# 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 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

#### 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

#### Chance

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116 - Scootle )
Numeracy

Interpreting statistical information
• Interpret chance events

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

• commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (rock-paper-scissors)
Literacy

Word Knowledge
• Understand learning area vocabulary

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

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

Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

Numeracy

Interpreting statistical information
• Interpret chance events

Recognise that probabilities range from 0 to 1 (ACMSP117 - Scootle )
Numeracy

Interpreting statistical information
• Interpret chance events

• investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1
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 chance events

#### Data representation and interpretation

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118 - Scootle )
Literacy

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

Grammar knowledge
• Use knowledge of sentence structures

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
• Pose questions

• posing questions about insect diversity in the playground, collecting data by taping a one-metre-square piece of paper to the playground and observing the type and number of insects on it over time
Numeracy

Interpreting statistical information
• Interpret data displays

Critical and Creative Thinking

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

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119 - Scootle )
Literacy

Visual Knowledge
• Understand how visual elements create meaning

Word Knowledge
• Understand learning area vocabulary

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

Numeracy

Interpreting statistical information
• Interpret data displays

Information and Communication Technology (ICT) Capability

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

• identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
Literacy

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

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

Reflecting on thinking and processes
• Reflect on processes

Numeracy

Interpreting statistical information
• Interpret data displays

Describe and interpret different data sets in context (ACMSP120 - 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

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

• using and comparing data representations for different data sets to help decision making
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

Reflecting on thinking and processes
• Reflect on processes

Literacy

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

Visual Knowledge
• Understand how visual elements create meaning

Personal and Social Capability

Social management
• Make decisions

Numeracy

Interpreting statistical information
• Interpret data displays

### 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.

## 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

#### Number and place value

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122 - 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 texts
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

Numeracy

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

• understanding that some numbers have special properties and that these properties can be used to solve problems
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
• Understand and use numbers in context

• representing composite numbers as a product of their prime factors and using this form to simplify calculations by cancelling common primes
Information and Communication Technology (ICT) Capability

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

Numeracy

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

• understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number (for example 216 is divisible by 8 because the number represented by the last three digits is divisible by 8, and hence 216 is also divisible by 2 and 4)
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
• Understand and use numbers in context

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123 - Scootle )
Literacy

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

Information and Communication Technology (ICT) Capability

Creating with ICT
• Generate solutions to challenges and learning area tasks
• Generate ideas, plans and processes

Numeracy

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

Critical and Creative Thinking

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

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

• applying strategies already developed for solving problems involving small numbers to those involving large numbers
Numeracy

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

Critical and Creative Thinking

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

• applying a range of strategies to solve realistic problems and commenting on the efficiency of different strategies
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
• Identify and clarify information and ideas
• Organise and process information

Reflecting on thinking and processes
• Reflect on processes

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

Numeracy

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

Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124 - Scootle )
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

• understanding that integers are ...-3, -2, -1, 0, 1, 2, 3,.....
Critical and Creative Thinking

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

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

Numeracy

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

• solving everyday additive problems using a number line
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

• investigating everyday situations that use integers, such as temperatures
Numeracy

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

Critical and Creative Thinking

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

• using number lines to position and order integers around zero
Numeracy

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

#### Fractions and decimals

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125 - Scootle )
Numeracy

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

• demonstrating equivalence between fractions using drawings and models
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
• Interpret proportional reasoning
• Apply proportional reasoning

Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126 - Scootle )
Critical and Creative Thinking

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

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

Numeracy

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

• understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Critical and Creative Thinking

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

• solving realistic additive (addition and subtraction) problems involving fractions to develop understanding of equivalent fractions and the use of fractions as operators
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
• Identify and clarify information and ideas
• Organise and process information

Numeracy

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

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

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

Numeracy

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

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127 - Scootle )
Numeracy

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

Information and Communication Technology (ICT) Capability

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

• recognising that finding one third of a quantity is the same as dividing by 3
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
• Organise and process information
• Identify and clarify information and ideas

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128 - Scootle )
Numeracy

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

Information and Communication Technology (ICT) Capability

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

• extending whole-number strategies to explore and develop meaningful written strategies for addition and subtraction of decimal numbers to thousandths
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
• Interpret proportional reasoning
• Apply proportional reasoning

Literacy

Word Knowledge
• Understand learning area vocabulary

Comprehending texts through listening, reading and viewing
• 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

• exploring and practising efficient methods for solving problems requiring operations on decimals, to gain fluency with calculating with decimals and with recognising appropriate operations
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
• Interpret and analyse learning area texts
• Navigate, read and view 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

