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

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

Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268)

Elaborations
  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Curves,  Polynomials

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

TIMES Module 39: Number and Algebra: polynomials - teacher guide

This is a 27-page guide for teachers. This module introduces addition, subtraction, multiplication and division of polynomials. Factorisation of polynomials and the solution of polynomial equations are also discussed.

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

reSolve: Algebra: Sums & Differences of Squares

This sequence of three lessons explores sums and differences of two squares. Students are introduced to the historical context of using lookup tables for multiplications and challenged to investigate and generalise the underlying process using algebraic means. In subsequent lessons students use visual and algebraic methods ...

Online

Trade and Investment at a Glance

Using an illustrated report from the Department of Foreign Affairs and Trade, this Teacher guide provides ten learning sequences that engage students in the analysis and interpretation of data about Australian imports and exports. Students: identify Australia's major exports and imports; investigate international trade ...

Online

TIMES Module 33: Number and Algebra: factorisation - teacher guide

This is a 17-page guide for teachers. It continues the discussion of factorisation. In particular, the techniques for the factorisation of quadratic expressions are presented.

Online

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.

Interactive

Algebra four

This is an interactive game for two students in which they solve algebraic equations, similar to 'Connect four'. The players can choose from problems that are one- or two-step, quadratic, have distributive properties or have variables on both sides, and more than one problem type can be chosen. The length of time each player ...

Interactive

Solving quadratic equations

A short introduction to quadratic equations and how they are solved.

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

reSolve: Pythagoras' Theorem - Bent bamboo

This lesson challenges students to use Pythagoras' Theorem to solve a problem from an ancient Chinese text. They make physical models of the problem and use this to construct a graph. They use algebra skills associated with binomial expansions and simplification of fractions to show that the general solution given in the ...

Online

reSolve: Algebra: Think of a number- Binomial Equations

This lesson engages students in investigating a 'think of a number' game and then model it visually and algebraically. This develops skills in algebraic operations including expanding, factorising and collecting like terms. Students investigate whether the game will work for any number and are challenged to generate the ...

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 ...