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

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

Simplify algebraic products and quotients using index laws (ACMNA231)

  • applying knowledge of index laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices
General capabilities
  • Numeracy Numeracy
ScOT terms

Indices,  Mathematical expressions

Moving Image

Graham's number

If you were asked what the biggest number you can think of is, what would you say? Infinity? Well, what about the biggest finite number you can think of? Mathematician Ron Graham came across such a gigantic number in his research that, to capture its massive size, he and his colleagues needed to come up with new methods ...


Using exponents in real-life contexts

This animated presentation provides four examples of the use of exponential functions to model real-life practical situations. The examples highlight the manipulation of indices (exponents) and the index laws.

Interactive Resource

Laptop wrap: Expanding on algebra

Students make a presentation on the index laws, investigate the visual representation of the binomial expansions and design an acronym to help recall the special products. 

Teacher resource

Secondary mathematics: using real data

These seven learning activities, which focus on the use of 'real data' 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 the three content strands ...

Teacher resource

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 ...

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

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 ...


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 ...


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 ...

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

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 ...

Interactive Resource

Solving quadratic equations

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

Teacher resource

TIMES Module 36: Number and Algebra: formulas - teacher guide

This is a 13-page guide for teachers. It introduces the use of formulas, and includes substitution and the solution of the resulting equations.

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 ...

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 ...


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.

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 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.

Teacher resource

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 ...

Teacher resource

TIMES Module 31: Number and Algebra: indices and logarithms - teacher guide

This is a 26-page guide for teachers. It extends the study of indices to rational indices and introduces logarithms.