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 4

Year 4 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 making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes
  • fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data
  • problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns
  • reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.

Year 4 Content Descriptions

Using units of measurement

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084 - Scootle )
Numeracy

Using measurement
  • Estimate and measure with metric units

  • reading and interpreting the graduated scales on a range of measuring instruments to the nearest graduation
    Literacy

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

    Numeracy

    Using measurement
    • Estimate and measure with metric units

Compare objects using familiar metric units of area and volume (ACMMG290 - Scootle )
Numeracy

Using measurement
  • Estimate and measure with metric units

  • comparing areas using grid paper
    Numeracy

    Using measurement
    • Estimate and measure with metric units

    Intercultural Understanding

    Recognising culture and developing respect
    • Explore and compare cultural knowledge, beliefs and practices

  • comparing volume using centicubes
    Numeracy

    Using measurement
    • Estimate and measure with metric units

    Critical and Creative Thinking

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

  • recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)
    • Asia and Australia’s Engagement with Asia
    Critical and Creative Thinking

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

Convert between units of time (ACMMG085 - Scootle )
Numeracy

Using measurement
  • Operate with clocks, calendars and timetables

  • identifying and using the correct operation for converting units of time
    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086 - Scootle )
Literacy

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

Numeracy

Using measurement
  • Operate with clocks, calendars and timetables

  • calculating the time spent at school during a normal school day
    Critical and Creative Thinking

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

    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

  • calculating the time required to travel between two locations
    Critical and Creative Thinking

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

    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

  • determining arrival time given departure time
    Critical and Creative Thinking

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

    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

Shape

Compare the areas of regular and irregular shapes by informal means (ACMMG087 - Scootle )
Numeracy

Using measurement
  • Estimate and measure with metric units

  • comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares
    Numeracy

    Using measurement
    • Estimate and measure with metric units

    Critical and Creative Thinking

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

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
  • Reflect on processes
  • Transfer knowledge into new contexts

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

Literacy

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

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

Word Knowledge
  • Understand learning area vocabulary

Information and Communication Technology (ICT) Capability

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

Numeracy

Using spatial reasoning
  • Visualise 2D shapes and 3D objects

  • identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes
    Numeracy

    Using spatial reasoning
    • Visualise 2D shapes and 3D objects

    Critical and Creative Thinking

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

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

  • creating a two-dimensional shapes from verbal or written instructions
    Literacy

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

    Word Knowledge
    • Understand learning area vocabulary

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

    Numeracy

    Using spatial reasoning
    • Visualise 2D shapes and 3D objects

Location and transformation

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
  • Transfer knowledge into new contexts

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

Analysing, synthesising and evaluating reasoning and procedures
  • Apply logic and reasoning

Literacy

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

Word Knowledge
  • Understand learning area vocabulary

Visual Knowledge
  • Understand how visual elements create meaning

Numeracy

Using spatial reasoning
  • Interpret maps and diagrams

  • identifying the scale used on maps of cities and rural areas in Australia and a city in Indonesia and describing the difference
    • Asia and Australia’s Engagement with Asia
    Critical and Creative Thinking

    Reflecting on thinking and processes
    • Transfer knowledge into new contexts

    Analysing, synthesising and evaluating reasoning and procedures
    • Apply logic and reasoning

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

    Literacy

    Grammar knowledge
    • Use knowledge of sentence structures

    Text knowledge
    • Use knowledge of text structures

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

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

    Word Knowledge
    • Understand learning area vocabulary

    Intercultural Understanding

    Recognising culture and developing respect
    • Explore and compare cultural knowledge, beliefs and practices

    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

  • using directions to find features on a map
    Literacy

    Visual Knowledge
    • Understand how visual elements create meaning

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

    Word Knowledge
    • Understand learning area vocabulary

    Critical and Creative Thinking

    Analysing, synthesising and evaluating reasoning and procedures
    • Apply logic and reasoning

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

    Reflecting on thinking and processes
    • Transfer knowledge into new contexts

    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091 - Scootle )
Numeracy

Using spatial reasoning
  • Visualise 2D shapes and 3D objects

Information and Communication Technology (ICT) Capability

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

  • using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art
    • Aboriginal and Torres Strait Islander Histories and Cultures
    • Asia and Australia’s Engagement with Asia
    Intercultural Understanding

    Recognising culture and developing respect
    • Explore and compare cultural knowledge, beliefs and practices

Geometric reasoning

Compare angles and classify them as equal to, greater than, or less than, a right angle (ACMMG089 - Scootle )
Numeracy

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

Using spatial reasoning
  • Visualise 2D shapes and 3D objects

Literacy

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

  • creating angles and comparing them to a right angle using digital technologies
    Information and Communication Technology (ICT) Capability

    Investigating with ICT
    • Select and evaluate data and information
    • Locate, generate and access data and information

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

    Numeracy

    Using spatial reasoning
    • Visualise 2D shapes and 3D objects

    Critical and Creative Thinking

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


Year 4 Achievement Standards

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify and explain strategies for finding unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.


Year 4 Work Sample Portfolios