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

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 ...

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

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.

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: 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

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 ...

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 ...

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

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 ...

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 ...

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 ...

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 ...

Downloadable

Two-up - The fairest game of all?

In this lesson, students look at the history and mathematics of Two-Up, exploring why it is considered such a fair game, and how the ‘boxer’ or game runner makes a profit. The lesson is outlined in detail including NSW curriculum links, learning intentions, discussion points, materials required, links to supporting videos ...

Online

Statistical analysis: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Statistical analysis. Students are competent with comparing data distributions and are fluent with the relevant mathematical vocabulary. Extend students to work with other data displays, such as box plots, to represent continuous numerical variables. Review the distinction ...

Online

Logarithmic scale: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Logarithmic scale. Students read and interpret different types of scales. They understand that that a logarithmic scale uses powers 10 and how it appears on a graph. Students know when the use of such a scale is appropriate and where logarithmic scales are used for ...

Downloadable

Easter Show games of chance

In this lesson, students will calculate the probability of an average person scoring a shot at a basketball game at the Easter Show. They will then use these probabilities to design a payout system which can absorb the losses from an average player winning big, whilst profiting from the average player who scores very poorly, ...