# Mathematics (Version 8.4)

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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 5

### Year 5 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, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry
• fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles
• problem-solving includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans
• reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets.

### Year 5 Content Descriptions

#### Number and place value

Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098 - 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
• Consider alternatives
• Seek solutions and put ideas into action

Reflecting on thinking and processes
• Reflect on processes

Numeracy

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

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

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

• exploring factors and multiples using number sequences
Numeracy

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

Critical and Creative Thinking

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

• using simple divisibility tests
Critical and Creative Thinking

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

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• recognising the usefulness of estimation to check calculations
Critical and Creative Thinking

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

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load
Critical and Creative Thinking

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

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100 - Scootle )
Critical and Creative Thinking

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

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

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

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

Information and Communication Technology (ICT) Capability

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

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers
Critical and Creative Thinking

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

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• applying the distributive law and using arrays to model multiplication and explain calculation strategies
Critical and Creative Thinking

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

Literacy

Grammar knowledge
• Use knowledge of sentence structures

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101 - 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
• Seek solutions and put ideas into action
• Consider alternatives

Reflecting on thinking and processes
• Reflect on processes

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

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

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• using the fact that equivalent division calculations result if both numbers are divided by the same factor
Critical and Creative Thinking

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

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

Reflecting on thinking and processes
• Reflect on processes

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• interpreting and representing the remainder in division calculations sensibly for the context
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Critical and Creative Thinking

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

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291 - 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
• Navigate, read and view learning area texts
• Comprehend texts
• Interpret and analyse 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

Estimating and calculating with whole numbers
• Estimate and calculate

• using calculators to check the reasonableness of answers
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Information and Communication Technology (ICT) Capability

Managing and operating ICT
• Select and use hardware and software

#### Fractions and decimals

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102 - Scootle )
Numeracy

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

• recognising the connection between the order of unit fractions and their denominators
Critical and Creative Thinking

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

Numeracy

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

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103 - Scootle )
Literacy

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

Critical and Creative Thinking

Analysing, synthesising and evaluating reasoning and procedures
• Evaluate procedures and outcomes

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

Numeracy

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

• modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes
Critical and Creative Thinking

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

Reflecting on thinking and processes
• Reflect on processes

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

Numeracy

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

Recognise that the place value system can be extended beyond hundredths (ACMNA104 - Scootle )
Numeracy

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

• using knowledge of place value and division by 10 to extend the number system to thousandths and beyond
Critical and Creative Thinking

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

Numeracy

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

• recognising the equivalence of one thousandths and 0.001
Numeracy

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

Critical and Creative Thinking

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

Compare, order and represent decimals (ACMNA105 - Scootle )
Numeracy

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

• locating decimals on a number line
Numeracy

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

#### Money and financial mathematics

Create simple financial plans (ACMNA106 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Use money
• Estimate and calculate

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

Critical and Creative Thinking

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

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

• creating a simple budget for a class fundraising event
Critical and Creative Thinking

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

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

Personal and Social Capability

Social awareness
• Contribute to civil society

Numeracy

Estimating and calculating with whole numbers
• Use money
• Estimate and calculate

Literacy

Word Knowledge
• Understand learning area vocabulary

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

• identifying the GST component of invoices and receipts
Literacy

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

Numeracy

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

#### Patterns and algebra

Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107 - Scootle )
Numeracy

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

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

Critical and Creative Thinking

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

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

Literacy

Comprehending texts through listening, reading and viewing
• 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

• using the number line or diagrams to create patterns involving fractions or decimals
Numeracy

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

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

Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division (ACMNA121 - Scootle )
Numeracy

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

Estimating and calculating with whole numbers
• Estimate and calculate

• using relevant problems to develop number sentences
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

Numeracy

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

Critical and Creative Thinking

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

### Year 5 Achievement Standards

By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They identify and explain strategies for finding unknown quantities in number sentences involving the four operations. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students interpret different data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12- and 24-hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.