your wage?
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 19
beaheadofthegame.com.auStudent worksheet – Budget task
12. What is discretionary spending? How much do you think should be
budgeted for discretionary spending each week? Month? Give reasons for
your choice. Discuss your answers with the class.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 20
beaheadofthegame.com.auStudent worksheet –
Creating a budget (part one)
Look at the three scenarios about personal budgets below and answer the
questions.
SCENARIO
Three 18-year-old friends have just finished school and need to create weekly
budgets to plan and monitor their spending.
• Perth is a full-time first-year apprentice mechanic who is earning $444.60 a
week after tax (net income). On average, each week Perth pays rent of $120,
food costs of $140, a phone bill of $20, car costs of $110, utilities (electricity,
water and gas) costs of $20 and clothing costs of $40.
• Ballarat is working full-time as a builder’s laborer and is earning $743.58 a week
net income. On average, each week Ballarat pays $250 board to their parents
for living at home, car costs of $150, a phone bill of $30 and clothing costs of
$50.
• Omeo is working 10 hours a week and is also completing a Diploma in Aged
Care. Omeo gets a weekly Youth Allowance payment of $142.70 and $188.20
after tax from a part-time job at an aged care facility. On average, each week
Omeo pays $200 board, myki costs of $25, a phone bill of $20 and clothing
costs of $45.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 21
beaheadofthegame.com.au1. Using the above information, work with your group to complete the tables
below. Perth’s budget has been completed as an example.
Perth’s budget items Weekly income Weekly expenses
Wage $444.60
Rent $120.00
Food $140.00
Phone $20.00
Car $110.00
Utilities $20.00
Clothing $40.00
Totals $444.60 $450.00
Ballarat’s budget items Weekly income Weekly expenses
Wage
Board
Phone
Car
Clothing
Totals
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 22
beaheadofthegame.com.auStudent worksheet – Creating a budget (part one)
Omeo’s budget items Weekly income Weekly expenses
Youth Allowance
Part-time wage
Board
Myki
Phone
Clothing
Totals
2. Using the above information, calculate the weekly spending money for
Ballarat and Omeo. Follow the example for Perth below.
a. Income minus expenses for Perth: $444.60 - $450.00 = -$5.40,
no spending money!
b. Income minus expenses for Ballarat:
c. Income minus expenses for Omeo:
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 23
beaheadofthegame.com.auStudent worksheet – Creating a budget (part two) In the table below, prioritise the expenses you have listed on your previous sheets from most to least important. Consider rent, groceries, power, water, phone as well as non-essential items like gifts, entertainment, etc. Item 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14 15. BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 24 beaheadofthegame.com.au
Student worksheet – Creating a budget (part two)
1. When budgeting, you have to prioritise your spending. What were your top
five spending priorities and why?
1.
2.
3.
4.
5.
2. Was entertainment in your top five? Why/why not?
3. Gambling could be considered an expense under ‘entertainment’. What
advice would you give to a friend over 18 who was spending part of their
budget on gambling?
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 25
beaheadofthegame.com.auStudent worksheet – Creating a budget (part two) 4. Consider this statement: ‘More money spent on gambling means less money available for other things.’ What other things might someone miss out on if they spend too much money on gambling? BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 26 beaheadofthegame.com.au
Student worksheet –
Understanding bills
A key part of budgeting is planning for and paying household bills.
Understanding how bills work and how to pay them on time can help you save
money. In this activity, you will look at a water bill and a gas bill and find out
about some key features and costs related to such bills.
Understanding a water bill
Service account
Water
co.
Date of Issue: 11th May 2020
4267006700
L&G
41 Aquatic Road
Diamond Beach $
VIC 3999 028
R0_149760 19th Jun 2020
41 Aquatic Road, Diamond Beach VIC 3999 Developed
Previous Balance We Received Adjustments Interest Opening Balance
$7.35 $7.35 $0.00 $0.00 $0.00
SERVICE CHARGES (Period 1st Mar 2020 - 30th Jun 2020)
Water $101.90
Waste Water $158.15
VOLUMETRIC CHARGES
SERIAL NO. PREVIOUS READING CURRENT READING CONSUMPTION
06W920069 18 Nov 19 432 28 Mar 20 461 29
29kL @ $1.84/kL $
kL
Total Current Charges $
Average daily Water
Usage in litres
Same Period This
Last Year account
107 221 TOTAL AMOUNT DUE $
Interest charged at 4% per annum on overdue accounts.
