Mathematics / Year 10 / Number and Algebra / Linear and non-linear relationships

Curriculum content descriptions

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

Elaborations
  • applying transformations, including translations, reflections in the axes and stretches to help graph parabolas, rectangular hyperbolas, circles and exponential functions
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Transformation (Geometry),  Exponential functions,  Hyperbolic functions,  Parabolic functions

Online

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.

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 ...

Online

reSolve: Trigonometric Trajectories

In this sequence of two lessons, students investigate trigonometric and Pythagorean relationships through two contexts: researching and building a model zipline ride and outlining a proposal for glider poles. In the first lesson, students apply trigonometric and Pythagorean relationships to investigate the dimensions of ...

Online

TIMES Module 24: Measurement and Geometry: further trigonometry - teacher guide

This is a 32-page guide for teachers. It provides an introduction to the sine rule and cosine rule and their applications.

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

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 ...

Downloadable

Understanding compound interest

In this lesson students learn how compound interest works. They explore the difference between simple interest and compound interest, apply compund interest to saving scenarios and calculate the outcomes from different deposit plans with compund interest applied. They then go on to consider the impact of compound interest ...

Interactive

Trigonometric Ratios

An animated introduction to the basic trigonometric ratios.

Interactive

The geometer's warehouse

This web-based, multimedia resource focuses on the geometry of the Stage 4 and Stage 5 Mathematics syllabus. It comprises 70 dynamic html worksheets, each exploring a different outcome in Stage 4 and Stage 5 geometry.

Interactive

Laptop wrap: Geometry gems

A page with a focus on using GeoGebra to enhance student understanding of various geometric properties and the importance of reasoning in proof. A laptop-friendly resource that includes supporting activities and links to resources.

Interactive

The Numberline

An interactive tool that can help students explore a number line, including points representing integers, fractions and decimals

Interactive

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 ...

Online

TIMES Module 22: Number and Algebra: consumer arithmetic - teacher guide

This is a 23-page guide for teachers, providing an introduction to the financial mathematics component of the number and algebra strands for years 9 and 10. A brief history of the concept of money concludes the module.

Online

TIMES Module 22: Measurement and Geometry: introductory trigonometry - teacher guide

This is a 20-page guide for teachers containing an introduction to the three basic trigonometric ratios. A history of trigonometry concludes the module.

Online

TIMES Module 25: Measurement and Geometry: trigonometric functions - teacher guide

This is a 21-page guide for teachers. It provides an introduction to the sine, cosine and tangent functions and applications of these.

Online

TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

This is a 41-page guide for teachers. It contains an introduction to scale drawings and similarity, and in particular the tests for triangles to be considered similar. Applications of similarity are included throughout the module.

Online

reSolve: Real World Algebra: Quadratic Functions

This sequence of three lessons explores different representations of quadratic functions, with particular emphasis on turning points in quadratic graphs. Students use images of trajectories, inscribe their own curves using Geogebra and then further explore the algebraic representation of their curves. Each lesson is outlined ...

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.

Online

Volume and surface area: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Volume and surface area. Students extend their application of volume and surface area to solve problems on composite solids. Students will need to be able to visualise the individual elements of the composite solids and identify the areas where these elements touch.

Online

Pythagoras and trigonometry: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Pythagoras and trigonometry. Students apply their knowledge of Pythagoras' theorem to solve problems involving angles of elevation and depression and direction. They explore how direction can be indicated using true bearings and compass points.