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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

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 ...

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

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 ...

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TIMES Module 22: Number and Algebra: consumer arithmetic - teacher guide

This is a 23-page guide for teachers, providing an introduction to the financial mathematics component of the number and algebra strands for years 9 and 10. A brief history of the concept of money concludes the module.

Interactive

Laptop wrap: Surveying statistics

In this laptop-friendly resource, students summarise the statistical process, design a sample survey and design a community brochure that displays large data sets using Excel charts.

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Data in Gapminder world

This resource is a dataset providing data for a number of indicators of development over time for more than 200 countries. The indicators fall into the following categories: population, health, economy, environment, work, infrastructure, energy and education, with over 500 sets of data in total. Each set of data can be ...

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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.

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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.

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Factorising Quadratics and Solving - Calculate

This activity explores the properties of the family of functions and their graphs known as parabolas. The unit includes an AMSI Interactive online module, a range of other AMSI Schools and external links and video tutorials and some extension or enrichment ideas to take their understanding further. A short quiz at the end ...

Interactive

Waste and materials – sustainability action process (Years 7–10)

This resource guides students through an extended school-based or local investigation focussed on waste and materials using the five-step sustainability action process. The resource supports the investigation of a real-world issue or problem. Students develop and implement a chosen sustainability action and then evaluate ...

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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 ...

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Amp up the volume

This set of learning activities challenges students to build a portable amplifier that passively amplifies the sound produced by a smartphone. The module includes a comprehensive teacher guide, curriculum links, materials lists, design process guides and printable student resource sheets. The resource also provides an editable ...

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Off the scale

This lesson introduces students to the idea of a log scale, a seemingly perplexing way to present data. The lesson begins with an exploration of examples when a linear scale is inappropriate and concludes with a plotting activity using authentic data from the COVID-19 pandemic.

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Would you rather …?

In this lesson students collect data, creating and analysing two-way tables, by playing the popular game ‘Would you rather…?’ Students collect data in a two-way table, extract and describe data in two-way tables using boolean statements, identify and begin to analyse/explain association between two variables.

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A piece of cake

In this lesson, students build on their skills in finding volumes and surface areas of prisms and cylinders to design a multi-level celebration cake for a party. They use mathematical modelling to vary the size and shape of the component cakes and to calculate how much frosting is needed.

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The Mathematics of Projectiles - Calculate

This activity provides a practical introduction to the motion of projectiles with a focus on angles. It is designed as a lead in to parabolic and quadratic functions.

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Linear Relationships (and how Maths can help you choose a great car) - Calculate

The activity has students collecting their own information from a well-known Australia car buying website and using this to find an estimated relationship between the ‘asking price’ for a used car and the distance it has traveled in kilometres.

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Work sample Year 10 Mathematics: Predict a winner

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

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

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 ...