Mathematics / Year 10 / Number and Algebra / Real numbers

Curriculum content descriptions

Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)

  • understanding that the real number system includes irrational numbers
  • extending the index laws to rational number indices
  • performing the four operations with surds
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Irrational numbers,  Fractional indices,  Rational numbers

Refine by resource type

Refine by year level

Refine by learning area

Refine by topic

Related topic

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 ...


MathXplosion, Ep 15: How many times can a sheet of paper be folded?

Why can a regular sheet of paper be folded only about six times? By folding a sheet of paper in half, over and over, the number of layers and the thickness of the paper doesn’t just double, they increase exponentially. Find out how many times a sheet of paper can actually be folded!


My Five Cents: What is opportunity cost?

What is the true cost of buying something? Gen Fricker explains that it's more than just money. Learn about opportunity cost - what it is, why it's a helpful tool and when to use it. Simple! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  


Laptop wrap: Investing wisely

In this laptop-friendly resource, students investigate unit pricing and explore the formulae and concepts of simple and compound interest.


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. 


The Numberline

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


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.


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.


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.


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.


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.


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 ...


Catalyst: 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 ...


Sites2See – applied mathematics

This collection of resources for Applied Mathematics has helpful links for the six Focus Studies - Communication, Driving, Design, Household Finance, Human Body and Personal Resource Usage. A laptop-friendly resource.


How does income tax work?

Gen Fricker makes income tax interesting! Learn about income tax - what it is, how it works and when you have to pay it. Easy-peasy! Then test yourself with ASIC Moneysmart's "Things to think about" classroom exercises.


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 ...


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 ...


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 ...


Formulate and manipulate expressions: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Formulate and manipulate expressions. Students extend the distributive law to expanding the product of two binomials (ax + b)(cx + d) and the factorisation of non-monic quadratic expressions with integer coefficients. Students practise algebraic manipulation involving ...


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 ...