Numeracy

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

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129 - Scootle )
Information and Communication Technology (ICT) Capability

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

Numeracy

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

• interpreting the results of calculations to provide an answer appropriate to the context
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Critical and Creative Thinking

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

Multiply and divide decimals by powers of 10 (ACMNA130 - Scootle )
Numeracy

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

• multiplying and dividing decimals by multiples of powers of 10
Numeracy

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

Make connections between equivalent fractions, decimals and percentages (ACMNA131 - Scootle )
Numeracy

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

• connecting fractions, decimals and percentages as different representations of the same number, moving fluently between representations and choosing the appropriate one for the problem being solved
Numeracy

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

#### Money and financial mathematics

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132 - Scootle )
Literacy

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

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
• Use money

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

Information and Communication Technology (ICT) Capability

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

• using authentic information to calculate prices on sale goods
Numeracy

Estimating and calculating with whole numbers
• Use money

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

Critical and Creative Thinking

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

#### Patterns and algebra

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133 - Scootle )
Critical and Creative Thinking

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

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
• Interpret proportional reasoning

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
• 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 generalising number patterns
Critical and Creative Thinking

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

Numeracy

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

• investigating additive and multiplicative patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern looking for patterns in the way the numbers increase/decrease
Critical and Creative Thinking

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

Numeracy

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

Explore the use of brackets and order of operations to write number sentences (ACMNA134 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• appreciating the need for rules to complete multiple operations within the same number sentence
Numeracy

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

#### Using units of measurement

Connect decimal representations to the metric system (ACMMG135 - Scootle )
Numeracy

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

Using measurement
• Estimate and measure with metric units

• recognising the equivalence of measurements such as 1.25 metres and 125 centimetres
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

Convert between common metric units of length, mass and capacity (ACMMG136 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• identifying and using the correct operations when converting units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
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

• recognising the significance of the prefixes in units of measurement
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

Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137 - Scootle )
Literacy

Comprehending texts through listening, reading and viewing
• Comprehend texts
• 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
• Compose texts

Word Knowledge
• Understand learning area vocabulary

Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

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

• recognising and investigating familiar objects using concrete materials and digital technologies
Information and Communication Technology (ICT) Capability

Investigating with ICT
• Define and plan information searches
• 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

Connect volume and capacity and their units of measurement (ACMMG138 - Scootle )
Literacy

Word Knowledge
• Understand learning area vocabulary

Numeracy

Using measurement
• Estimate and measure with metric units

• recognising that 1ml is equivalent to 1cm3
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

Interpret and use timetables (ACMMG139 - Scootle )
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

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
• Operate with clocks, calendars and timetables

• planning a trip involving one or more modes of public transport
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

Personal and Social Capability

Social awareness
• Contribute to civil society

Critical and Creative Thinking

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

• developing a timetable of daily activities
Literacy

Word Knowledge
• Understand learning area vocabulary

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

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

Personal and Social Capability

Social awareness
• Contribute to civil society

Critical and Creative Thinking

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

#### Shape

Construct simple prisms and pyramids (ACMMG140 - Scootle )
Numeracy

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

• considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia
Intercultural Understanding

Interacting and empathising with others
• Consider and develop multiple perspectives

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

• constructing prisms and pyramids from nets, and skeletal models
Numeracy

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

Critical and Creative Thinking

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

#### Location and transformation

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142 - Scootle )
Numeracy

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

Information and Communication Technology (ICT) Capability

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

Critical and Creative Thinking

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

• designing a school or brand logo using transformation of one or more shapes
Critical and Creative Thinking

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

Literacy

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

• understanding that translations, rotations and reflections can change the position and orientation but not shape or size
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

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143 - Scootle )
Literacy

Visual Knowledge
• Understand how visual elements create meaning

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• understanding that the Cartesian plane provides a graphical or visual way of describing location
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

#### Geometric reasoning

Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141 - Scootle )
Numeracy

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

Information and Communication Technology (ICT) Capability

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

Critical and Creative Thinking

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

• identifying the size of a right angle as 90° and defining acute, obtuse, straight and reflex angles
Numeracy

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

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

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
• Organise and process information
• Identify and clarify information and ideas

• measuring, estimating and comparing angles in degrees and classifying angles according to their sizes
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

• investigating the use of rotation and symmetry in the diagrammatic representations of kinship relationships of Central and Western Desert people
Critical and Creative Thinking

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

Intercultural Understanding

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

• recognising and using the two alternate conventions for naming angles
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

#### 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.