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.

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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.

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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.

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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.

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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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Glossary

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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


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 4 Work Sample Portfolios