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

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.

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 ...

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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.

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

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 ...

Interactive

Water use and efficiency – sustainability action process (Years 7–10)

This resource guides students through an extended school-based or local investigation focussed on water use and efficiency 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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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.

Downloadable

Understanding compound interest

In this lesson students learn how compound interest works. They explore the difference between simple interest and compound interest, apply compund interest to saving scenarios and calculate the outcomes from different deposit plans with compund interest applied. They then go on to consider the impact of compound interest ...

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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 ...

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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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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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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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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 ...

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Australia's Trade through Time

Using an interactive timeline created by the Department of Foreign Affairs and Trade, this teacher guide provides 12 series of learning experiences that engage students in the analysis and interpretation of data about Australian trade from 1900 to the present day. Students study videos, tables, images and texts in order ...

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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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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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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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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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.

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!