# My Dream Job

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```					INVESTIGATION                                                                  MATHEMATICS
Levels 5 and 6

My Dream Job
Strands                Topics
Number                 Percentages, rates and ratios

Chance and Data        Tables and graphs
Outcomes N 5.1 N 5.2, N 5.3, N 6.1, N 6.2, N 6.3 CD 5.2,
CD 6.2, NDB 6.1b

Investigation
Students compare rates of pay that apply to different methods of earning an income,
including hourly rates, piece rates, overtime and penalty rates, retainers and commission,
and the direct and indirect taxes they may be required to pay.

Students beyond level 6
You have developed a business plan for a new exciting company and you are ready to
employ some people to help make and market the product. You decide to appoint a
marketing manager and an operations manager at individual salaries, manufacturing staff
at an hourly rate with penalties for overtime and sales staff on retainer-plus-commission.
You have decided to take orders and manage the accounts yourself. You will need to
decide:
 The salary, hourly wage and commission structures for your staff
 What deductions and rebates you will be able to claim as a business

Students working towards level 6
You are planning an overseas adventure and want to make as much money as possible in
the next few years in order to pay for the trip. You want to work as many hours as possible
to receive the maximum amount of pay. You decide to compare the different pay structures
of jobs against the amount of tax you will need to pay to maximise your cash in hand. You
will need:
 Cutouts/printouts of job ads which detail the amount and method of pay
 Tables indicating the various tax brackets
 Information about deductions and rebates you can claim on tax
(note: you haven’t been to university yet and cannot work as a high-powered executive)

Students working towards level 5
You are planning your career and are deciding what would be the best job that suits you
financially as well as emotionally. You compare jobs with different types of pay structures
to determine which ones are the most efficient use of your time. You will need:
 Cutouts/printouts of job ads which detail the amount and method of pay
 Tables indicating the various tax brackets
 Information about deductions and rebates you can claim on tax

1
Overview

The following table shows how this investigation is organised in phases associated with
thinking, reasoning and working mathematically.

Thinking, reasoning and working mathematically

1. Identifying and describing   2. Understanding and applying   3. Communicating and justifying

Setting the scene               Comparing data                  Financial decision
Students:                       Students:                       making
 Discuss the                    Develop tables of data        Students:
investigation and               based on real-life jobs       Complete a profile for a
identify what they              found in the research           job of their choosing
know and what they            Determine the taxable            which outlines the type
need to find out to             income for each job and         of pay received, the
decide what the best            then decide how much            amount of pay including
way is to be paid.              tax is to be paid               any commissions or
 Look through the                                                 penalty rates, the tax
employment sections          Working with data                  bracket they will be in,
of the newspaper and         Students:                          any deductions or
employment websites           Develop a list of                rebates, and the final
to find jobs with               methods to minimize tax         amount of tax payable
specific pay rates or         Decide which methods             at the end of the year.
methods.                        apply to the different
jobs found in the
Working with tables of             research.
data, rates and
percentages
Students:
 Investigate different
methods of taxation.
 Investigate tax as a
percentage of wage.
 Investigate rates of
pay including
commission and
penalty rates.

2
Core Learning Outcomes

This investigation focuses on the following core learning outcomes from the Years 1 to 10
Mathematics Syllabus:

N 5.1 Students compare and order integers, use and interpret index notation, rates and
ratios, and analyse options to make informed financial decisions about saving, credit and
debit.

N 5.2 Students identify and solve addition and subtraction problems involving positive
rational numbers, using a range of computation methods and strategies.

N 5.3 Students identify and solve multiplication and division problems involving positive
rational numbers, rates, ratios and direct proportions, using a range of computation
methods and strategies.

N 6.1 Students compare and order rational numbers, interpret and use scientific notation
and analyse options to make informed personal budgeting and other financial decisions.
N 6.2 Students identify and solve addition and subtraction problems involving rational
numbers using a range of computation methods and strategies.

N 6.3 Students identify and solve multiplication and division problems involving rational
numbers, rates, ratios and direct and inverse proportions using a range of computation
methods and strategies.

CD 5.2 Students plan investigations involving discrete and continuous data, produce and
compare data displays involving grouping, and compare measures of location.

CD 6.2 Students use and interpret cross-sectional data and data collected over time to
identify the nature of variations and relationships.

N DB 6.1b Students make informed decisions regarding earning, spending and saving
money, with reference to schedules of government and business charges.

Using this investigation

The sequence of activities suggested in this investigation provides opportunities for
students to demonstrate learning described by core learning outcomes or aspects of core
learning outcomes.

