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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

Interactive

Desmos Graphing Calculator - Google Play app

Plot functions, create tables, add sliders and animate your graphs. Touch points of interest on the graph to show maximums, minimums and points of intersection. Type in an equation and watch the calculator solve the problem. Free when reviewed on 12/5/2015.

Online

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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8A03A Linear relationships - Ochre Education

This ten lesson unit of work focuses on linear relationships. Students define, identify, and plot linear and non-linear relations, determine coordinates of points on linear graphs, sketch linear graphs using two points, solve linear equations graphically, understand the effect of the coefficients of linear equations by ...

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8A04A Inequalities - Ochre Education

This three lesson unit of work focuses on algebraic inequalities. Students explore and graph one-variable inequalities on number lines and Cartesian planes, solve linear inequalities and graph the solutions and identify regions of the Cartesian plane that the y-value is greater or less than a plotted linear relation. The ...

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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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Representing Patterns (Year 7) - Calculate

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

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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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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 ...

Downloadable

How many in the queue?

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

Online

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.

Online

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 ...

Video

Modelling climate changes

There is a saying: 'climate is what you expect and weather is what you get'. |Understanding climate change is very difficult for most people, especially when the weather we experience is different from the information we are given by scientists about the climate changing. The difference is that weather reflects short-term ...

Interactive

The geometer's warehouse

This web-based, multimedia resource focuses on the geometry of the Stage 4 and Stage 5 Mathematics syllabus. It comprises 70 dynamic html worksheets, each exploring a different outcome in Stage 4 and Stage 5 geometry.

Video

Catalyst: Graham's number

If you were asked what the biggest number you can think of is, what would you say? Infinity? Well, what about the biggest finite number you can think of? Mathematician Ron Graham came across such a gigantic number in his research that, to capture its massive size, he and his colleagues needed to come up with new methods ...

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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' ...

Interactive

Syllabus Bites: Revisiting proportion

This is the first in a series of Syllabus Bites related to direct and indirect proportion. Students revise the concept of ratio. They create short visual explanations showing how problems can be solved.

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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.

Downloadable

Algebra: Foundation to Year 9

This comprehensive resource describes the progression of algebra-related ideas and algebraic thinking. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in algebra including teaching and cultural implications.

Online

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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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.