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

Curriculum content descriptions

Plot linear relationships on the Cartesian plane with and without the use of digital technologies (ACMNA193)

Elaborations
  • completing a table of values, plotting the resulting points and determining whether the relationship is linear
  • finding the rule for a linear relationship
General capabilities
  • Numeracy Numeracy
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Linear equations,  Cartesian planes

Online

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 ...

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 ...

Downloadable

How many in the queue?

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

Text

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 ...

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.

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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 ...

Video

Are plants mathematicians?

Ever noticed that plants are examples of Fibonacci numbers? Watch Vi Hart draw examples of flower petals and leaf growth that follow this pattern. See how plants seem to use Phi (.), the golden ratio. Find out how to make your own 'angle-a-tron' to create interesting petal designs. This is the second in a series of two.

Interactive

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

Interactive

Syllabus bites – turbo turning

The fourth in a series of Syllabus bites related to transformations on the Cartesian plane. This Bite covers rotation of points.

Online

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.

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 ...

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.

Interactive

Syllabus Bites: Direct proportion

This is the second in a series of Syllabus Bites related to direct and indirect proportion. Interactive applets and dynamic geometry software allow students to explore quantities in direct proportion. Students draw conclusions about relationships between the variables and consolidate their understanding by playing a simple game.

Interactive

Plotting Points in a Quadrant

An animated tutorial demonstrating how to locate and plot points on the Cartesian plane, given coordinates. An interactive quiz is included.

Online

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.

Interactive

Syllabus bites – mixing it up

The fifth in a series of Syllabus bites related to transformations on the Cartesian plane. This bite covers combinations (composition) of transformations.

Interactive

Syllabus bites – frenzied flipping

This is the second in a series of Syllabus bites related to transformations on the Cartesian plane. This Bite covers reflection of points.

Interactive

Syllabus Bites: Graphing direct proportion

This is the third in a series of Syllabus Bites related to direct and indirect proportion. Students draw graphs to represent relationships between variables in direct proportion. They associate the gradient of the graph with the constant of proportionality. They investigate practical contexts that give rise to direct proportion.

Interactive

Syllabus bites – flipping and sliding

This is the third in a series of Syllabus bites related to transformations on the Cartesian plane. Students further their understanding of translation and reflection and explore relationships between these two transformations.

Interactive

Simultaneous Equations: animation

A short animated introduction to simultaneous equations and a demonstration of the elimination method of solution, followed by an interactive quiz.