3
Contribution to the attributes of a lifelong learner

Knowledgeable person         Students learn how to use percentages, ratios and rates
with deep understanding      when manipulating data on different pay rates. Students
also learn where and when to use percentages, ratios and
rates with respect to money, income, savings and tax.
Complex thinker              Students make conjectures and inferences regarding the
types of employment available and the relative pay
structures.
Active investigator          Students develop a questioning habit of mind when thinking
of possible ways of maximising income through different
types of pay structures and minimising tax.
Effective Communicator       Students select appropriate mathematical language to
convey their understandings of the taxation system and
various methods of income accumulation.
Participant in the           Students appreciate, evaluate and challenge different
interdependent world         perspectives of thinking and reasoning about the best
method of earning money.
Reflective and self-directed Students learn how to mathematics relates to them
learner                      personally through the possible employment opportunities
open to them. Students draw on what they know to
investigate ideas and apply knowledge, procedures and
strategies to a variety of situations.

Core Content

Number – level 5                                         Number – level 6
Numeration                                               Numeration
 Integers                                                rational numbers
 Index notation (whole number indices only)              Index notation (integer indicies)
 Square root                                             Scientific notation (positive and negative powers
 Percentage                                                of 10)
- whole percentages (eg 65%)
- fractional percentages (eg 12.5%)                   Number sense
- greater than 100%                                    Position and order of numbers within the set of
rational numbers
Number sense                                                - Sensible adjustments of numbers
 Position and order of numbers including integers
- relationships between numbers                          connections between scientific notation and other
- sensible adjustments of number                          representations of numbers
 connections between percentages and fractions
Money
Money                                                     financial decisions
 financial decisions                                          - income (gross, net)
 percentages                                                  - saving for a purpose
- interest                                                  - consequences of over-commitment
- discounts                                            percentages
 comparison of rates, fees and charges
 positive rational numbers                              Addition and Subtraction
- whole numbers                                        rational numbers
- decimal fractions

4
-   common fractions                              Connections
 inverse (backtracking)
Connections
 inverse (backtracking)                              Computation methods
 Mental computations
Computation methods                                         - exact
 Mental computations                                       - approximate
- exact                                          Written recordings
- approximate                                         - student generated
 Written recordings                                        - traditional methods
- student generated                              Calculators, computers
 Calculators, computers                              Multiplication
 rational numbers
Multiplication                                                - Negative numbers (with calculator)
 Positive rational numbers
- whole numbers                               Connections
- common fractions                             inverse (backtracking)
- decimal fractions
- numbers with indices                        Fractions and Proportion
 fractional percentages of numbers
Division
 positive rational numbers                           Rates
- whole numbers                                comparison of rates expressed in various forms
- common fractions
- decimal fractions                           Ratio and Proportion
 as direct proportion
 as inverse proportion
Connections
 inverse (backtracking)

Fractions and Proportion
 percentages, common fractions, decimal
fractions

Rates
 calculations involving everyday rates

Ratio
 simple everyday ratios
 symbol for ratio

Direct Proportion
 calcuations with direct proportion (including
graphical representations)

5
Chance and Data – level 5                               Chance and Data – level 6
Collecting and handling data                            Collecting and handling data
 studies involving observations, experiments and        data over time (time a major focus)
surveys                                              cross sectional data (time not a major focus)
 templates for recording data                           nature of types of data sets
 consistency of units and conditions                   Exploring and presenting data
 detect errors                                          displays
 discrete data                                                - plots over time
 continuous data                                              - scatter plots
 groups (bins)                                                - two way tables
- histograms
Exploring and presenting data
 displays                                              Identifying and interpreting variation
- two way tables                                  comparison of features of graphs and plots
- compound bar graphs                                    - location (mean, median)
- shape
Identifying and interpreting variation
 features of data                                         relationships between variables
- spread                                                 - through scatterplots for continuous data
- range                                                  - through two-way tables for categorical
- measures of location (central tendency)                    data
and limitations
- shape (eg asymmetry, unusual features)

Resources

   Computers and internet for same and to find information on taxation in Australia
   Tables of data relating to tax brackets, deductions and rebates.
   Glossary of terms

Identifying and Describing

Setting the scene for the investigation
Students:
 Identify which task they would prefer and thus which level they are working towards.
 Establish which types of jobs they will be looking at in order to fulfill the task.
information on amount of pay and of method of payment.
 Look through employment websites for same.
 Speak to people they know within the community about methods of payment for
various jobs.
Focus questions could include:
 What types of jobs have hourly rates? Wages? Commissions?
 How do people get paid for overtime?
 How do we get information on different pay rates?

