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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Linear Relationships (and how Maths can help you choose a great car) - Calculate

The activity has students collecting their own information from a well-known Australia car buying website and using this to find an estimated relationship between the ‘asking price’ for a used car and the distance it has traveled in kilometres.

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Work sample Year 8 Mathematics: Linear Relationships in the real world

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 8 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

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8A02A Equations - Ochre Education

This unit of work focuses on equations. Students solve linear equations involving integers and rational numbers as coefficients and solutions, the unknown on one or both sides of the equation, expanding brackets and simplifying expressions on one or both sides of the equation including verifying solutions; solve pure quadratic ...

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Representing Patterns (Year 7) - Calculate

Patterns can be represented in several ways and this unit will explore five different representations.

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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.

Downloadable

How many in the queue?

Students use visualising and movement activities to develop an understanding of the relationship between variables.

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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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Triathlon and Fitness

This resource is a web page containing an investigative task that explores rate. The estimated rate at which a competitor burns calories per hour for each discipline of triathlon is used to answer a problem. A 'Getting started' and 'Solutions' page is also available to support the task. This resource is an activity from ...

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Mixing More Paints

This resource is a web page containing an investigative task to explore ratios and is a follow up to the task Mixing Paints. The context of mixing paints to particular ratios of colours provides a useful task to model practical situations involving ratios. A 'Getting started' and 'Solutions' page is also available to support ...

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Burning Down

This resource is a web page containing a challenging problem solving task that requires an understanding of rate and proportion. It can be solved in a number of ways for example graphically, using fractions or equations and all involve reasoning. A printable resource and solution is also available to support the task. This ...

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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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Mixing Paints

This resource is a web page containing an investigative task to explore ratios. The context of mixing paints to particular ratios of colours provides a useful task to model practical situations involving ratios. A 'Getting started' and 'Solutions' page is also available to support the task. This resource is an activity ...

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Six Notes All Nice Ratios

This resource is a web page containing a short task to explore ratio and fractions. The task is based on the Pythagoreans discovery that simple ratios of string length made nice sounds together. A 'Getting started' page, printable resource and solution is also available to support the task.This resource is an activity ...

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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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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' ...

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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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The Geometry and Algebra of Honeycomb - Calculate

This integrated unit of work explores the amazing structures of honeycomb by examining the properties of regular and irregular polygons and polyhedra. Students then move on to solve problems using geometric and algebraic reasoning.

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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 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.