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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

Solve simple exponential equations (ACMNA270)

Elaborations
  • investigating exponential equations derived from authentic mathematical models based on population growth
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Exponential functions,  Equations

Video

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!

Video

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.

Online

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.

Video

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.

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 ...

Video

What is a physics engine?

Video games have evolved over the years to become more realistic. One reason for this could be that when objects move in video games, they seem to obey the laws of physics. The software that allows for this is called a physics engine. One equation that game programmers might be using when programming their physics engine ...

Interactive

The take-away bar: go figure

This tutorial is suitable for use with a screen reader. It explains strategies for solving subtractions in your head such as 87-39. Work through sample questions and instructions explaining how to use linear partitioning techniques. Solve subtractions by breaking them up into parts that are easy to work with, work out each ...

Online

Introduction to differential calculus

This collection of 17 digital curriculum resources (all learning objects) is organised into three sections: rates of change; differential calculus; and review of differential calculus via three learning objects. Students explore rates of change through liquid-pouring activities, and are introduced to the gradient of secants ...

Interactive

Simultaneous Equations: animation

A short animated introduction to simultaneous equations and a demonstration of the elimination method of solution, followed by an interactive quiz.

Interactive

Simultaneous Equations

A short introduction to simultaneous equations and how they are solved.

Interactive

Acid Base Reactions

Students use this resource consisting of eleven slides with diagrams, written explanation and voice-over to understand that different bases react with acids and how word and chemical equations summarise the reactions. There is a two-question quiz and a summary slide.

Interactive

Laptop wrap: Parallelendicular

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 

Online

TIMES Module 36: Number and Algebra: formulas - teacher guide

This is a 13-page guide for teachers. It introduces the use of formulas, and includes substitution and the solution of the resulting equations.

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, ...