# Mathematics

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### Rationale

Learning mathematics creates opportunities for and enriches the lives of all Australians. The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in number and algebra, measurement and geometry, and statistics and probability.

### Aims

The Australian Curriculum: Mathematics aims to ensure that students:

are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens.

### Key ideas

In Mathematics, the key ideas are the proficiency strands of understanding, fluency, problem-solving and reasoning. The proficiency strands describe the actions in which students can engage when learning and using the content.

### Structure

The Australian Curriculum: Mathematics is organised around the interaction of three content strands and four proficiency strands.
The content strands are number and algebra, measurement and geometry, and statistics and probability. They describe what is to be taught and learnt.

### PDF documents

Resources and support materials for the Australian Curriculum: Mathematics are available as PDF documents.
Mathematics: Sequence of content
Mathematics: Sequence of achievement

## Year 2

### Year 2 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 calculations with counting sequences, partitioning and combining numbers flexibly and identifying and describing the relationship between addition and subtraction and between multiplication and division
• fluency includes readily counting numbers in sequences, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time durations
• problem-solving includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape
• reasoning includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models of operations and creating and interpreting simple representations of data.

### Year 2 Content Descriptions

#### Number and place value

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026 - Scootle )
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

• developing fluency and confidence with numbers and calculations by saying number sequences
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
• Estimate and calculate
• Understand and use numbers in context

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

• recognising patterns in number sequences, such as adding 10 always results in the same final digit
Critical and Creative Thinking

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

Numeracy

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

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

Recognise, model, represent and order numbers to at least 1000 (ACMNA027 - 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
• Interpret and analyse learning area texts

Word Knowledge
• Understand learning area vocabulary

Numeracy

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

• recognising there are different ways of representing numbers and identifying patterns going beyond 100
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

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

• developing fluency with writing numbers in meaningful contexts
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

Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028 - Scootle )
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

• using an abacus to model and represent numbers
Numeracy

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

• understanding three-digit numbers as comprised of hundreds, tens and ones/units
Numeracy

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

• demonstrating and using models such as linking blocks, sticks in bundles, place-value blocks and Aboriginal bead strings and explaining reasoning
Intercultural Understanding

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

Literacy

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

Composing texts through speaking, writing and creating
• Use language to interact with others
• 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

Explore the connection between addition and subtraction (ACMNA029 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• becoming fluent with partitioning numbers to understand the connection between addition and subtraction
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 counting on to identify the missing element in an additive problem
Numeracy

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

Literacy

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

Word Knowledge
• Understand learning area vocabulary

Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030 - Scootle )
Critical and Creative Thinking

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

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

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

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

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

• becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10
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

• modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines
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

Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• representing array problems with available materials and explaining reasoning
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
• Use language to interact with others

Grammar knowledge
• Use knowledge of sentence structures

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Critical and Creative Thinking

Reflecting on thinking and processes
• Think about thinking (metacognition)

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

• visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups
Numeracy

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

Estimating and calculating with whole numbers
• Estimate and calculate

Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032 - 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
• Reflect on processes

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

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

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

Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

• dividing the class or a collection of objects into equal-sized groups
Numeracy

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

• identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three
Numeracy

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

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

#### Fractions and decimals

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033 - 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

• recognising that sets of objects can be partitioned in different ways to demonstrate fractions
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
• Identify and clarify information and ideas
• Organise and process information

• relating the number of parts to the size of a fraction
Numeracy

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

#### Money and financial mathematics

Count and order small collections of Australian coins and notes according to their value (ACMNA034 - Scootle )
Numeracy

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

• identifying equivalent values in collections of coins or notes, such as two five-cent coins having the same value as one 10-cent coin
Critical and Creative Thinking

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

Numeracy

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

• counting collections of coins or notes to make up a particular value, such as that shown on a price tag
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
• Use money
• Understand and use numbers in context

#### Patterns and algebra

Describe patterns with numbers and identify missing elements (ACMNA035 - Scootle )
Numeracy

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

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

Critical and Creative Thinking

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

• describing a pattern created by skip counting and representing the pattern on a number line
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

Critical and Creative Thinking

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

Numeracy

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

• investigating features of number patterns resulting from adding twos, fives or 10s
Critical and Creative Thinking

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

Numeracy

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

Solve problems by using number sentences for addition or subtraction (ACMNA036 - 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 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

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

• representing a word problem as a number sentence
Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

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

• writing a word problem to represent a number sentence
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

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

### Year 2 Achievement Standards

By the end of Year 2, students recognise increasing and decreasing number sequences involving 2s, 3s and 5s. They represent multiplication and division by grouping into sets. They associate collections of Australian coins with their value. Students identify the missing element in a number sequence. Students recognise the features of three-dimensional objects. They interpret simple maps of familiar locations. They explain the effects of one-step transformations. Students make sense of collected information.

Students count to and from 1000. They perform simple addition and subtraction calculations using a range of strategies. They divide collections and shapes into halves, quarters and eighths. Students order shapes and objects using informal units. They tell time to the quarter-hour and use a calendar to identify the date and the months included in seasons. They draw two-dimensional shapes. They describe outcomes for everyday events. Students collect, organise and represent data to make simple inferences.