For concession eligibility refer to back of account.
L
0 41 Aquatic Rd, Diamond Beach VIC 3999
4 00
BPAY View Registration No.: 0
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 27
beaheadofthegame.com.auStudent worksheet – Understanding bills
1. Explain mathematically how the consumption charge of $53.36 was
calculated.
2. Calculate and complete the totals owed in the circles. To do this add the
service and volumetric charges together.
3. What time period does this bill cover for water and wastewater?
4. Describe the different ways this bill could be paid.
5. Water supply and wastewater are fixed charges per bill. How much were
these charges?
Water supply: Wastewater:
What percentage of the bill did these fixed charges comprise?
6. It is recommended that, in Victoria, average daily water use is 155L per
person per day.
How many litres are in 29 KL?
How many litres were used per day?
7. Interest is charged at 4% per annum on overdue accounts. Describe what
this means in your own words.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 28
beaheadofthegame.com.auStudent worksheet – Understanding bills
8. Explain what might happen if the bill is not paid on time.
Understanding a gas bill
55 POWER STREET, SPRINGFIELD VIC 3955
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 29
beaheadofthegame.com.auStudent worksheet – Understanding bills 1. How was the last bill paid? 2. How much is the supply charge? BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 30 beaheadofthegame.com.au
Student worksheet – Understanding bills
3. Suggest reasons why this bill may be larger than the previous bill.
4. How much would the total be without GST?
5. Given the supply charge was $36.96 at 77c per day. How many days does
the supply charge cover?
Explore energy.gov.au/households an Australian Government website for householders to help
people manage their energy needs and consumption.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 31
beaheadofthegame.com.auStudent worksheet –
How much are people spending?
(part one)
In this activity, you will look at some data and information related to gambling in the Victorian
community.
Gambling data
Below is information provided by the Victorian Responsible Gambling Foundation. This data
is about the Victorian Local Government Area of Greater Dandenong. The graphic is based on
Australian gambling data from 2019 to 2020.
$327,454 $87,430,092
spent on pokies per day spent on pokies per year
15 927
pokies
venues with pokies
(this is 94% of allowable machines)
6.9 4th 2nd
pokie machines highest pokies expenditure In Victoria for socio-
per 1000 adults in Victoria economic disadvantage
Source: responsiblegambling.vic.gov.au/resources/gambling-victoria/pokies-across-victoria/
$24.89 b $539 x 1.5 374 $5.81 b
Total gambling losses Average pokies losses Average sports betting losses gambling ads a day on Total gambling losses were
were $24.89 billion, were $539 per per Victorian adult have risen Australian free-to-air TV in 2016 $5.81 billion, up by 6.2%
up by 5.0% Victorian adult by more than 50% in 5 years:
from $46.90 to $74.34
Source: responsiblegambling.vic.gov.au/resources/gambling-victoria/expenditure-on-gambling-victoria-and-australia/
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 32
beaheadofthegame.com.auStudent worksheet – How much are people spending? (part one)
1. What is one piece of the data about Greater Dandenong that surprised you?
Explain why.
2. What is one piece of the Australian gambling data that surprised you?
Explain why.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 33
beaheadofthegame.com.auStudent worksheet – How much are people spending? (part one)
Matching pairs
First, review with your teacher the different ways you can write out a thousand, a
hundred thousand, a million, a billion, etc.
In the activity below, each shaded card reflects a cost related to gambling. The
unshaded cards represent other kinds of spending.
Each shaded card matches an unshaded card in terms of the dollar value
indicated. Cut out the cards and then match them in pairs.
$5.81 billion total
$326,882 spent on $119,311,878 spent on
gambling losses in
pokies per day pokies each year
Victoria in 2017
$539 average loss to
$24.89 billion gambling $74.34 average loss
pokies per Victorian
losses in 2017 per bet
adult in 2017
374 TV gambling ads
Two Sydney airports at
per day at an average A new PlayStation
$12.5 billion each
of $5000 per ad
A $2 million house in Two new hoodies
House worth $300,000
an expensive suburb at $37 each
11 Airbus 380 40 Commercial
private jumbo jets wind turbines at
at $500 million each $3 million each
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 34
beaheadofthegame.com.auStudent worksheet –
How much are people spending?
