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

Curriculum content descriptions

Solve linear equations involving simple algebraic fractions (ACMNA240)

Elaborations
  • solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question
General capabilities
  • Numeracy Numeracy
ScOT terms

Simple fractions,  Linear equations,  Algebraic terms

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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 ...

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 ...

Online

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 ...

Online

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. ...

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 ...

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.  

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

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 ...

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

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

Simultaneous Equations

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

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 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 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

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. 

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. 

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.

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

The Numberline

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