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

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)

Elaborations
  • 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

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.

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

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 ...

Online

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 ...

Online

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, ...

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.

Online

Graphs: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Graphs. Students connect the graphical representation of exponential functions and their corresponding exponential rule. They use digital tools to explore how systematically making changes to the value of the base, pronumerals or variables changes the shape of the corresponding ...

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

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.

Online

Life expectancy PowerPoint

This teacher resource is a PowerPoint presentation designed to address common student misunderstandings about life expectancy. It emphasises that life expectancy is an average, that most people live for much longer or shorter than their life expectancy and that, when life expectancy is low, it is mostly because of a very ...

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

The Numberline

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

Online

Australia's population: countries of birth - dataset

The dataset provides statistics about the estimated resident population, median age and sex ratio by countries of birth for the latest year of available data. It is periodically updated by the Australian Bureau of Statistics (ABS). The dataset is included in the list of related datasets on the page in MS Excel format.

Online

Data representation and interpretation - years 9 and 10

This is a teacher resource describing a set of student activities based on temperature and rainfall data and climate graphs for a number of cities in the Asia region, including Australian cities. The activities focus on constructing graphs from climate data and interpreting climate graphs. The resource encourages students ...

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!

Online

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 ...

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 ...

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 ...

Online

The Sydney Metro rail project – Stage 5

This inquiry-based unit of work was created, trialled and peer reviewed as part of a professional learning program in inquiry-based learning for school teachers. The professional learning courses were part of a pilot partnership between the NSW Government’s Sydney Metro transport agency and Western Sydney University. The ...

Online

Sustainable agriculture: agri-environmental indicators

This is a web resource that provides a database of agri-environmental indicators for environmental performance of agriculture in OECD countries between 1990 and 2008. The data table can be customised, with options to view by country or by theme: land, energy, air, nutrients, soil, biodiversity, pesticides, water, farm management ...