Mathematics / Year 10 / Number and Algebra / Linear and non-linear relationships

Curriculum content descriptions

Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology (ACMNA237)

Elaborations
  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs
General capabilities
  • Numeracy Numeracy
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Linear equations,  Simultaneous equations

Interactive

Simultaneous Equations: animation

A short animated introduction to simultaneous equations and a demonstration of the elimination method of solution, followed by an interactive quiz.

Interactive

Simultaneous Equations

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

Online

Linear expressions and equations: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Linear expressions and equations. Students have developed confidence from their prior learning to algebraically solve linear equations of the form ax + b = c and can represent the solution graphically. They extend this to solving pairs of simultaneous linear equations ...

Text

Voronoi Diagrams - Calculate

This unit of work explores coordinate geometry in the context of Voronoi diagrams. Students use linear coordinate geometry to construct Voronoi diagrams by finding the gradient of a line segment, then finding the midpoint, a perpendicular line and finally the perpendicular bisector.

Online

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 ...

Text

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 ...

Online

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 ...

Video

My Five Cents: Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Online

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 ...

Text

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 ...

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 ...

Online

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.

Online

TIMES Module 8: Statistics and Probability: data investigation and interpretation, year 10 - teacher guide

This is a 29-page guide for teachers. Box plots are introduced as another graphical tool and are used for comparisons of data. Scatter plots are used to explore relationships between quantitative (usually continuous) variables.

Online

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.

Online

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.

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 ...

Online

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

Desmos Graphing Calculator - Google Play 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.

Interactive

Syllabus Bites: Proportionality problems

This is the fourth in a series of Syllabus Bites related to direct and indirect proportion. Students use graphs, equations and numerical methods to solve problems involving direct proportion.