Close message Scootle has stopped supporting resources that use the Adobe Flash plug-in from 18 Dec 2020. Learning paths that include these resources will have alerts to notify teachers and students that one or more of the resources will be unavailable. Click here for more info.

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

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)

Elaborations
  • investigating graphical and algebraic techniques for finding midpoint and gradient
  • recognising that the gradient of a line is the same as the gradient of any line segment on that line
General capabilities
  • Numeracy Numeracy
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Cartesian coordinates,  Gradients,  Midpoints

Online

reSolve: Gradient and Tangent

This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign ...

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 ...

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. 

Interactive

Laptop wrap – a slippery slope

Distance, midpoint and gradient are investigated as students design an Excel spreadsheet and make a Smart Notebook presentation on ski-lifts. Students then contribute to a discussion on the steepest street in the world. 

Online

reSolve: Directed number

This sequence of two lessons explores directed numbers in real world situations and games, abstracting understanding to applications using the number line. In the first lesson, students develop their understanding of directed numbers by engaging in a game involving hotel elevator floors, in the second lesson students represent ...

Online

reSolve: Real World Algebra: Linear Functions

This sequence of two lessons explores real world, algebraic, numeric and graphical representations of linear functions, focussing on the gradient of linear functions. Students use images of everyday objects and inscribe straight lines, then use Geogebra to explore the algebraic representation of their lines. Each lesson ...

Online

reSolve: Location - My Place in Space

This series of two lessons explores locating points and calculating distances using the Cartesian plane. In the first lesson, students locate and describe points on the Cartesian plane using ordered pairs of coordinates. They then search for squares on a given plane and find the side lengths of the squares. In the second ...

Online

Bee habitat lesson

This lesson plan introduces students to some of Australia's native bee species. Organised in five stages, the lesson plan includes links to videos, scientific and bee-related websites, an information sheet, and downloadable versions of a pictorial slideshow, lesson plan and an assessment rubric. The resource includes suggestions ...

Online

Triathlon: assessment: teacher guide

Use this resource with 'Triathlon: assessment' (L8274). First, see a profile of that assessment object, which gives you some helpful background information. Then follow clear guidelines on the interpretation of student's responses to questions based on interpreting information on a distance–time graph in the assessment object.

Interactive

Simple coordinates game

This is an interactive resource about plotting and identifying points on the Cartesian plane. The resource can be used in one of two modes. In the View mode, the student can enter the coordinates, and the corresponding point is identified on the coordinate plane when the 'Plot' button is selected. In the Guess mode, the ...

Online

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.

Online

TIMES Module 29: Number and Algebra: introduction to coordinate geometry - teacher guide

This is a 22-page guide for teachers. This module introduces coordinate geometry. The introduction includes finding the distance between two points, finding the coordinates of the midpoint between two points, determining the gradient of a line and determining the equation of a line.

Online

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 ...

Online

Introducing the Cartesian coordinate system

This is a website designed for both teachers and students that refers to the Cartesian coordinate system from the Australian Curriculum for year 6 students. It contains material on the Cartesian plane and includes plotting points and determining coordinates of points shown on a grid. There are pages for both teachers and ...

Online

Introduction to differential calculus

This is a teacher resource for an introduction to differential calculus, consisting of a website and a PDF with identical content. It contains an introduction to differentiation. It contains a discussion of the properties of the derivative of a given function and introduces and proves the chain rule, product rule and quotient ...

Interactive

Syllabus bites – Cartesian coordinate system

This Bite is an introduction to the history, terminology, components and use of the Cartesian coordinate system. After completing the resource, students can proceed to six related Syllabus bites modules focusing on transformations on the Cartesian plane.