# Percentages and GST

SubjectMathematics YearYear 8 CurriculumAC v9.0 Time170

## Introduction

This set of resources provides opportunities for students to solve problems involving percentages, rates and proportions using technology (spreadsheets) in the context of the goods and services tax GST).

Australian Curriculum or Syllabus

## Achievement standard

By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools.

Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.

They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.

## Content descriptions

Use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate (AC9M8N04).

Use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (AC9M8N05).

Recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure (AC9M8M05).

Use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (AC9M8M07).

## Teacher resources

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Video

Visualiser

## Student learning resources

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Worksheet

Investigation

## Suggested activity sequence

This sequence is intended as a framework to be modified and adapted by teachers to suit the needs of a class group. If you assign this activity to a class, your students will be assigned all student resources on their 'My learning' page. You can also hand-pick the resources students are assigned by selecting individual resources when you add a work item to a class in 'My classes'.

Part A: What is GST?

1. Begin by playing the Goods and services tax (GST) video to give students an overview of GST.
2. Discuss how GST works for businesses that collect GST, including how they can get credits for the GST they paid on goods and services.

GST collected - GST credits = Amount owed to the ATO.

Part B: Calculating GST

1. Explicitly teach students how to calculate GST from both the GST exclusive price and the GST inclusive price (that is, working forwards and backwards). Calculating GST at 10 percent – How-to-sheet might be a helpful resource for students.
2. You might like to get students to complete a table like this one as a practice activity:

Price (excluding GST)

GST

Price (including GST)

\$30.00

\$30.00

\$2,000.00

\$2,000.00

\$350.00

\$350.00

\$90.00

\$90.00

\$45.00

\$45.00

3. Students complete part 1 of the worksheet.

Part C: Investigating GST, profit and profit margins

1. As a class, read through part 2 of the worksheet. If necessary, use examples to demonstrate how to calculate profit, profit margins and percentage increase and decrease.
2. Display and explain how to use spreadsheets using the visualiser.
3. Reinforce learning by modelling the process of setting up an excel spreadsheet using the following scenario. If you’re all working together on this, everyone will need access to a computer with spreadsheet software.
1. You work in an outdoor store and one of your tasks is to price items. The store wants to sell its down jackets for \$118, beanies for \$11, hiking shoes for \$145 and backpacks for \$46. How much GST do they need to add to each one and what will the final price on the price tag be?

It might be useful for students to have a copy of Making an Excel spreadsheet using GST as an example – How-to-sheet before you start so they can follow along.

4. Students complete part 2 of the worksheet.
5. Walk students through the investigation instructions, reminding them of the similarities to the problem you modelled.
6. Students complete the investigation. Students may benefit from working individually and/or in small discussion groups.
7. As a class, discuss students’ findings.