# 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

#### Using units of measurement

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns
Numeracy

Using measurement
• Estimate and measure with metric units

Critical and Creative Thinking

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

• investigating alternative measures of scale to demonstrate that these vary between countries and change over time, for example temperature measurement in Australia, Indonesia, Japan and USA
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
• Organise and process information

Numeracy

Using measurement
• Estimate and measure with metric units

Calculate perimeter and area of rectangles using familiar metric units (ACMMG109 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• exploring efficient ways of calculating the perimeters of rectangles such as adding the length and width together and doubling the result
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
• Estimate and measure with metric units

• exploring efficient ways of finding the areas of rectangles
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

Compare 12- and 24-hour time systems and convert between them (ACMMG110 - Scootle )
Numeracy

Using measurement
• Operate with clocks, calendars and timetables

• investigating the ways time was and is measured in different Aboriginal Country, such as using tidal change
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
• Identify and clarify information and ideas
• Organise and process information

Numeracy

Using measurement
• Operate with clocks, calendars and timetables

• using units hours, minutes and seconds
Numeracy

Using measurement
• Operate with clocks, calendars and timetables

#### Shape

Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111 - Scootle )
Numeracy

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

• identifying the shape and relative position of each face of a solid to determine the net of the solid, including that of prisms and pyramids
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

• representing two-dimensional shapes such as photographs, sketches and images created by digital technologies
Information and Communication Technology (ICT) Capability

Investigating with ICT
• Locate, generate and access data and information

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

Numeracy

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

#### Location and transformation

Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113 - Scootle )
Literacy

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

Visual Knowledge
• Understand how visual elements create meaning

Word Knowledge
• Understand learning area vocabulary

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• comparing aerial views of Country, desert paintings and maps with grid references
Critical and Creative Thinking

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

Literacy

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

Intercultural Understanding

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

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another
Literacy

Comprehending texts through listening, reading and viewing
• 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

Visual Knowledge
• Understand how visual elements create meaning

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

Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114 - Scootle )
Numeracy

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

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 texts
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

• identifying and describing the line and rotational symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies
Information and Communication Technology (ICT) Capability

Investigating with ICT
• Locate, generate and access data and information

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

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

• identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies
Information and Communication Technology (ICT) Capability

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

Investigating with ICT
• 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

Numeracy

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

Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115 - Scootle )
Numeracy

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

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

• using digital technologies to enlarge shapes
Information and Communication Technology (ICT) Capability

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

• using a grid system to enlarge a favourite image or cartoon
Numeracy

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

#### Geometric reasoning

Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112 - Scootle )
Numeracy

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

• measuring and constructing angles using both 180° and 360° protractors
Numeracy

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

• recognising that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other
Numeracy

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

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.