(part two)
The Victorian Responsible Gambling Foundation (VRGF) collects data about pokies in local
councils in Victoria. These statistics include the number of pokies machines and the amount spent
on pokies per day in different council areas.
Go to responsiblegambling.vic.gov.au/resources/gambling-victoria/pokies-across-victoria/
1. Choose eight different councils or Local Government Areas (LGA) from the
interactive map at the link above.
2. Open spreadsheet software and create a new file. (Your teacher will advise
you which software to use.)
3. Find the data ‘amount spent on pokies per day’ for each of your eight
councils and enter this data into your spreadsheet. (Your teacher may ask
you to email your spreadsheet to them.)
Below is a sample of the data for three LGAs.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 35
beaheadofthegame.com.auStudent worksheet – How much are people spending? (part two)
4. Using the spreadsheet tools, create a graph to show your data.
5. Answer the following questions:
a. Which of the LGAs had the greatest gambling losses in total? Name one
factor that might contribute to this.
b. What is the difference between the highest and lowest amount spent on
pokies per day for your chosen LGAs?
c. If the average gambling expenditure per adult in Australia was $12,000*,
does that mean that every adult spent this amount on gambling in 2020?
Why or why not?
*Source: savings.com.au/savings-accounts/gambling-statistics-australia
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 36
beaheadofthegame.com.auStudent worksheet – How much are people spending? (part two)
d. Use the data from your spreadsheet to identify another feature or
pattern of gambling and show evidence to support this.
e. Are there more pokies in metropolitan areas than in country areas? Use
the interactive tool on the VRGF website (above) to help you make a
decision. Give examples to support your decision.
f. Which LGAs have the highest density of pokies? Do people living in
these areas spend more on pokies? Show evidence of this possible
pattern.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 37
beaheadofthegame.com.auStudent worksheet – How much are people spending? (part two)
6. Explain what is meant by the term ‘per capita’.
7. Complete the table below by turning these figures into percentages of the
total per capita expenditure for Victoria in 2017–2018.
Type of gambling Spending per capita % of total
Racing $86.89
Casino $196.55
Poker machines $256.91
Sports betting $7.91
Lotteries – Lotto etc. $171.51
Total 100%
Source: qgso.qld.gov.au/issues/2646/australian-gambling-statistics-35th-edn-1992-93-2017-18-summary-tables.pdf
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 38
beaheadofthegame.com.auStudent worksheet –
Coin experiment
In this activity you will conduct an experiment with a coin and make predictions
about the chance of an event occurring.
1. Bright tossed a coin 12 times and recorded the results in a pie graph. They
did this experiment a total of six times and graphed the results, as shown
below.
a. Bright was pleased that there were more heads than tails thrown. Bright
regarded this as lucky. Do you think Bright was lucky in this experiment?
State your reasons.
b. Repeat Bright’s experiment with a partner or in a group and record your
results in the pie graphs below. Before you begin, predict the number of
heads you think you will toss (out of 72 tosses) and state why you chose
this number.
Prediction:
Reason:
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 39
beaheadofthegame.com.auStudent worksheet – Coin experement
Now record your results in the graph/diagrams below by colouring heads in
red and tails in blue.
c. Compare your prediction for the number of heads you would get (out
of 72 tosses) to the actual number of heads you got. What is your
explanation for any difference between your prediction and the actual
result?
d. Do you think luck played a part in your experiment? Discuss your
response with a classmate or your teacher.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 40
beaheadofthegame.com.auStudent worksheet – Odds
The likelihood or chance of an event occurring is known as the odds. Probability
can be expressed in different ways, such as fractions, ratios or even as a positive
or negative number.
It is important to remember that, in the gambling industry, odds are calculated
to ensure profit for the gambling company or bookmaker.
Odds are one way of telling you the likelihood or chance of an event occurring.
Odds can be expressed as a ratio with a colon ‘:’
For example, what are the odds of tossing a coin and getting a head or a tail?
