Mathematics

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Understand how Mathematics works

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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Foundation Year

Foundation Year 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 names, numerals and quantities
  • fluency includes readily counting numbers in sequences, continuing patterns and comparing the lengths of objects
  • problem-solving includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer
  • reasoning includes explaining comparisons of quantities, creating patterns and explaining processes for indirect comparison of length.

Foundation Year Content Descriptions

Measurement and Geometry

Using units of measurement

Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006 - Scootle )
Literacy

Word Knowledge
  • Understand learning area vocabulary

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

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

Critical and Creative Thinking

Analysing, synthesising and evaluating reasoning and procedures
  • Apply logic and reasoning
  • Draw conclusions and design a course of action

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
  • Think about thinking (metacognition)

Numeracy

Using measurement
  • Estimate and measure with metric units

  • comparing objects directly, by placing one object against another to determine which is longer or by pouring from one container into the other to see which one holds more
    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

  • using suitable language associated with measurement attributes, such as ‘tall’ and ‘taller’, ‘heavy’ and ‘heavier’, ‘holds more’ and ‘holds less’
    Literacy

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

    Word Knowledge
    • Understand learning area vocabulary

    Numeracy

    Using measurement
    • Estimate and measure with metric units

Compare and order duration of events using everyday language of time (ACMMG007 - Scootle )
Literacy

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

Numeracy

Using measurement
  • Operate with clocks, calendars and timetables

  • knowing and identifying the days of the week and linking specific days to familiar events
    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

  • sequencing familiar events in time order
    Critical and Creative Thinking

    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

    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

Connect days of the week to familiar events and actions (ACMMG008 - Scootle )
Numeracy

Using measurement
  • Operate with clocks, calendars and timetables

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

  • choosing events and actions that make connections with students’ everyday family routines
    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

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

    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

Shape

Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment (ACMMG009 - 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 spoken, written, visual and multimodal learning area texts
  • Compose texts

Word Knowledge
  • Understand learning area vocabulary

Numeracy

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

  • sorting and describing squares, circles, triangles, rectangles, spheres and cubes
    Literacy

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

    Word Knowledge
    • Understand learning area vocabulary

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

    Numeracy

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

Location and transformation

Describe position and movement (ACMMG010 - Scootle )
Numeracy

Using spatial reasoning
  • Interpret maps and diagrams

Literacy

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

Word Knowledge
  • Understand learning area vocabulary

  • interpreting the everyday language of location and direction, such as ‘between’, ‘near’, ‘next to’, ‘forward’, ‘toward’
    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

    Literacy

    Word Knowledge
    • Understand learning area vocabulary

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

  • following and giving simple directions to guide a friend around an obstacle path and vice versa
    Literacy

    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
    • Interpret maps and diagrams

Foundation Year Achievement Standards

Achievement Standard

By the end of the Foundation year, students make connections between number names, numerals and quantities up to 10. They compare objects using mass, length and capacity. Students connect events and the days of the week. They explain the order and duration of events. They use appropriate language to describe location.

Students count to and from 20 and order small collections. They group objects based on common characteristics and sort shapes and objects. Students answer simple questions to collect information and make simple inferences.

Foundation Year Work Sample Portfolios