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

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

Online

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 ...

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Work sample Year 10 Mathematics: Mathematics assignment

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 10 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

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Geometry of water sources and landforms

Indigenous cultures have always been deeply aware of the location of water and its significance. In this resource students will apply geometric, trigonometric, and algebraic techniques to analyse idealised water body shapes and associated landforms. They will calculate surface areas, volumes, angles, and heights of these ...

Video

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.

Video

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!

Video

What are pixels?

Meet Kevin Systrom and Piper Hanson as they explain how digital images work. What are pixels, those tiny dots of light, made from? How are colours created and represented? What does Kevin say about the way mathematical functions are used to create different image filters. What is the difference between image resolution ...

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Big data, better hospitals

Overcrowding in hospitals is one of the biggest challenges facing our healthcare system . In order to reduce hospital waiting times, the Patient Admission Prediction Tool (PAPT) uses historical data to predict how many patients, and with what kinds of injuries, are expected to arrive at the emergency department each day ...

Online

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 ...

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Round and Round and Round

This resource is a web page containing an interactive that can be used to explore the relationships between the angles of turn that produce the same vertical and horizontal displacements. The task provides an opportunity to apply their understanding of division and recurring decimals. A 'Getting started' page, printable ...

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Tuning and Ratio

This resource is a web page containing a challenging problem solving task that requires an understanding of ratios and logarithms. It explains how intervals such as an octave corresponds to a particular ratio of string lengths which produce the notes. Two types of tuning based on ratios; The Pythagorean Scale and Just Intonation ...

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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

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 ...

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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.

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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.

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Logarithmic scale: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Logarithmic scale. Students read and interpret different types of scales. They understand that that a logarithmic scale uses powers 10 and how it appears on a graph. Students know when the use of such a scale is appropriate and where logarithmic scales are used for ...

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 ...

Downloadable

Lucky lottery

In this lesson, students play a simple lottery game, analyse their odds of winning and how this influences the decisions they made. Students determine the differences between experimental and mathematical probability, conduct a simulation modelling an event and critically evaluate the odds of winning the lottery. The lesson ...

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 ...

Video

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 ...