Mathematics

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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 3

Year 3 Level Description

The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.

At this year level:

  • understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry
  • fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions
  • problem-solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns
  • reasoning includes using generalising from number properties and results of calculations, comparing angles and creating and interpreting variations in the results of data collections and data displays.

Year 3 Content Descriptions

Number and place value

Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051 - Scootle )
Critical and Creative Thinking

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

Generating ideas, possibilities and actions
  • Imagine possibilities and connect ideas

Numeracy

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

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

  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
    Critical and Creative Thinking

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

    Literacy

    Composing texts through speaking, writing and creating
    • Compose spoken, written, visual and multimodal learning area texts

    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

  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
    Literacy

    Composing texts through speaking, writing and creating
    • Use language to interact with others
    • Compose spoken, written, visual and multimodal learning area texts

    Grammar knowledge
    • Use knowledge of sentence structures

    Word Knowledge
    • Understand learning area vocabulary

    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

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

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052 - Scootle )
Numeracy

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

Literacy

Composing texts through speaking, writing and creating
  • Compose texts
  • Compose spoken, written, visual and multimodal learning area texts

Comprehending texts through listening, reading and viewing
  • Navigate, read and view learning area texts
  • Interpret and analyse learning area texts
  • Comprehend texts

Word Knowledge
  • Understand learning area vocabulary

  • placing four-digit numbers on a number line using an appropriate scale
    Literacy

    Composing texts through speaking, writing and creating
    • Compose spoken, written, visual and multimodal learning area texts

    Word Knowledge
    • Understand learning area vocabulary

    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
    • Understand and use numbers in context

  • reproducing numbers in words using their numerical representations and vice versa
    Literacy

    Composing texts through speaking, writing and creating
    • Compose spoken, written, visual and multimodal learning area texts

    Word Knowledge
    • Understand learning area vocabulary

    Numeracy

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

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053 - Scootle )
Numeracy

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

Literacy

Composing texts through speaking, writing and creating
  • Compose texts
  • Compose spoken, written, visual and multimodal learning area texts

Comprehending texts through listening, reading and viewing
  • Comprehend texts
  • Navigate, read and view learning area texts

Word Knowledge
  • Understand learning area vocabulary

Critical and Creative Thinking

Generating ideas, possibilities and actions
  • Seek solutions and put ideas into action
  • Consider alternatives

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

  • recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones
    Numeracy

    Estimating and calculating with whole numbers
    • 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

  • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations
    Critical and Creative Thinking

    Reflecting on thinking and processes
    • Think about thinking (metacognition)
    • Reflect on processes

    Analysing, synthesising and evaluating reasoning and procedures
    • Evaluate procedures and outcomes

    Literacy

    Word Knowledge
    • Understand learning area vocabulary

Recognise and explain the connection between addition and subtraction (ACMNA054 - Scootle )
Literacy

Composing texts through speaking, writing and creating
  • Compose spoken, written, visual and multimodal learning area texts
  • Use language to interact with others
  • Compose texts

Comprehending texts through listening, reading and viewing
  • Interpret and analyse learning area texts
  • Navigate, read and view learning area texts
  • Comprehend texts

Word Knowledge
  • Understand learning area vocabulary

Critical and Creative Thinking

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

Reflecting on thinking and processes
  • Reflect on processes

Numeracy

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

  • demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences
    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    Composing texts through speaking, writing and creating
    • Compose spoken, written, visual and multimodal learning area texts

    Numeracy

    Estimating and calculating with whole numbers
    • 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

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055 - Scootle )
Numeracy

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

  • recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger 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

  • combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1)
    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
    • Organise and process information
    • Identify and clarify information and ideas

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056 - Scootle )
Numeracy

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

  • establishing multiplication facts using number sequences
    Critical and Creative Thinking

    Reflecting on thinking and processes
    • Transfer knowledge into new contexts

    Numeracy

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

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057 - Scootle )
Critical and Creative Thinking

Generating ideas, possibilities and actions
  • Consider alternatives
  • Seek solutions and put ideas into action

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

Information and Communication Technology (ICT) Capability

Creating with ICT
  • Generate solutions to challenges and learning area tasks

Numeracy

Estimating and calculating with whole numbers
  • Estimate and calculate

Literacy

Comprehending texts through listening, reading and viewing
  • Interpret and analyse learning area texts
  • Navigate, read and view learning area texts
  • Comprehend texts

Word Knowledge
  • Understand learning area vocabulary

Composing texts through speaking, writing and creating
  • Compose texts
  • Compose spoken, written, visual and multimodal learning area texts

  • writing simple word problems in numerical form and vice versa
    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate

    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    Composing texts through speaking, writing and creating
    • Compose spoken, written, visual and multimodal learning area texts

  • using a calculator to check the solution and reasonableness of the answer
    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate

Fractions and decimals

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058 - Scootle )
Numeracy

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

Using fractions, decimals, percentages, ratios and rates
  • Apply proportional reasoning
  • Interpret proportional reasoning

  • partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes
    Critical and Creative Thinking

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

    Numeracy

    Using fractions, decimals, percentages, ratios and rates
    • Apply proportional reasoning
    • Interpret proportional reasoning

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

  • locating unit fractions on a number line
    Numeracy

    Using fractions, decimals, percentages, ratios and rates
    • Interpret proportional reasoning
    • Apply proportional reasoning

  • recognising that in English the term ‘one third’ is used (order: numerator, denominator) but that in other languages this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator) for example Japanese
    • Asia and Australia’s Engagement with Asia
    Intercultural Understanding

    Recognising culture and developing respect
    • Investigate culture and cultural identity

    Interacting and empathising with others
    • Communicate across cultures

    Critical and Creative Thinking

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

Money and financial mathematics

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059 - Scootle )
Numeracy

Estimating and calculating with whole numbers
  • Estimate and calculate
  • Use money

Critical and Creative Thinking

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

  • recognising the relationship between dollars and cents, and that not all countries use these denominations and divisions (for example Japanese Yen)
    • Asia and Australia’s Engagement with Asia
    Intercultural Understanding

    Recognising culture and developing respect
    • Investigate culture and cultural identity

    Critical and Creative Thinking

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

Patterns and algebra

Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060 - Scootle )
Literacy

Comprehending texts through listening, reading and viewing
  • Comprehend texts
  • Navigate, read and view learning area texts

Composing texts through speaking, writing and creating
  • Compose texts
  • Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
  • Understand learning area vocabulary

Critical and Creative Thinking

Generating ideas, possibilities and actions
  • Consider alternatives
  • Seek solutions and put ideas into action
  • Imagine possibilities and connect ideas

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

Numeracy

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

  • identifying and writing the rules for number patterns
    Literacy

    Comprehending texts through listening, reading and viewing
    • Navigate, read and view learning area texts

    Word Knowledge
    • Understand learning area vocabulary

    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

  • describing a rule for a number pattern, then creating the pattern
    Numeracy

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

    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    Comprehending texts through listening, reading and viewing
    • Navigate, read and view learning area texts

    Composing texts through speaking, writing and creating
    • Compose spoken, written, visual and multimodal learning area texts

    Critical and Creative Thinking

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


Year 3 Achievement Standards

By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single-digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They conduct simple data investigations for categorical variables.


Year 3 Work Sample Portfolios