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

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239)

  • sketching graphs of parabolas, and circles
  • applying translations, reflections and stretches to parabolas and circles
  • sketching the graphs of exponential functions using transformations
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Exponential functions,  Graphs (Data representation),  Quadratics,  Circular functions


Exponential growth and doubling time

This resource aims to guide and support a mathematics teacher of Year 10 across three main areas as the class explores the mathematics of exponential growth. The contexts used are compound interest, animal and human population growth, and the growth (and decay) of bacteria populations.


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.


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 ...


Maths of mouse plagues

How do pests such as mice reach plague proportions? The answer is that they can grow at an exponential rate. Watch this clip to see how that happens, but first enjoy (or squirm at) some footage of a real mouse plague.


reSolve: Real World Algebra: Quadratic Functions

This sequence of three lessons explores different representations of quadratic functions, with particular emphasis on turning points in quadratic graphs. Students use images of trajectories, inscribe their own curves using Geogebra and then further explore the algebraic representation of their curves. Each lesson is outlined ...


reSolve: Real World Algebra: Exponential Functions

This sequence of two lessons explores exponential functions as seen in the real world, linking the representations of function rules, graphs and tables of values. Students consider real world objects and data that can be described using exponential functions. They use simulations and modelling to investigate transformations, ...


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 ...


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.


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 ...


Calculations involving exponential growth: world population

Recently the world's population passed seven billion and it continues to grow by 200,000 people every day. Listen to some reasons why our population is growing at such a rate, and the strain this will put on resources such as food and water. This clip provides context for calculations involving exponential growth.


Leisure survey

Explore how kids use their leisure time. Choose questions to ask in a survey. For example, look at the percentages of kids that play tennis, basketball or netball. Examine a table of results. Sort the data and use it to answer questions. Display the results using a suitable type of graph such as a pie chart, bar graph or ...


Biography: Federation people: Thomas Roberts

Investigate famous artist Thomas (Tom) Roberts's role in Federation. Examine two different types of biographies of Roberts: one short and the other more detailed. Inspect examples of how he was visually depicted in his time. This learning object is one in a series of objects in the 'Biography: Federation people' series.


Forbes Carlile discusses development of Australian sports science, 2008

This is an edited sound recording of the leading sports scientist and swimming coach Forbes Carlile speaking about his work in sports science. Carlile says that he worked under the 'father of sports science in Australia', Professor Frank Cotton. His own interest in the field was as a physiologist, measuring physical changes ...


reSolve: Sport Stats

In this lesson, students examine sporting scores and explore the concept of the average of a set of scores. Students collect sporting scores from real and hypothetical games, use blocks to visualise an even distribution of scores across matches and then explore how to calculate the average of a set of scores. The lesson ...


reSolve: Statistics - Student Profiling

In this sequence of two lessons, students critically assess the Census@School 2014 Questionnaire and make decisions on how they would analyse the data given the types of questions and response. They describe the life of a single participant using their survey data and use a range of statistical tools to compare their participant ...


reSolve: What a Load of Rubbish

In this series of three lessons, students conduct an audit of the rubbish they find in their playground. They use a range of categories to sort, display and interpret the data and make simple inferences. They then reclassify the rubbish collected as to whether it can be recycled, composted or if it needs to go into the ...


Classroom Antarctica: Twilight zone

In this sequence of learning, students investigate the significant variation in sunlight hours that occur across Antarctica and in comparison to other locations on Earth. They interpret graphs of daylight hours and compare daylight and darkness received by places at different locations across Antarctica, Australia and the ...


Exploring farms that produce our meat and wool

This is a teacher resource containing a sequence of activities relating to meat and wool production in Australia. It contains material to assist planning and implementing a study of where farmers live, where our meat and wool comes from, technologies used in production and resource management, and how farm environment and ...


reSolve: Reconciliation data

This lesson prompts students to examine data from the Reconciliation Barometer report, collect their own local data and compare with the national findings. Students discuss the meaning of reconciliation, explore statements from Reconciliation Barometer report, design a survey to collect local data relating to the statements ...


Create your own card game

Grab a deck of cards and a bunch of friends and create your own card game. What sort of rules will you decide on? Get a pen and some paper out and brainstorm some possibilities. You might decide on something like 'If I draw a red card, I get a point' and 'If I draw a black card, you get a point.' What other rules can you ...