Mathematics / Year 8 / Number and Algebra / Linear and non-linear relationships

Curriculum content descriptions

Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

Elaborations
  • solving real life problems by using variables to represent unknowns
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Linear equations,  Substitution,  Intersecting lines

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Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

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Graphs: formulas and variables

In this lesson, students use algebra and linear equations to model two real-world scenarios to find information to make the best choice. Students set the aim of saving for a mobile phone (or similar goal) and use linear equations to model the pay rates of two part-time jobs to help make the better decision. This lesson ...

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Graphs: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Graphs. Students explore linear relationships in the context of the Cartesian plane using digital tools. Students will then go on to find the rule for a linear relationship and solve linear equations, both graphically and algebraically.

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TIMES Module 9: Measurement and Geometry: introduction to plane geometry - teacher guide

This is a 16-page guide for teachers. It provides an introduction to the initial ideas of plane geometry. Points and lines are introduced as fundamental objects in the study of geometry. Angles and parallelism are the initial areas of attention in a more formal approach to geometry that occurs from year 7.

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TIMES Module 9: Number and Algebra: multiplication of whole numbers - teacher guide

This is a 23-page guide for teachers. This module contains a description of suitable models for multiplication, a discussion of the types of problems that require multiplication for their solution, and mental and written strategies for multiplication. The use of the commutative, associative and distributive laws is described. ...

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TIMES Module 20: Measurement and Geometry: parallelograms and rectangles - teacher guide

This is a 17-page guide for teachers. It contains the definitions, properties and tests for parallelograms and rectangles. Proofs of the properties and tests are given. Constructions for parallelograms and rectangles are given.

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Plotting linear relationships and examples of linear relations

This is a website designed for both teachers and students, which addresses content on plotting linear relationships from the Australian Curriculum for year 8 students. It contains material on plotting points on the Cartesian plane, working with tables of values, and looking at the gradient and the equation of a line. There ...

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TIMES Module 13: Measurement and Geometry: construction - teacher guide

This is a 30-page guide for teachers that explains the central role of construction and presents examples of constructions.

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TIMES Module 21: Number and Algebra: rates and ratios - teacher guide

This is a 17-page guide for teachers. This module introduces the idea of ratios and rates. Ratios are used to compare two quantities. The emphasis is usually on comparing parts of the whole. Rates are a measure of how one quantity changes for every unit of another quantity. It relates the ideas of ratios, gradient and fractions.

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TIMES Module 32: Number and Algebra: fractions and the index laws in algebra - teacher guide

This is a 24-page guide for teachers. This module extends the use of pronumerals to include algebraic fractions. It includes substitution, adding like terms, the use of brackets and multiplying terms, the use of algebra to describe number patterns and extending the use of the index laws. Algebraic notation is discussed.

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Trade and Investment at a Glance

Using an illustrated report from the Department of Foreign Affairs and Trade, this Teacher guide provides ten learning sequences that engage students in the analysis and interpretation of data about Australian imports and exports. Students: identify Australia's major exports and imports; investigate international trade ...

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reSolve: Fibonacci Miles

This lesson introduces students to a trick for quick conversion between miles and kilometres using the Fibonacci sequence. Students are challenged to explain why the trick works. They investigate using their knowledge of ratio and discover that the miles/kilometres conversion rate is close to the golden ratio. The lesson ...

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Mathematical modelling (Algebra): Year 8 – planning tool

This planning resource for Year 8 is for the topic of Mathematical modelling. Students model linear relationships to solve real-world applications that they can relate to, such as financial contexts (for example, pay rates for part-time work) or measurements (for example, cooking, constant speed and distance/time graphs, ...

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Patterns and number facts: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Patterns and number facts. Students bring together knowledge and skills on linear functions and relations and experiment with digital tools to investigate systematic variation of parameters to show the effect. Students cement their understanding of the 'm' and the 'c' ...