Mathematics / Year 10 / Number and Algebra / Patterns and algebra

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

Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)

Elaborations
  • using the distributive law and the index laws to factorise algebraic expressions
  • understanding the relationship between factorisation and expansion
General capabilities
  • Numeracy Numeracy
ScOT terms

Factors,  Mathematical expressions

Teacher resource

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.

Interactive Resource

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 ...

Teacher resource

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 ...

Teacher resource

reSolve: Pythagoras' Theorem

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 ...

Teacher resource

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 ...

Teacher resource

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 ...

Interactive Resource

Linear equations and inequalities

This resource is a collection of screen displays of questions relating to linear equations and inequations. Graphing tasks involve determining the coordinates of two points on the linear function. Other tasks are presented as multiple-choice questions and involve finding slopes of lines, calculating intercepts with the ...

Interactive resource

EagleCat: parabola

Explore the graphs of quadratic equations in two forms: (a) the turning point form, y = a(x – h)² + k, and (b) the intercept form, y = (x – a)(x – b). Observe changes to the turning point and the shape of parabolic graphs through various transformations. Alternately, change the equation and observe changes in the x-intercepts ...

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Perpendicular lines and linear equations

This digital presentation demonstrates solving a problem about finding the equation of a line perpendicular to a given line and passing through a specific point. The workings and solution are revealed slowly and in sequential steps with explanations provided at some points. The steps can be seen more quickly by selecting ...

Video

Using linear equations to model population growth, Hooke's Law and parcel shipping charges

In this animated presentation students are provided with three examples of mathematical modelling in real-world settings. Linear functions are used to model population growth, Hooke's Law and parcel shipping charges.

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BBC Bitesize: more on equations - revision

These illustrated information sheets revise the methods of solving linear equations from simple ones with one unknown term to ones with the unknown on both sides. The solution of equations containing brackets or fractions is also considered. Full algebraic working is shown for sample equations. Students solve equations ...

Interactive resource

Graphing: line of best fit

Plot some data points on a graph. Estimate the position for a line of best fit. Use a graphing tool to check your estimate. Add more points to see how they affect the position of the line of best fit.

Teacher resource

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 ...

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BBC Bitesize: graphs - revision

These illustrated information sheets revise the rules for vertical and horizontal lines and the meaning of m and c in the rule y = mx + c. Students find the rule for a given linear graph. Tables of values are created so that graphs can be plotted. This resource is one of a series of online resources from the BBC's Bitesize ...

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Parallel lines and linear equations

This digital presentation demonstrates solving a problem about finding the equation of a line parallel to a given line and passing through a specific point. The workings and solution are revealed slowly and in sequential steps with explanations provided at some points. The steps can be seen more quickly by selecting the ...

Interactive Resource

Solving quadratic equations

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

Teacher resource

Data representation and interpretation using scatterplots - teacher resource

This resource is a professional learning package designed for pre-service teachers. It demonstrates and investigates the interrelated content, pedagogy and technology knowledge used in a series of mathematics lessons that focus on looking for a relationship between two variables. The resource provides video footage of a ...

Teacher resource

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 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.

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.