Mathematics (Version 8.4)

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Rationale

Learning mathematics creates opportunities for and enriches the lives of all Australians. The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in number and algebra, measurement and geometry, and statistics and probability.

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Aims

The Australian Curriculum: Mathematics aims to ensure that students:

are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens.

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Key ideas

In Mathematics, the key ideas are the proficiency strands of understanding, fluency, problem-solving and reasoning. The proficiency strands describe the actions in which students can engage when learning and using the content.

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Structure

The Australian Curriculum: Mathematics is organised around the interaction of three content strands and four proficiency strands.
The content strands are number and algebra, measurement and geometry, and statistics and probability. They describe what is to be taught and learnt.

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PDF documents

Resources and support materials for the Australian Curriculum: Mathematics are available as PDF documents. 
Mathematics: Sequence of content
Mathematics: Sequence of achievement

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Glossary

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Year 10A

Year 10A Level Description

The 10A content descriptions are optional and are intended for students who require additional content to enrich and extend their mathematical study whilst completing the common Year 10 curriculum. It is not anticipated that all students will attempt the 10A content, but doing so would be advantageous for those intending to pursue Mathematical Methods (Course C) or Specialist Mathematics (Course D) in the senior secondary years. A selection of topics from the 10A curriculum can be completed according to the needs and interests of students.


Year 10A Content Descriptions

Real numbers

Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264 - Scootle )
Numeracy

Estimating and calculating with whole numbers
  • Estimate and calculate
  • Understand and use numbers in context

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

  • understanding that the real number system includes irrational numbers
    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Identify and clarify information and ideas
    • Organise and process information

    Numeracy

    Estimating and calculating with whole numbers
    • Understand and use numbers in context
    • Estimate and calculate

  • extending the index laws to rational number indices
    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate
    • Understand and use numbers in context

  • performing the four operations with surds
    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate
    • Understand and use numbers in context

Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
  • Transfer knowledge into new contexts

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

Numeracy

Estimating and calculating with whole numbers
  • Understand and use numbers in context
  • Estimate and calculate

  • investigating the relationship between exponential and logarithmic expressions
    Numeracy

    Estimating and calculating with whole numbers
    • Understand and use numbers in context
    • Estimate and calculate

    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

  • simplifying expressions using the logarithm laws
    Numeracy

    Estimating and calculating with whole numbers
    • Understand and use numbers in context
    • Estimate and calculate

    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

Patterns and algebra

Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266 - Scootle )
Numeracy

Estimating and calculating with whole numbers
  • Understand and use numbers in context
  • Estimate and calculate

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

Reflecting on thinking and processes
  • Transfer knowledge into new contexts

  • investigating the relationship between algebraic long division and the factor and remainder theorems
    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate
    • Understand and use numbers in context

Linear and non-linear relationships

Solve simple exponential equations (ACMNA270 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

Numeracy

Estimating and calculating with whole numbers
  • Estimate and calculate
  • Understand and use numbers in context

Recognising and using patterns and relationships
  • Recognise and use patterns and relationships

  • investigating exponential equations derived from authentic mathematical models based on population growth
    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

    Numeracy

    Recognising and using patterns and relationships
    • Recognise and use patterns and relationships

    Estimating and calculating with whole numbers
    • Understand and use numbers in context
    • Estimate and calculate

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

Numeracy

Recognising and using patterns and relationships
  • Recognise and use patterns and relationships

  • applying transformations, including translations, reflections in the axes and stretches to help graph parabolas, rectangular hyperbolas, circles and exponential functions
    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

    Reflecting on thinking and processes
    • Reflect on processes

    Numeracy

    Recognising and using patterns and relationships
    • Recognise and use patterns and relationships

Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268 - Scootle )
Numeracy

Recognising and using patterns and relationships
  • Recognise and use patterns and relationships

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors
    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Organise and process information
    • Identify and clarify information and ideas

    Numeracy

    Recognising and using patterns and relationships
    • Recognise and use patterns and relationships

Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (ACMNA269 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
  • Identify and clarify information and ideas

Numeracy

Recognising and using patterns and relationships
  • Recognise and use patterns and relationships

Estimating and calculating with whole numbers
  • Understand and use numbers in context
  • Estimate and calculate

  • writing quadratic equations that represent practical problems
    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate
    • Understand and use numbers in context

    Critical and Creative Thinking

    Inquiring – identifying, exploring and organising information and ideas
    • Identify and clarify information and ideas
    • Organise and process information


Year 10A Achievement Standards

There are no achievement standards for Year 10A in the Australian Curriculum: Mathematics. Please refer to the Year 10 Achievement Standards.