# 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

## 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

#### Chance

Describe probabilities using fractions, decimals and percentages (ACMSP144 - Scootle )
Numeracy

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

Interpreting statistical information
• Interpret chance events

Literacy

Word Knowledge
• Understand learning area vocabulary

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

• investigating games of chance popular in different cultures and evaluating the relative benefits to the organisers and participants (for example Pachinko)
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

Intercultural Understanding

Reflecting on intercultural experiences and taking responsibility
• Reflect on intercultural experiences

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

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145 - Scootle )
Numeracy

Interpreting statistical information
• Interpret chance events

Information and Communication Technology (ICT) Capability

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

• conducting repeated trials of chance experiments, identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret chance events

Compare observed frequencies across experiments with expected frequencies (ACMSP146 - Scootle )
Critical and Creative Thinking

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

Literacy

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

Numeracy

Interpreting statistical information
• Interpret chance events

• predicting likely outcomes from a run of chance events and distinguishing these from surprising results
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
• Seek solutions and put ideas into action

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

Interpreting statistical information
• Interpret chance events

#### Data representation and interpretation

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147 - 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

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

Visual Knowledge
• Understand how visual elements create meaning

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

Numeracy

Interpreting statistical information
• Interpret data displays

• comparing different student-generated diagrams, tables and graphs, describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret data displays

• understanding that data can be represented in different ways, sometimes with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements

Numeracy

Interpreting statistical information
• Interpret data displays

Critical and Creative Thinking

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

Interpret secondary data presented in digital media and elsewhere (ACMSP148 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

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

Numeracy

Interpreting statistical information
• Interpret data displays

Information and Communication Technology (ICT) Capability

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

• investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
Literacy

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

Visual Knowledge
• Understand how visual elements create meaning

Word Knowledge
• Understand learning area vocabulary

Numeracy

Interpreting statistical information
• Interpret data displays

Critical and Creative Thinking

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

Ethical Understanding

Reasoning in decision making and actions
• Reason and make ethical decisions
• Consider consequences

• identifying potentially misleading data representations in the media, such as graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made, and pie charts in which the whole pie does not represent the entire population about which the claims are made
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

Ethical Understanding

Reasoning in decision making and actions
• Consider consequences
• Reason and make ethical decisions

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

Numeracy

Interpreting statistical information
• Interpret data displays

### 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.