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 6

Year 6 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 describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations
  • fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables
  • problem-solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles
  • reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.

Year 6 Content Descriptions

Using units of measurement

Connect decimal representations to the metric system (ACMMG135 - Scootle )
Numeracy

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

Using measurement
  • Estimate and measure with metric units

  • recognising the equivalence of measurements such as 1.25 metres and 125 centimetres
    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
    • Identify and clarify information and ideas

Convert between common metric units of length, mass and capacity (ACMMG136 - Scootle )
Numeracy

Using measurement
  • Estimate and measure with metric units

  • identifying and using the correct operations when converting units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
    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
    • Estimate and measure with metric units

  • recognising the significance of the prefixes in units of measurement
    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
    • Estimate and measure with metric units

Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137 - Scootle )
Literacy

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

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

Word Knowledge
  • Understand learning area vocabulary

Critical and Creative Thinking

Reflecting on thinking and processes
  • Reflect on processes

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

Numeracy

Using measurement
  • Estimate and measure with metric units

  • recognising and investigating familiar objects using concrete materials and digital technologies
    Information and Communication Technology (ICT) Capability

    Investigating with ICT
    • Define and plan information searches
    • Locate, generate and access data and information

    Critical and Creative Thinking

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

Connect volume and capacity and their units of measurement (ACMMG138 - Scootle )
Literacy

Word Knowledge
  • Understand learning area vocabulary

Numeracy

Using measurement
  • Estimate and measure with metric units

  • recognising that 1ml is equivalent to 1cm3
    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
    • Identify and clarify information and ideas

Interpret and use timetables (ACMMG139 - Scootle )
Literacy

Word Knowledge
  • Understand learning area vocabulary

Visual Knowledge
  • Understand how visual elements create meaning

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

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

  • planning a trip involving one or more modes of public transport
    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

    Personal and Social Capability

    Social awareness
    • Contribute to civil society

    Critical and Creative Thinking

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

  • developing a timetable of daily activities
    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    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

    Personal and Social Capability

    Social awareness
    • Contribute to civil society

    Critical and Creative Thinking

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

Shape

Construct simple prisms and pyramids (ACMMG140 - Scootle )
Numeracy

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

  • considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia
    • Asia and Australia’s Engagement with Asia
    Intercultural Understanding

    Interacting and empathising with others
    • Consider and develop multiple perspectives

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

  • constructing prisms and pyramids from nets, and skeletal models
    Numeracy

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

    Critical and Creative Thinking

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

Location and transformation

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142 - 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

Critical and Creative Thinking

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

  • designing a school or brand logo using transformation of one or more shapes
    Critical and Creative Thinking

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

    Literacy

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

  • understanding that translations, rotations and reflections can change the position and orientation but not shape or size
    Critical and Creative Thinking

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

    Numeracy

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

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143 - Scootle )
Literacy

Visual Knowledge
  • Understand how visual elements create meaning

Numeracy

Using spatial reasoning
  • Interpret maps and diagrams

  • understanding that the Cartesian plane provides a graphical or visual way of describing location
    Critical and Creative Thinking

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

    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

Geometric reasoning

Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141 - 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

Critical and Creative Thinking

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

  • identifying the size of a right angle as 90° and defining acute, obtuse, straight and reflex angles
    Numeracy

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

    Literacy

    Comprehending texts through listening, reading and viewing
    • Interpret and analyse 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

    Critical and Creative Thinking

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

  • measuring, estimating and comparing angles in degrees and classifying angles according to 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 spatial reasoning
    • Visualise 2D shapes and 3D objects

  • investigating the use of rotation and symmetry in the diagrammatic representations of kinship relationships of Central and Western Desert people
    • Aboriginal and Torres Strait Islander Histories and Cultures
    Critical and Creative Thinking

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

    Intercultural Understanding

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

  • recognising and using the two alternate conventions for naming angles
    Critical and Creative Thinking

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

    Numeracy

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


Year 6 Achievement Standards

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They interpret secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students describe probabilities using simple fractions, decimals and percentages.


Year 6 Work Sample Portfolios