Heads Tails
1 : 1
50% 50%
A coin toss has odds of 1:1
Even odds
There are 2 possible outcomes with Even or equal chance
• 1 chance of obtaining a head 50:50 chance
• 1 chance of obtaining a tail
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 41
beaheadofthegame.com.auStudent worksheet – Odds
Odds may be expressed as a ratio with a slash ‘/’
For example, what are the odds of a car winning a race?
9/1
9:1
90% 10%
If a car in the race had odds of 9/1 Uneven odds
There are 10 possible outcomes with Unequal chance
• 1 chance in (9+1) 10 of winning 1 chance in 10 of winning
• 9 chances in (9+1) 10 of losing
When working out odds we need to know the total number of possible
outcomes. Total outcomes = total winning outcomes plus total losing outcomes.
1. Represent the ratios by sketching each using boxes. For example, odds of 1/5
would be represented by:
a. 1/4 b. 3/1
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 42
beaheadofthegame.com.auStudent worksheet – Odds
Favourites
A favourite has the smallest value of mathematical odds. It has the lowest
proportion of losing outcomes to total outcomes, e.g. 1/10 is a smaller odd
than 10/1 and so 1/10 will be the favourite. Bookies will offer lower payouts on
favourites as there is a higher probability that a favourite will win.
Payouts are calculated on odds. For example:
• 4/1 odds mean that for every $1 bet, you can win $4. Winning is unlikely. This
would not be a favourite.
Conversely:
• 1/4 odds mean that for every $4 bet, you can win $1. Winning is more likely.
This would be a favourite.
2. What are the disadvantages of betting on the favourite?
3. What are the disadvantages of betting on something that is not the
favourite?
4. Explain the risk and challenge of betting on something that is not the
favourite.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 43
beaheadofthegame.com.auStudent worksheet – Odds
5. Complete the sentences using the following chance words.
‘expected’ ‘is not expected’ ‘likely’ ‘unlikely’ ‘is’ ‘is not’
If the fraction is less than 1 (e.g. 1/4) this means that the event is
to occur.
• This is to happen.
• This the favourite.
If the fraction is greater than 1 (e.g. 3/1) this means that the event is
to occur.
• This is to happen.
• This the favourite.
6. Odds may be expressed as a ratio which can be converted to a percentage.
Plug the following equations into your calculator to find the percentage
chance an event will happen:
Odds of 1/1 The ratio of 1/1 can be expressed as a fraction
1 posible outcome
=
(1 + 1) total number of outcomes
= 0.50
(Hint to get to a percentage × 100)
0.50 × 100 = 50%
= 50% chance that the event will happen
Odds of 9/1 are the same as
1
(9 + 1)
= 0.10
= % chance of winning
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 44
beaheadofthegame.com.auStudent worksheet – Odds
Odds of 1/4 are the same as
4
(1 + 4)
=
= % chance of winning
Odds of 1/5 are the same as
(1+ )
=
= % chance of winning
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 45
beaheadofthegame.com.auStudent worksheet –
Odds at the racetrack
Racing odds are typically expressed as a fraction or as a ratio. In this activity you
will make calculations with ratios and consider a scenario of a day at the races.
You will consider the risks involved and learn about commissions.
Fraction odds and calculations in
horse racing
The payout = the odds × the amount you spend + your original spend back
For example:
A bet of $20 with 2/5 odds
Payout = (2/5 × $20) + $20
= $8 + $20
Payout = $28 if your horse wins
Profit = $8 as the original bet was $20
However, if your horse loses, it means you lose your entire bet.
Loss = $20
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 46
beaheadofthegame.com.auStudent worksheet – Odds at the racetrack
Consider the following bets on different horse races on the same day and
perform calculations using the example above to find either the payout or loss
for each.
Race Bets and result Result Payout or loss
A bet of $30 with The horse Payout = (3/5 × $30) + $30
1
odds at 3/5 wins =
A bet of $50 with The horse
2
odds at 5/1 loses
A bet of $25 with The horse
3
odds 1/10 wins
A bet of $40 at The horse
4
3/5 loses
A bet of $100 with The horse
5
2/5 odds loses
1. How much money has been paid out for the day? (sum of payouts)
2. How much profit has been made for the day? (profit = total payouts - costs
of the bets)
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 47
beaheadofthegame.com.auStudent worksheet – Odds at the racetrack
3. How much money has been lost for the day? (sum of losses)
4. Was money won or lost for the day?
Risk
1. What do you think risk means in relation to gambling? Write your own
definition of risk here.
