NSW Syllabuses

# Mathematics K–10 - Stage 5.1 - Number and Algebra Financial Mathematics

## Outcomes

#### A student:

• MA5.1-1WM

uses appropriate terminology, diagrams and symbols in mathematical contexts

• MA5.1-2WM

selects and uses appropriate strategies to solve problems

• MA5.1-3WM

provides reasoning to support conclusions that are appropriate to the context

• MA5.1-4NA

solves financial problems involving earning, spending and investing money

Related Life Skills outcomes: MALS-12NA, MALS-13NA, MALS-14NA, MALS-15NA, MALS-16NA, MALS-17NA

## Content

• Students:
• Solve problems involving earning money
• calculate earnings from wages for various time periods, given an hourly rate of pay, including penalty rates for overtime and special rates for Sundays and public holidays
• use classifieds and online advertisements to compare pay rates and conditions for different positions (Problem Solving)
• read and interpret examples of pay slips (Communicating)
• calculate earnings from non-wage sources, including commission and piecework
• calculate weekly, fortnightly, monthly and yearly earnings
• calculate leave loading as 17.5% of normal pay for up to four weeks
• research the reasons for inclusion of leave loading provisions in many awards (Reasoning)
• use published tables or online calculators to determine the weekly, fortnightly or monthly tax to be deducted from a worker's pay under the Australian 'pay-as-you-go' (PAYG) taxation system
• determine annual taxable income by subtracting allowable deductions and use current tax rates to calculate the amount of tax payable for the financial year
• determine a worker's tax refund or liability by comparing the tax payable for a financial year with the tax already paid under the Australian PAYG system (Problem Solving)
• investigate how rebates and levies, including the Medicare levy and Family Tax Benefit, affect different workers' taxable incomes (Problem Solving)
• calculate net earnings after deductions and taxation are taken into account
• calculate simple interest using the formula $$I=PRN$$ where $$I$$ is the interest, $$P$$ is the principal, $$R$$ is the interest rate per time period (expressed as a fraction or decimal) and $$N$$ is the number of time periods
• apply the simple interest formula to solve problems related to investing money at simple interest rates
• find the total value of a simple interest investment after a given time period (Problem Solving)
• calculate the principal or time needed to earn a particular amount of interest, given the simple interest rate (Problem Solving)
• calculate the cost of buying expensive items by paying an initial deposit and making regular repayments that include simple interest
• investigate fees and charges related to 'buy today, no more to pay until …' promotions (Problem Solving)
• compare the total cost of buying on terms to paying by cash (Problem Solving)
• recognise that repossession does not remove financial debt (Reasoning)
• Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)
• calculate compound interest for two or three years using repetition of the formula for simple interest
• connect the calculation of the total value of a compound interest investment to repeated multiplication using a calculator, eg a rate of 5% per annum leads to repeated multiplication by 1.05 (Communicating)
• compare simple interest with compound interest in practical situations, eg to determine the most beneficial investment or loan (Communicating, Reasoning)
• compare simple interest with compound interest on an investment over various time periods using tables, graphs or spreadsheets (Communicating, Reasoning)

### Background Information

Pay-as-you-go (PAYG) is the Australian taxation system for withholding taxation from employees in their regular payments from employers. The appropriate level of taxation is withheld from an employee's payment and passed on to the Australian Taxation Office. Deduction amounts will reduce the taxation debt that may be payable following submission of a tax return, or alternatively will be part of the refund given for overpayment.

Simple interest is commonly used for short-term investments or loans. Calculations can involve an annual simple interest rate with a time period given in months or even days.

Internet sites may be used to find commercial interest rates for home loans and to provide 'home loan calculators'.

### Language

Students may have difficulty interpreting the language of financial problems. For example, references to 'hourly rate', 'weekly earnings', 'monthly pay', etc need to be interpreted as the amount earned in one hour, one week, one month, etc.

When solving financial problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, and to conclude with a statement in words.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA5.1-4NA the sub-elements (and levels) of Operating with percentages (OwP5- OwP6), Number patterns and algebraic thinking (NPA7) and Comparing units (CoU3) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.