NSW Syllabuses

# Mathematics K–10 - Stage 4 - Number and Algebra Financial Mathematics

## Outcomes

#### A student:

• MA4-1WM

communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

• MA4-2WM

applies appropriate mathematical techniques to solve problems

• MA4-3WM

recognises and explains mathematical relationships using reasoning

• MA4-6NA

solves financial problems involving purchasing goods

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

## Content

• Students:
• Investigate and calculate the Goods and Services Tax (GST), with and without the use of digital technologies
• calculate GST and GST-inclusive prices for goods purchased in Australia, given the pre-GST price
• interpret GST information contained on receipts (Communicating)
• investigate efficient methods of computing the GST and GST-inclusive prices (Problem Solving)
• explain why the value of the GST itself is not equivalent to 10% of the GST-inclusive price (Communicating, Reasoning)
• determine the pre-GST prices for goods, given the GST-inclusive price
• explain why the pre-GST price is not equivalent to 10% off the GST-inclusive price (Communicating, Reasoning)
• Investigate and calculate 'best buys', with and without the use of digital technologies (ACMNA174)
• solve problems involving discounts, including calculating the percentage discount
• evaluate special offers, such as percentage discounts, 'buy-two-get-one-free', 'buy-one-get-another-at-half-price', etc, to determine how much is saved (Communicating, Problem Solving)
• calculate 'best buys' by comparing price per unit, or quantity per monetary unit, eg 500 grams for $4.50 compared with 300 grams for$2.75
• investigate 'unit pricing' used by retailers and use this to determine the best buy (Problem Solving)
• recognise that in practical situations there are considerations other than just the 'best buy', eg the amount required, waste due to spoilage (Reasoning)
• use price comparison websites to make informed decisions related to purchases under given conditions (Problem Solving)
• Solve problems involving profit and loss, with and without the use of digital technologies (ACMNA189)
• calculate the selling price, given the percentage profit/loss on the cost price
• express profit/loss as a percentage of the cost price
• calculate the cost price, given the selling price and percentage profit/loss

### Background Information

The Goods and Services Tax (GST) in Australia is a value-added tax on the supply of goods and services. It was introduced by the Australian Government and took effect from 1 July 2000. Prior to the GST, Australia operated a wholesale sales tax implemented in the 1930s, when its economy was dominated by the production and sale of goods. In Australia, the GST is levied at a flat rate of 10% on most goods and services, apart from GST-exempt items (which include basic necessities such as milk and bread).

#### Purpose/Relevance of Substrand

'Financial mathematics' is used in important areas relating to an individual's daily financial transactions, money management, and financial decision making. Such areas include earning and spending money (eg calculating 'best buys', discounts, GST, personal taxation, profit and loss, investing money, credit and borrowing, hire purchase, simple and compound interest, loan repayments, and depreciation.

### Language

GST stands for 'Goods and Services Tax'. The difference between the GST-inclusive price, the pre-GST price, and the amount of the GST itself should be made explicit.

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.

Students' understanding may be increased if they write calculations in words first, before substituting the appropriate values, eg $$\mbox{percentage discount} = \frac{\mbox{discount}}{\mbox{retail price}} \times 100\%$$.

Students may need assistance with the subtleties of language used in relation to financial transactions, eg the difference between '$100 has been discounted by$10' and '$100 has been discounted to$10'.

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

When working towards the outcome MA4‑6NA the sub-elements (and levels) of Operating with percentages (OwP3-OwP6) and Comparing units (CoU2) 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.