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Mathematics / Year 9 / Number and Algebra / Linear and non-linear relationships

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296)

  • graphing parabolas, and circles connecting x-intercepts of a graph to a related equation
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Circles,  Parabolas,  Hyperbolas


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.


The Mathematical Toolkit

A 2D Shapes tool that can be used to create geometric objects such as quadrilaterals, circles, triangles, lines, arcs, rays, segments and vectors on a coordinate grid. Plot and label the vertices to reveal the internal angles, side lengths, area and perimeter, then manipulate the shapes on a grid to transform their shape ...


reSolve: Trigonometry: Rule of Twelfths

This sequence of three lessons gives students the opportunity to explore how tidal variations can be modelled and predicted using trigonometric functions and approximated with useful 'rules of thumb'. Students use real tidal data to explore how sailors make predictions at sea, draw their own graphs using a range of approximation ...


reSolve: Circumference

This sequence of three lessons explores the properties of circles, in particular the relationship between the diameter and circumference. In the first lesson, students use a cylinder containing three tennis balls to understand that a circumference is 'three and a bit' times the diameter. They then complete five different ...


Mixed-Up Maths

Join our host, Ed, as he finds himself in all types of situations where only his knowledge of Maths can help him. From saving the planet from Aliens, to creating a superhero that can stop a strawberry milkshake tidal wave. From searching for buried treasure, to jumping like a daredevil, or planning the greatest circus party ...


Daredevil geometry

What does a daredevil jumps rider need to know about geometry? Find out as we discover angles for take off and for landing. But before we do that sit down for some angles basics! A good place to start is angles of turn through a circle from a 1/4, 1/2, 3/4, all the way to one full turn. See how many each represents as an angle.


reSolve: Area of a circle

This lesson explores the formula for calculating the area of a circle. Students estimate the area of a circle using inscribed and circumscribed squares, and investigate proofs of the area formula. Each lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, supporting PowerPoint ...


reSolve: Mechanical Linkages: Geometry Proofs

This series of six lessons explores geometry proofs using real world contexts focused on the dynamics of linkages and moving joints. Students use physical models and computer simulations, the lessons move from a view of geometry as a study to static diagrams to encompass movement. Each lesson is outlined in detail including ...


Introduction to differential calculus

This collection of 17 digital curriculum resources (all learning objects) is organised into three sections: rates of change; differential calculus; and review of differential calculus via three learning objects. Students explore rates of change through liquid-pouring activities, and are introduced to the gradient of secants ...


Indigo Interior

This resource is a web page containing a problem solving task that requires an understanding of Pythagoras' theorem. The task involves finding the area of shaded region with a circle with a known area. To solve the problem students need to establish a right angled triangle and apply Pythagoras' theorem. A printable resource ...


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.


TIMES Module 17: Measurement and Geometry: the circle - teacher guide

This is a 15-page guide for teachers. In the module the formulas for finding the circumference and area of a circle are introduced. The history and significance of the number pi is also included in this module.


TIMES Module 35: Number and Algebra: proportion - teacher guide

This is a 22-page guide for teachers. The module introduces the idea of direct proportion and illustrates its many uses in science, commerce and measurement. It looks at ratios, gradients and fractions. A history of the development and use of proportion concludes the module.


Yulunga: kai

In this game from the Torres Strait Islands, a number of players stood in a circle and sang the kai wed (ball song) as they hit a ball up in the air with the palms of their hands. The game was played using the thick, oval, deep-red fruit of the kai tree, which is quite light when dry. This is a hand-hitting (volley) game ...


TIMES Module 34: Number and Algebra: quadratic equations - teacher guide

This is a 19-page guide for teachers. It introduces quadratic equations and methods for solving them.


TIMES Module 35: Number and Algebra: the quadratic function - teacher guide

This is a 29-page guide for teachers. It introduces graphing of quadratic functions.


Coordinate geometry

This is a website designed for both teachers and students that addresses coordinate geometry from the Australian Curriculum for year 9 students. It contains material that shows the connection between algebra and geometry through graphs of lines and curves. There are pages for both teachers and students. The student pages ...



This is a website designed for both teachers and students that refers to the properties of circles including the circumference and area from the Australian Curriculum for year 8 students. It contains material on finding circumferences and areas of circles, and the areas and perimeters of shapes formed from circles and other ...


Investigating irrational numbers including pi

This is a website designed for both teachers and students that refers to irrational numbers including pi from the Australian Curriculum for year 8 students. It contains material on the real number system and explains how irrational numbers were introduced historically to this system. Information on constructing rational ...