6
Working with Number Concepts
Students:
 Identify numbers as integers, rational or percentages.
 Discuss the reasons for using different forms of numbers.
 Use multiplication and division to convert rates and ratios into the same form.
 Discuss reasons for having different methods of payment.
 Compare rates of pay to determine which ones generate more money for the
employee.
 Predict the difference in money earned as you change the number of hours worked.
 Investigate the differences in amount of money earned as you manipulate factors
such as hours worked or amount of product sold.
Focus questions could include:
 Why do different jobs have different methods of payment?
 How can we compare different methods of payment?
 Do all types of pay increase as you increase the number of hours worked?
 When do you change to a different pay rate?
 What other factors could influence the amount of pay received?
 What is the maximum hours a person can work?
 Is there a limit to the amount of commission you can earn?

Working with Data
Students:
 Identify differences between discrete and continuous data.
 Create a data table for their chosen job advertisements which outline variations in
pay rates compared to hours worked, product sold and other possible variables.
 Convert data tables to graphs using technology or by hand.
 Describe the effects which this manipulation of data has on the total amount of
money paid.
Focus questions could include:
 How do we graph the changes to data?
 Are different methods of payment given as a lump sum or are they all dependant on
variables?
 What types of technology are used to analyse data of this type?

Assessing Learning
Sources of evidence could include:
 Observation notes of discussions.
 Responses to questions posed in relation to number concepts and data
interpretation.
 Graphs and tables produced by the students

When making judgments, teachers consider whether the student has:
 Interpreted realistic problems related to accumulation of income.
 Interpreted advertisements for method of payment and amount of pay referring to
numbers as percentages, fractions, rates or ratios.
 Collected data in a meaningful way.

7
Understanding and Applying

Manipulating data to maximise income
Students:
 Use data tables and graphs to determine the maximum amount of pay available for
each type of job.
 Determine what constraints may be applied to these figures (eg: only 24 hours in a
day, shop hours, human requirement for sleep etc.)
 Analyse taxation tables to determine what amount of tax they would pay for each
job.
 Using a range of computational methods, determine the most efficient use of time.
 Discuss how tax deductions and rebates work and their effect on your net income.

Focus questions could include:
 How do the different jobs compare with each other after you factor in tax?
 What are the skills required for each job? Does this affect the pay structure?
 What are the different ways of minimising the amount of tax payable?
 How do sick days and holidays affect the amount of income earned?

Assessing Learning
Sources of evidence could include:
 Observations made during problem solving activities
 Responses to questions about the impact of different criteria on income
 Graphs and tables produced by the students
 Mathematical calculations which demonstrate income maximization
 Use of rates, ratios and percentages

When making judgments, teachers consider whether the student has:
 Interpreted realistic problems related to accumulation of income.
 Solved realistic problems in relation to income attainment.
 Used data to explain how tax can have an adverse effect on some levels of income.
 Used problem solving to determine which jobs have more deductions or rebates.

Communicating and Justifying

Students working beyond level 6
 Develop a pay structure for 3 types of employees for your business
 Develop a proposed budget for your business income and tax payable
 Ensure that you include:
- The salary, hourly wage and commission structures for your staff
- How many hours you expect your staff to work per day/ per week
- The amount of holiday pay and sick leave your staff are entitled to
- What deductions and rebates you will be able to claim as a business

8
   Research and present your business plan and explain the procedures and strategies
used to formulate it.

Students working toward level 6

   Decide what job best suits the purpose of making the most money in the least
amount of time.
   Decide whether or not you will take on a second job for your purpose
   Outline the job which you will take on including:
- how many hours you plan to work each week
- what the ordinary pay rate is
- any commissions or overtime benefits you plan to receive
- what tax bracket you will be in
- what your planned annual income will be
- how much tax you will pay on this income
- what deductions and rebates you will claim

Students working towards level 5

   Decide what job best suits the career you would like to consider
   Outline the job which you will take on including:
- how many hours you plan to work each week
- what the ordinary pay rate is
- any commissions or overtime benefits you plan to receive
- what tax bracket you will be in
- what your planned annual income will be
- how much tax you will pay on this income
- what deductions and rebates you will claim

Assessing Learning
Sources of evidence could include:
 Presentations of their job or business plan
 Peer or self assessment

When making judgments, teachers consider whether the student has:
 Interpreted realistic problems related to accumulation of income.
 Solved realistic problems in relation to income attainment including the use of
commissions and penalty rates.
 Used data to explain how tax affects their income
 Used problem solving to determine what deductions and rebates they can claim

9
This investigation could be connected to core learning outcomes from other subjects.

Strand Information Procedures

Students understand how changes in the nature of information influence design and
production decisions. They evaluate methods of information management. They
understand accounting principles and prepare financial reports. They select techniques to
process, manage and present information. Students understand issues related to the
ownership and control of information. They evaluate the ways information is managed in
organisations. They recommend ways to improve financial operations. They use
specialised techniques to present information

IP 5.2 Students analyse and evaluate the methods used to manage information.

