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

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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Representing Patterns (Year 7) - Calculate

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

Downloadable

How many in the queue?

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

Interactive

Laptop wrap: Parallelendicular

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 

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Tuning and Ratio

This resource is a web page containing a challenging problem solving task that requires an understanding of ratios and logarithms. It explains how intervals such as an octave corresponds to a particular ratio of string lengths which produce the notes. Two types of tuning based on ratios; The Pythagorean Scale and Just Intonation ...

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Round and Round and Round

This resource is a web page containing an interactive that can be used to explore the relationships between the angles of turn that produce the same vertical and horizontal displacements. The task provides an opportunity to apply their understanding of division and recurring decimals. A 'Getting started' page, printable ...

Interactive

Syllabus bites – speedy sliding

This is the first in a series of Syllabus bites related to transformations on the Cartesian plane aimed at Stage 4 Mathematics. Students find the coordinates of image points after translation. In doing so, they develop fluency in using coordinates and familiarity with the Cartesian plane, providing a basis for the investigations ...

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.

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

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.

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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.

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 ...

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 – turbo turning

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

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.

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.

Online

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. ...

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

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.