# 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.

### 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.

### 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.

### 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.

### PDF documents

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

## 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

#### Number and place value

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting point (ACMNA001 - Scootle )
Literacy

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

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

• reading stories from other cultures featuring counting in sequence to assist students to recognise ways of counting in local languages and across cultures
Literacy

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

Intercultural Understanding

Interacting and empathising with others
• Communicate across cultures

• identifying the number words in sequence, backwards and forwards, and reasoning with the number sequences, establishing the language on which subsequent counting experiences can be built
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

Literacy

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

• developing fluency with forwards and backwards counting in meaningful contexts, including stories and rhymes
Numeracy

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

Literacy

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

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

• understanding that numbers are said in a particular order and there are patterns in the way we say them
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

Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002 - Scootle )
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

Numeracy

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

• understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the ‘how many’ question
Numeracy

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

• using scenarios to help students recognise that other cultures count in a variety of ways, such as the Wotjoballum number systems
Numeracy

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

Intercultural Understanding

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

Critical and Creative Thinking

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

Subitise small collections of objects (ACMNA003 - Scootle )
Numeracy

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

• using subitising as the basis for ordering and comparing collections of numbers
Numeracy

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

Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289 - Scootle )
Critical and Creative Thinking

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

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

Numeracy

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

Literacy

Word Knowledge
• Understand learning area vocabulary

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

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

• comparing and ordering items of like and unlike characteristics using the words ‘more’, ‘less’, ‘same as’ and ‘not the same as’ and giving reasons for these answers
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
• Use language to interact with others
• Compose spoken, written, visual and multimodal learning area texts

Grammar knowledge
• Use knowledge of words and word groups

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

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

• understanding and using terms such as ‘first’ and ‘second’ to indicate ordinal position in a sequence.
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

Text knowledge
• Use knowledge of text structures

Word Knowledge
• Understand learning area vocabulary

• using objects which are personally and culturally relevant to students
Intercultural Understanding

Recognising culture and developing respect
• Investigate culture and cultural identity

Represent practical situations to model addition and sharing (ACMNA004 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• using a range of practical strategies for adding small groups of numbers, such as visual displays or concrete materials
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• using Aboriginal and Torres Strait Islander methods of adding, including spatial patterns and reasoning
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

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

Intercultural Understanding

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

#### Patterns and algebra

Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005 - 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
• Consider alternatives

Literacy

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

Visual Knowledge
• Understand how visual elements create meaning

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

Numeracy

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

• observing natural patterns in the world around us
Numeracy

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

• creating and describing patterns using materials, sounds, movements or drawings
Critical and Creative Thinking

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

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
• Use language to interact with others
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

Visual Knowledge
• Understand how visual elements create meaning

Numeracy

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

#### 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

#### Data representation and interpretation

Answer yes/no questions to collect information and make simple inferences (ACMSP011 - Scootle )
Numeracy

Interpreting statistical information
• Interpret data displays

• posing questions about themselves and familiar objects and events
Literacy

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
• Pose questions

• representing responses to questions using simple displays, including grouping students according to their answers
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret data displays

• using data displays to answer simple questions such as ‘how many students answered “yes” to having brown hair?’
Literacy

Comprehending texts through listening, reading and viewing
• 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
• Use language to interact with others

Numeracy

Interpreting statistical information
• Interpret data displays

### Foundation Year Achievement Standards

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.