# 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

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## Year 3

### Year 3 Level Description

The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.

At this year level:

• understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry
• fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions
• problem-solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns
• reasoning includes using generalising from number properties and results of calculations, comparing angles and creating and interpreting variations in the results of data collections and data displays.

### Year 3 Content Descriptions

#### Number and place value

Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051 - Scootle )
Critical and Creative Thinking

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

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

Numeracy

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

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

• identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
Critical and Creative Thinking

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

Literacy

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

Numeracy

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

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

• explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
Literacy

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

Grammar knowledge
• Use knowledge of sentence structures

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
• Understand and use numbers in context

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

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052 - Scootle )
Numeracy

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

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
• Interpret and analyse learning area texts
• Comprehend texts

Word Knowledge
• Understand learning area vocabulary

• placing four-digit numbers on a number line using an appropriate scale
Literacy

Composing texts through speaking, writing and creating
• 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

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

• reproducing numbers in words using their numerical representations and vice versa
Literacy

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
• Understand and use numbers in context

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053 - Scootle )
Numeracy

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

Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

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

Reflecting on thinking and processes
• Reflect on processes

• recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones
Numeracy

Estimating and calculating with whole numbers
• 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

• justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

Literacy

Word Knowledge
• Understand learning area vocabulary

Recognise and explain the connection between addition and subtraction (ACMNA054 - Scootle )
Literacy

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

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

Reflecting on thinking and processes
• Reflect on processes

Numeracy

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

• demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences
Literacy

Word Knowledge
• Understand learning area vocabulary

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

Critical and Creative Thinking

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

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055 - Scootle )
Numeracy

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

• recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers
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
• Estimate and calculate

• combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1)
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
• Organise and process information
• Identify and clarify information and ideas

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056 - Scootle )
Numeracy

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

• establishing multiplication facts using number sequences
Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

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

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057 - 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

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

Literacy

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

Word Knowledge
• Understand learning area vocabulary

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

• writing simple word problems in numerical form and vice versa
Numeracy

Estimating and calculating with whole numbers
• 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

• using a calculator to check the solution and reasonableness of the answer
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

#### Fractions and decimals

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058 - Scootle )
Numeracy

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

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

• partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with 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 fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

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

• locating unit fractions on a number line
Numeracy

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

• recognising that in English the term ‘one third’ is used (order: numerator, denominator) but that in other languages this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator) for example Japanese
Intercultural Understanding

Recognising culture and developing respect
• Investigate culture and cultural identity

Interacting and empathising with others
• Communicate across cultures

Critical and Creative Thinking

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

#### Money and financial mathematics

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059 - Scootle )
Numeracy

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

Critical and Creative Thinking

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

• recognising the relationship between dollars and cents, and that not all countries use these denominations and divisions (for example Japanese Yen)
Intercultural Understanding

Recognising culture and developing respect
• Investigate culture and cultural identity

Critical and Creative Thinking

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

#### Patterns and algebra

Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060 - Scootle )
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

Critical and Creative Thinking

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

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

Numeracy

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

• identifying and writing the rules for number patterns
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
• Organise and process information
• Identify and clarify information and ideas

Numeracy

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

• describing a rule for a number pattern, then creating the pattern
Numeracy

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

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

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

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

Literacy

Word Knowledge
• Understand learning area vocabulary

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

• recognising the importance of using common 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

• recognising and using centimetres and metres, grams and kilograms, and millilitres and litres
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

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

Tell time to the minute and investigate the relationship between units of time (ACMMG062 - Scootle )
Literacy

Word Knowledge
• Understand learning area vocabulary

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

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

Numeracy

Using measurement
• Operate with clocks, calendars and timetables

• recognising there are 60 minutes in an hour and 60 seconds in a minute
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

#### Shape

Make models of three-dimensional objects and describe key features (ACMMG063 - Scootle )
Numeracy

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

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

• exploring the creation of three-dimensional objects using origami, including prisms and pyramids
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

Numeracy

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

#### Location and transformation

Create and interpret simple grid maps to show position and pathways (ACMMG065 - Scootle )
Critical and Creative Thinking

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

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

Literacy

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

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

Visual Knowledge
• Understand how visual elements create meaning

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• creating a map of the classroom or playground
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Critical and Creative Thinking

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

Literacy

Visual Knowledge
• Understand how visual elements create meaning

Identify symmetry in the environment (ACMMG066 - Scootle )
Numeracy

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

• identifying symmetry in Aboriginal rock carvings or art
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

Numeracy

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

• identifying symmetry in the natural and built environment
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

#### Geometric reasoning

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064 - Scootle )
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

• opening doors partially and fully and comparing the size of the angles created
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

• recognising that analogue clocks use the turning of arms to indicate time, and comparing the size of angles between the arms for familiar times
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

Using measurement
• Operate with clocks, calendars and timetables

#### Chance

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067 - Scootle )
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
• Comprehend texts
• Navigate, read and view learning area texts
• Interpret and analyse learning area texts

Numeracy

Interpreting statistical information
• Interpret chance events

Critical and Creative Thinking

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

• conducting repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials
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

Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068 - 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
• Pose questions
• Identify and clarify information and ideas

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
• Interpret and analyse learning area texts

Numeracy

Interpreting statistical information
• Interpret data displays

• refining questions and planning investigations that involve collecting data, and carrying out the investigation (for example narrowing the focus of a question such as ‘which is the most popular breakfast cereal?’ to ‘which is the most popular breakfast cereal among Year 3 students in our class?’)
Literacy

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
• Pose questions

Reflecting on thinking and processes
• Reflect on processes

Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069 - Scootle )
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
• Transfer knowledge into new contexts

Literacy

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

Word Knowledge
• Understand learning area vocabulary

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

Information and Communication Technology (ICT) Capability

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

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

Numeracy

Interpreting statistical information
• Interpret data displays

• exploring meaningful and increasingly efficient ways to record data, and representing and reporting the results of investigations
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
• Transfer knowledge into new contexts

Literacy

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

Visual Knowledge
• Understand how visual elements create meaning

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

Numeracy

Interpreting statistical information
• Interpret data displays

• collecting data to investigate features in the natural environment
Literacy

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

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

Interpret and compare data displays (ACMSP070 - Scootle )
Critical and Creative Thinking

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

Literacy

Composing texts through speaking, writing and creating
• 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
• Comprehend texts
• Interpret and analyse learning area texts

Word Knowledge
• Understand learning area vocabulary

Visual Knowledge
• Understand how visual elements create meaning

Numeracy

Interpreting statistical information
• Interpret data displays

• comparing various student-generated data representations and describing their similarities and differences
Literacy

Composing texts through speaking, writing and creating
• 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

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

### Year 3 Achievement Standards

By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single-digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They conduct simple data investigations for categorical variables.

## Year 4

### Year 4 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, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes
• fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data
• problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns
• reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.

### Year 4 Content Descriptions

#### Number and place value

Investigate and use the properties of odd and even numbers (ACMNA071 - Scootle )
Numeracy

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

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

• using the four operations with pairs of odd or even numbers or one odd and one even number, then using the relationships established to check the accuracy of calculations
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
• Understand and use numbers in context
• Estimate and calculate

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

Recognise, represent and order numbers to at least tens of thousands (ACMNA072 - Scootle )
Numeracy

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

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
• Comprehend texts

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

• reproducing five-digit numbers in words using their numerical representations, and vice versa
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

Numeracy

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

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

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
• Understand and use numbers in context
• Estimate and calculate

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

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
• Navigate, read and view learning area texts
• Comprehend texts

• recognising and demonstrating that the place-value pattern is built on the operations of multiplication or division of tens
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

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

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074 - Scootle )
Numeracy

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

• recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences
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
• Understand and use numbers in context

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

Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075 - Scootle )
Numeracy

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

• using known multiplication facts to calculate related division facts
Critical and Creative Thinking

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

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

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

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076 - Scootle )
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

Numeracy

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

Estimating and calculating with whole numbers
• Estimate and calculate

Information and Communication Technology (ICT) Capability

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

Investigating with ICT
• Select and evaluate data and information

• using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

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

#### Fractions and decimals

Investigate equivalent fractions used in contexts (ACMNA077 - 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
• Interpret and analyse learning area texts
• Comprehend texts
• Navigate, read and view learning area texts

Word Knowledge
• Understand learning area vocabulary

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

• exploring the relationship between families of fractions (halves, quarters and eighths or thirds and sixths) by folding a series of paper strips to construct a fraction wall
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
• Interpret proportional reasoning
• Apply proportional reasoning

Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078 - Scootle )
Numeracy

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

• converting mixed numbers to improper fractions and vice versa
Numeracy

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

Critical and Creative Thinking

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

• investigating the use of fractions and sharing as a way of managing Country: for example taking no more than half the eggs from a nest to protect future bird populations
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 fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079 - Scootle )
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

• using division by 10 to extend the place-value system
Numeracy

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

Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

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

• using knowledge of fractions to establish equivalences between fractions and decimal notation
Numeracy

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

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

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

#### Money and financial mathematics

Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080 - Scootle )
Literacy

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

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

Numeracy

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

Information and Communication Technology (ICT) Capability

Investigating with ICT
• Select and evaluate data and information

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

Critical and Creative Thinking

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

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

• recognising that not all countries use dollars and cents, eg India uses rupees.
Intercultural Understanding

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

• carrying out calculations in another currency as well as in dollars and cents, and identifying both as decimal systems
Numeracy

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

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

Reflecting on thinking and processes
• Transfer knowledge into new contexts

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

#### Patterns and algebra

Explore and describe number patterns resulting from performing multiplication (ACMNA081 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

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

Critical and Creative Thinking

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

• identifying examples of number patterns in everyday life
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

Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

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

Estimating and calculating with whole numbers
• Estimate and calculate

• representing a word problem as a number sentence
Numeracy

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

Literacy

Comprehending texts through listening, reading and viewing
• Interpret and analyse learning area texts
• 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
• Identify and clarify information and ideas