IP 5.4 Students compare and select techniques for processing, managing and presenting
information for specific users. (Tech INF 5.2)

IP 6.4 Students use specialised techniques for managing and organising the presentation
of information to meet detailed specifications. (Tech INF 6.2)

Strand Enterprise and Ventures

Students understand how to use opportunities within a marketplace to generate positive
outcomes. They develop detailed plans for investigation, and consider options and
resource management within their enterprise or venture proposals. They make products
that meet detailed specifications, and understand methods used to evaluate commercial
and industrial products and processes.

EV 6.2 Students formulate detailed plans for gathering knowledge, ideas and data and
validate choices of information, sources and methods.

Strand Work Environments

Students understand the rights and responsibilities of employers and workers. They
investigate the role of employer and employee groups in regulating business and work.
They identify the expectations of different work arrangements and the nature of enterprise
bargaining.

WE 5.1 Students analyse the rights and responsibilities of employers and employees.

WE 5.2 Students investigate the changing nature of employer, employee, union and work-
related groups in regulating business and work activity.

WE 5.3 Students examine the nature of enterprise bargaining and identify the contractual
differences between different types of work arrangements

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YEAR 10 MATHEMATICS - My Dream Job
Assessment criteria sheet
A                              B                            C                         D                    E
Identifying and   The student has:               The student has:              The student has:              The student has:      The student has
Describing        - identified three (3) or      - identified two (2) or       - identified at least one     - identified at       failed to identify
more employment options        more employment options       (1) employment options        least one (1)         one
with different methods of      with different methods of     with method of payment.       employment            employment
payment.                       payment.                       - arranged information       options with          option with
about these methods of         about these methods of        payment into a table          payment.              on method of
payment into a table           payment into a table          converting figures in         Attempts have         payment. No
converting figures in such a   converting figures in such    such a way as to              been made to          attempt has
way as to compare these        a way as to compare these     compare annually,             complete              been made at
with each other. No errors     with each other. Minimal      weekly and hourly rates       calculations          calculations.
are present in calculations    errors are present in         of pay.
calculations                  Some errors are present
in calculations
Understanding     The student has:               The student has:              The student has:              The student has:      The student has
and Applying      - compared rate of pay to      - compared rate of pay to     - compared rate of pay to     - compared rate       incomplete data
conditions such as hourly      conditions such as hourly     conditions such as hourly     of pay to             for comparison
rate, commission or other      rate, commission or other     rate, commission or other     conditions such       or rates of pay.
variables for three (3)        variables for two (2)         variables for one (1)         as hourly rate,       No attempt has
different methods of           different methods of          method of payment             commission or         been made at
payment mathematically.        payment mathematically.       mathematically.               other variables for   calculations.
- compiled this information    - compiled this information   - compiled this               one (1) method of
in a table                     in a table or a graph         information in a table or     payment
- compare this information     - applied the taxation rate   a graph                       mathematically.
on a graph                     to each method of             - applied the taxation rate   Attempts have
- applied the taxation rate    payment for at least one      to this method of             been made to
to each method of payment      scenario (number of hours/    payment for at least one      complete
for at least one scenario      sales).                       scenario (number of           calculations
(number of hours/ sales).      Minimal errors are present    hours/ sales). Some
No errors are present in       in calculations.              errors are present in
calculations                                                 calculations

11
Communicating    The student has:                The student has:               The student has:            The student has:      The student has
and Justifying   - developed a scenario in       - developed a scenario in      - developed a scenario in   - attempted to        not included any
which three (3) different job   which two (2) different job    which one job type has      develop a             of the key
types have been                 types have been                been implemented            scenario but has      information
implemented                     implemented                    - outlined how many         not included all of   required to
- outlined how many hours       - outlined how many hours      hours are worked            the key               develop a
are worked                      are worked                     - calculated how much       information.          scenario.
- outlined extra information    - outlined extra information   tax is to be paid
such as penalty rates,          such as penalty rates or       - calculated net amount
commissions, sick leave         commission                     of pay for the year
and holiday pay                 - calculated how much tax      - justified some
- calculated how much tax       is to be paid                  decisions.
is to be paid                   - calculated net amount of
- outlined extra information    pay for the year
such as tax deductions and      - justified some decisions
rebates                         in writing
- calculated net amount of
pay for the year
- justified all decisions in
writing

12

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