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

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

Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)

Elaborations
  • expressing the sum and difference of algebraic fractions with a common denominator
  • using the index laws to simplify products and quotients of algebraic fractions
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Simple fractions,  Algebraic terms,  Number operations

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 ...

Video

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

The Numberline

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

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 ...

Interactive Resource

Tax, super and you

The 'Tax, super and you' website is designed for use by students in years 10 to 12 and their teachers. It includes four modules: Tax 101 is a general introduction, Your tax focuses on individuals, Business tax on companies and the final module explores the concept of superannuation. Six interactive resources accompany the ...

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 ...

Teacher resource

Top drawer teachers

This is a website that covers five mathematical topics: fractions, mental computation, patterns, statistical literacy and ‘reasoning’. It also explores good teaching practice linked to classroom activities including how to address common misunderstandings. There is also a section for assessment, as well as worksheets with ...

Text

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 ...

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 ...

Text

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.

Teacher resource

Australia's Trade through Time

Using an interactive timeline created by the Department of Foreign Affairs and Trade, this Teacher guide provides 12 series of learning experiences that engage students in the analysis and interpretation of data about Australian trade from 1900 to the present day. Students study videos, tables, images and texts in order ...

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 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

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

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 ...

Moving Image

Space debris: the accuracy of space lasers

In space there are thousands of human-made objects (satellites and space junk) orbiting Earth. To avoid collision with space debris, satellites are manoeuvred out of its path. Discover how space debris is tracked using lasers, and about accuracy's effects on the lifetime of the satellite. Find out, using trigonometry, the ...

Teacher resource

Exponential growth and doubling time

This resource aims to guide and support a mathematics teacher of Year 10 across three main areas as the class explores the mathematics of exponential growth. The contexts used are compound interest, animal and human population growth, and the growth (and decay) of bacteria populations.

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.

Moving Image

Calculations involving exponential growth: world population

Recently the world's population passed seven billion and it continues to grow by 200,000 people every day. Listen to some reasons why our population is growing at such a rate, and the strain this will put on resources such as food and water. This clip provides context for calculations involving exponential growth.