• writing a word problem using a given number sentence
Literacy

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

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

Numeracy

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

Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083 - Scootle )
Numeracy

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

Estimating and calculating with whole numbers
• Estimate and calculate

• writing number sentences to represent and answer questions such as: ‘When a number is added to 23 the answer is the same as 57 minus 19. What is the number?’
Critical and Creative Thinking

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

Numeracy

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

Estimating and calculating with whole numbers
• Estimate and calculate

• using partitioning to find unknown quantities in number sentences
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

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

Word Knowledge
• Understand learning area vocabulary

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

#### Using units of measurement

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• reading and interpreting the graduated scales on a range of measuring instruments to the nearest graduation
Literacy

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

Numeracy

Using measurement
• Estimate and measure with metric units

Compare objects using familiar metric units of area and volume (ACMMG290 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• comparing areas using grid paper
Numeracy

Using measurement
• Estimate and measure with metric units

Intercultural Understanding

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

• comparing volume using centicubes
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

• recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)
Critical and Creative Thinking

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

Convert between units of time (ACMMG085 - Scootle )
Numeracy

Using measurement
• Operate with clocks, calendars and timetables

• identifying and using the correct operation for converting units of time
Numeracy

Using measurement
• Operate with clocks, calendars and timetables

Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086 - 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

Using measurement
• Operate with clocks, calendars and timetables

• calculating the time spent at school during a normal school day
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

• calculating the time required to travel between two locations
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

• determining arrival time given departure time
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

#### Shape

Compare the areas of regular and irregular shapes by informal means (ACMMG087 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares
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

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes
• Transfer knowledge into new contexts

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

Literacy

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

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

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

• identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes
Numeracy

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

Critical and Creative Thinking

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

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

• creating two-dimensional shapes from verbal or written instructions

Literacy

Comprehending texts through listening, reading and viewing
• Listen and respond to 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

Numeracy

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

#### Location and transformation

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

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

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

Visual Knowledge
• Understand how visual elements create meaning

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• identifying the scale used on maps of cities and rural areas in Australia and a city in Indonesia and describing the difference
Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

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

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

Literacy

Grammar knowledge
• Use knowledge of sentence structures

Text knowledge
• Use knowledge of text structures

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

Intercultural Understanding

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

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• using directions to find features on a map
Literacy

Visual Knowledge
• Understand how visual elements create meaning

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

Word Knowledge
• Understand learning area vocabulary

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

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091 - 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

• using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art
Intercultural Understanding

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

#### Geometric reasoning

Compare angles and classify them as equal to, greater than, or less than, a right angle (ACMMG089 - Scootle )
Numeracy

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

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
• 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

• creating angles and comparing them to a right angle using digital technologies
Information and Communication Technology (ICT) Capability

Investigating with ICT
• Select and evaluate data and information
• 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

Critical and Creative Thinking

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

#### Chance

Describe possible everyday events and order their chances of occurring (ACMSP092 - Scootle )
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

Numeracy

Interpreting statistical information
• Interpret chance events

Critical and Creative Thinking

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

• using lists of events familiar to students and ordering them from ‘least likely’ to ‘most likely’ to occur
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

Interpreting statistical information
• Interpret chance events

Critical and Creative Thinking

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

Identify everyday events where one cannot happen if the other happens (ACMSP093 - Scootle )
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret chance events

• using examples such as weather, which cannot be dry and wet at the same time
Literacy

Word Knowledge
• Understand learning area vocabulary

Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094 - Scootle )
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

• explaining why the probability of a new baby being either a boy or a girl does not depend on the sex of the previous baby
Numeracy

Interpreting statistical information
• Interpret chance events

Literacy

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

Grammar knowledge
• Use knowledge of sentence structures

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

#### Data representation and interpretation

Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095 - Scootle )
Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

Interpreting statistical information
• Interpret data displays

Critical and Creative Thinking

Generating ideas, possibilities and actions
• Consider alternatives

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

• comparing the effectiveness of different methods of collecting data
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

• choosing the most effective way to collect data for a given investigation
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret data displays

Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096 - Scootle )
Literacy

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
• Comprehend texts

Visual Knowledge
• Understand how visual elements create meaning

Word Knowledge
• Understand learning area vocabulary

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
• Define and plan information searches

Numeracy

Interpreting statistical information
• Interpret data displays

• exploring ways of presenting data and showing the results of investigations
Numeracy

Interpreting statistical information
• Interpret data displays

Literacy

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

Word Knowledge
• Understand learning area vocabulary

Visual Knowledge
• Understand how visual elements create meaning

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

Critical and Creative Thinking

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

• investigating data displays using many-to-one correspondence
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

Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret data displays

Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097 - Scootle )
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

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

Numeracy

Interpreting statistical information
• Interpret data displays

• interpreting data representations in the media and other forums in which symbols represent more than one data value
Literacy

Visual Knowledge
• Understand how visual elements create meaning

Word Knowledge
• Understand learning area vocabulary

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

Interpreting statistical information
• Interpret data displays

• suggesting questions that can be answered by a given data display and using the display to answer questions
Critical and Creative Thinking

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

Literacy

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

Numeracy

Interpreting statistical information
• Interpret data displays

### Year 4 Achievement Standards

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify and explain strategies for finding unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.

## 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.