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)

Elaborations
  • 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

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Year level 9-10
Resource type
Learning area Mathematics
Interactive Resource

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 ...

Interactive Resource

Identifying a possible non-linear rule for a given table of values

This is a five-page HTML resource about solving problems involving the identification of possible non-linear rules matching given tables of values. It contains five questions, two of which are interactive, and one video. The resource discusses and explains identifying a possible non-linear rule that matches a given table ...

Moving Image

Non-linear systems of equations

This digital resource presents a video demonstration, with commentary, of the pen-and-paper technique of constructing the graphs of linear and quadratic functions to find the solutions to a non-linear system of equations. In a single example, a step-by-step illustration of the written method is presented, complemented by ...

Interactive Resource

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.

Interactive Resource

Graphing calculator by Desmos - iTunes 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.

Text

BBC Bitesize: quadratic sequences - revision

In these illustrated information sheets, students revise finding the next term in a quadratic sequence through annotated diagrams and explanations. The rule for the nth term is developed for sequences of increasing complexity. Students attempt questions, with worked solutions being accessible by selecting the Show answer ...

Interactive resource

EagleCat: spin graph

Investigate the beautiful patterns that can emerge from the locus of a point on one circle rolling around another circle. Investigate families of curves that can be produced by: (a) changing the size of the rolling circle only, (b) changing the size of the fixed circle only or (c) changing the position of the point only.

Teacher resource

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 ...

Text

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 ...

Teacher resource

Starting Smart: how can I use measurement relationships to solve problems? - years 7-9

This curriculum resource package is a ten-week middle years teaching plan and set of supporting resources to extend students' knowledge and skills in the measurement of area and volume and to develop their ability to solve practical measurement problems. Students use counting methods and develop formulas to calculate areas ...

Teacher resource

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.

Teacher resource

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.