2. In the scenario above, were any of the bets risky?
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 48
beaheadofthegame.com.auStudent worksheet – Odds at the racetrack 3. What are some factors that can increase risk? 4. Is betting on the favourite more or less risky? Why? Commissions Any winning bet you make will be charged a commission fee by the booking agent. • This is called a commission or house edge. • It is usually between 2 – 5% but it may be a flat fee. • This will come off your payout, reducing the amount of money you receive. For example, Perth placed a bet with an online betting app for his favourite AFL team to win. Regardless of whether Perth wins or loses the bet, a commission fee of 2.5% was charged to Perth’s account. If Perth placed a bet of $100, a commission fee of $2.50 will be automatically deducted from Perth’s account. This fee is final and non-refundable, and separate to any winnings or losses. BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 49 beaheadofthegame.com.au
Student worksheet – Odds at the racetrack Complete the following calculations to determine the commission fees. Find the 5% commission fee on a payout of: a. $100 b. $20 c. $350 $100 × 5/100 = Find the 3% commission fee on a payout of: a. $100 b. $20 c. $350 $100 × 3/100 = Find the 2% commission fee on a payout of: a. $100 b. $20 c. $350 $100 × 2/100 = BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 50 beaheadofthegame.com.au
Student worksheet –
Lottery odds
Lotteries are common to many countries and the prize money is often
considerable. This is because many people buy tickets and, if there is no winner,
the prize money accumulates, becoming larger and larger. These huge prizes
are often reported in the news. What is not reported are the odds of actually
winning.
Powerball Lotto $80 million
jackpot winner left in tears
after incredible discovery.
Source: https://www.news.com.au/finance/money/wealth/powerball-lotto-jackpots-to-80-million/news-
story/c996ef3c631094786e8f70eb4822c18a
Calculating the chances of winning
a lottery
To find the chance of winning any lottery (or lotto), you need to divide the
number of possible winning lottery numbers by the total number of possible
lottery numbers. If the order of the numbers doesn't matter, you can use the
formula below:
n!
Total number of possible lottery numbers = r! (n–r)!
In the formula:
n is the number of numbers you can choose from
r is how many numbers you choose
"!" is the mathematical symbol for ‘factorial’. This is when you multiply
the number by all the preceding positive integers,
e.g. 5! = 5 × 4 × 3 × 2 × 1.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 51
beaheadofthegame.com.auStudent worksheet – Lottery odds
Example
Imagine you have to choose two numbers and you can pick the numbers from 1
to 5. This means that r = 2 and n = 5.
5!
Total number of possible lottery numbers = 2! (5–2)!
5×4×3×2×1
= 2 × 1 (3 × 2 × 1)!
120
= 12
= 10
Your odds of choosing the two "correct" numbers
1
(the winning numbers) would, therefore, be 1 chance in 10 or 10 .
Lottery example
In a hypothetical lottery, the first prize is obtained by
choosing all five correct numbers + the powerball.
In this lottery, there are 45 balls to choose from in the barrel. Five are drawn
at random and their numbers recorded. An additional ball is drawn and this is
called the powerball. To win the first prize, you must have chosen all the correct
numbers, including the powerball.
Calculate the odds of getting a first prize in the lottery using:
n!
r! (n–r)!
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 52
beaheadofthegame.com.auStudent worksheet – Lottery odds
First, find the odds of getting the first 5 numbers correct.
(Hint: use the ‘!’ function on your calculator or device.)
n = 45
r=5
Substitute n and r ! to get a
into your formula ! ( – )! fraction of:
Then, find the odds of getting the powerball correct.
n = 45
r=1
Substitute n and r ! to get a
into your formula ! ( – )! fraction of:
Finally, multiply your two fractions together to find the probability of first prize.
x =
Challenge
Work out the odds for a second division prize, i.e. guess the first five numbers
correctly but not the powerball.
