# Percentages and income tax

SubjectMathematics YearYear 8 CurriculumAC v9.0 Time105

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## Introduction

This set of resources provides opportunities for students to solve problems involving percentages, rates and proportions using technology (spreadsheets) in the context of income tax. It provides an opportunity for students to use mathematical modelling to solve practical and real-world problems involving percentage increases and decreases.

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)

## Teacher resources

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Video

Explainer

Calculator

## Student learning resources

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How to

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 income tax and how does it work?

1. Play the video How does Australia's income tax system work? as an introduction to Australia's progressive income tax system.
2. Use a grouping strategy to organise students in groups of 3 or 4.
3. Students read the explainer and in groups construct a brief definition of income tax and tax rates. Each group writes their definition on the board.
4. 4. When all definitions are displayed, discuss and refine the descriptions to come to a shared class understanding of Australia’s progressive income tax system.

Part B: Calculating income tax

1. Explicitly teach students how to calculate income tax. Use the Calculating income tax – How-to-sheet as a guide.
2. Students complete the part 1 of the worksheet.

Refer students to Calculating income tax - How-to-sheet to support them to complete the worksheet.
3. Review how to calculate averages. For example, the average rate of tax (ART). If income is \$45,000 and total income tax is \$4,288. ART = (\$4,288 ÷ \$45,000) x 100 = 9.53%.
4. Revise how to calculate percentages, percentage increases and decreases. Use the Calculating percentage change – How-to-sheet as a guide.
5. Students complete part 2 of the worksheet. (Note: students can do just a couple of the questions depending on the available time.)

Refer students to Calculating percentages or ratios - How-to-sheet and Calculating percentage change - How-to-sheet to support them to complete the worksheet

Part C: Investigating income tax

1. Walk students through the investigation instructions, reminding them of the similarities to the problem you modelled.
2. Before students embark on their investigation, you may want to show them how to use ATO’s simple tax calculator. If necessary, refer to Using the simple tax calculator – How-to-sheet. This will enable students to focus on developing an understanding of progressive tax rather than getting bogged down in calculations.
3. Students may benefit from working individually and/or in small discussion groups.
4. Discuss student answers as a class.