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

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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 ...

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 ...

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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Mathematical modelling (Algebra): Year 10 – planning tool

This planning resource for Year 10 is for the topic of Mathematical modelling. Students apply linear, quadratic and exponential functions to modelling contexts and outline reasons for selecting a particular model. They use tables of values to look for patterns in data, recognising that linear functions have constant first ...

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Patterns and number facts: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Patterns and number facts. Students work with a variety of functions and relations and their rules, tables of values and graphs using digital tools. Students manipulate, explore, investigate, make conjectures and identify emerging patterns from functions and relations. ...

Interactive

Simultaneous Equations

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

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.

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

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.

Interactive

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

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.

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.

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 ...

Interactive

Laptop wrap: Parallelendicular

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 

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.

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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.

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.

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.  

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.