First, find the odds of getting the initial five numbers correct.
n=
r=5
Substitute n and r ! to get a
into your formula ! ( – )! fraction of:
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 53
beaheadofthegame.com.auStudent worksheet – Lottery odds
Then find the odds of getting the powerball incorrect.
n=
r=5
Substitute n and r ! to get a
into your formula ! ( – )! fraction of:
Finally, multiply your two fractions together to find the probability of second
prize:
x =
And, if you’re really keen, you can find the odds of getting other combinations,
such as three of the five numbers and the powerball by using the following
formula:
r! (n–r)!
x
k! (r – k)! (n – r) – (r – k)! (r – k)!
where
k is the number of correct balls
n is the number of numbers
r is how many numbers are chosen
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 54
beaheadofthegame.com.auStudent worksheet –
Odds with pokies
In 2019, it was reported that there were 26,448 pokies machines in Victoria.
In this worksheet, you will learn how pokies are based on random number
generators and how chance determines if you win or lose.
Pokies, or slot machines, have an inbuilt random number generator. Your teacher
will show you how to use a random number generator on your device.
Instructions
1. On your calculator, phone or internet device, open a random number
generator.
2. With a partner, or with your class, choose five numbers between 0-100 and
write these down.
3. Run the random number generator and see how many spins are needed
before each of your numbers is displayed.
4. Keep a tally.
Example: the number 83 was chosen by the class. Fourteen spins were needed
before the number 83 was selected by the random number generator. These 14
attempts were recorded as follows.
1. How would you describe the odds of your numbers occurring?
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 55
beaheadofthegame.com.auStudent worksheet – Odds with pokies
2. Give a possible reason why a machine might be programmed to always pay
less to the customer.
Pokies example
Today’s pokies are electronic machines driven by
random number generators that determine each result
digitally. However, in this example, we imagine a much
simpler analogue pokies machine that displays three
symbols, each on a spinning reel containing 50 possible
symbols. When you play the machine, each of the reels spins around until
randomly stopping on a symbol. If the symbols that line up in the window match
one of the displayed winning combinations, the machine pays out money.
• On each reel, there is only one cherry symbol. So, the probability of obtaining
one cherry is 1/50 (1 out of 50 chances).
• Therefore, the probability of obtaining three cherries is
1/50 × 1/50 × 1/50 = 1/125,000
The probabilities are different for each winning combination of symbols. These
probabilities are deliberately set on the machine to maximise profit for the
venue.
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 56
beaheadofthegame.com.auStudent worksheet – Odds with pokies
1. Complete the following table for a slot machine.
Note, for the machine described in the table below, there are more bananas on each reel than apples,
more apples than oranges, more oranges than watermelons, and more watermelons than cherries.
Combination Winnings Probability of The machine return
the outcome This is proportional to each
This is the dollar the casino pays out to all
probability of all customers over a long period
three of the same of time
fruit occurring at = winnings × probability
the same time of the outcome
3 cherries $2000 1/125000 $2000 × 1/125000 = 0.016
3 watermelon $1000 3/20000
3 oranges $400 1/2000
3 apples $50 1/200
3 bananas $5 1/14
TOTAL ODDS
(sum of the returns)
2. Why are some returns higher than others? For example, why are the odds
better for bananas than for cherries?
3. Why do the odds not add up to one?
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 57
beaheadofthegame.com.auStudent worksheet –
An experiment with odds
Chance can be investigated by conducting an experiment with dice. In this
activity, you will use dice to make predictions about outcomes and then to see if
the predictions have a mathematical pattern.
Epping rolled a six-sided die 60 times. The results of the experiment were
recorded in the table below and then a column graph was constructed:
Face number on die Tally Frequency
1 //// / 6
2 //// //// // 12
3 //// //// 9
4 //// //// //// 14
5 //// //// // 12
6 //// // 7
TOTAL 60
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 58
beaheadofthegame.com.auStudent worksheet – An experiment with odds
1. Epping drew this column graph of the results but made two mistakes.
What did they get wrong?
2. Epping was happy with the result, as they had chosen 4 as a lucky number.
Do you think being a ‘lucky number’ influenced the result? State your reason.
3. Repeat Epping’s experiment with a partner or in a group and record it in the
table below. Before you begin, predict the number of sixes you think you will
toss.
Prediction:
Face number on die Tally Frequency
1
2
3
4
5
6
TOTAL 60
BE AHEAD OF THE GAME VCAL – NUMERACY: BUDGETING, ODDS AND PROBABILITY 59
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