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 1

Year 1 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 names, numerals and quantities, and partitioning numbers in various ways
  • fluency includes readily counting number in sequences forwards and backwards, locating numbers on a line and naming the days of the week
  • problem-solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer
  • reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data and explaining patterns that have been created.

Year 1 Content Descriptions

Number and place value

Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012 - Scootle )
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

  • using the popular Korean counting game (sam-yuk-gu) for skip counting
    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

    Intercultural Understanding

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

  • developing fluency with forwards and backwards counting in meaningful contexts such as circle games
    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    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, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013 - Scootle )
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

Visual Knowledge
  • Understand how visual elements create meaning

Numeracy

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

  • modelling numbers with a range of material and images
    Literacy

    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

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

  • identifying numbers that are represented on a number line and placing numbers on a prepared number line
    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

    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

Count collections to 100 by partitioning numbers using place value (ACMNA014 - Scootle )
Numeracy

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

  • understanding partitioning of numbers and the importance of grouping in tens
    Numeracy

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

  • understanding two-digit numbers as comprised of tens and ones/units
    Numeracy

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

Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015 - 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

Numeracy

Estimating and calculating with whole numbers
  • Estimate and calculate

  • developing a range of mental strategies for addition and subtraction problems
    Numeracy

    Estimating and calculating with whole numbers
    • Estimate and calculate

    Critical and Creative Thinking

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

Fractions and decimals

Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016 - Scootle )
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 spoken, written, visual and multimodal learning area texts
  • Compose texts

Word Knowledge
  • Understand learning area vocabulary

Numeracy

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

  • sharing a collection of readily available materials into two equal portions
    Numeracy

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

  • splitting an object into two equal pieces and describing how the pieces are equal
    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
    • Interpret and analyse learning area texts

    Word Knowledge
    • Understand learning area vocabulary

    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

Money and financial mathematics

Recognise, describe and order Australian coins according to their value (ACMNA017 - Scootle )
Literacy

Comprehending texts through listening, reading and viewing
  • Comprehend texts
  • 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 texts
  • Compose spoken, written, visual and multimodal learning area texts

Numeracy

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

  • showing that coins are different in other countries by comparing Asian coins to Australian coins
    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

    Numeracy

    Estimating and calculating with whole numbers
    • Use money

    Intercultural Understanding

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

  • understanding that the value of Australian coins is not related to size
    Numeracy

    Estimating and calculating with whole numbers
    • Use money

  • describing the features of coins that make it possible to identify them
    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

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

    Word Knowledge
    • Understand learning area vocabulary

Patterns and algebra

Investigate and describe number patterns formed by skip-counting and patterns with objects (ACMNA018 - Scootle )
Literacy

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

Word Knowledge
  • Understand learning area vocabulary

Numeracy

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

  • using place-value patterns beyond the teens to generalise the number sequence and predict the next number
    Critical and Creative Thinking

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

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

    Numeracy

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

  • investigating patterns in the number system, such as the occurrence of a particular digit in the numbers to 100
    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

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

Using units of measurement

Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019 - Scootle )
Numeracy

Using measurement
  • Estimate and measure with metric units

  • understanding that in order to compare objects, the unit of measurement must be the same size
    Critical and Creative Thinking

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

    Numeracy

    Using measurement
    • Estimate and measure with metric units

Tell time to the half-hour (ACMMG020 - 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

Word Knowledge
  • Understand learning area vocabulary

Numeracy

Using measurement
  • Operate with clocks, calendars and timetables

  • reading time on analogue and digital clocks and observing the characteristics of half-hour times
    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

    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

Describe duration using months, weeks, days and hours (ACMMG021 - Scootle )
Literacy

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

Word Knowledge
  • Understand learning area vocabulary

Numeracy

Using measurement
  • Operate with clocks, calendars and timetables

  • describing the duration of familiar situations such as ‘how long is it until we next come to school?’
    Literacy

    Word Knowledge
    • Understand learning area vocabulary

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

    Numeracy

    Using measurement
    • Operate with clocks, calendars and timetables

Shape

Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022 - Scootle )
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

  • focusing on geometric features and describing shapes and objects using everyday words such as 'corners', 'edges' and 'faces'
    Critical and Creative Thinking

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

    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    Grammar knowledge
    • Use knowledge of words and word groups

    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

Give and follow directions to familiar locations (ACMMG023 - Scootle )
Numeracy

Using spatial reasoning
  • Interpret maps and diagrams

Literacy

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

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

Word Knowledge
  • Understand learning area vocabulary

  • understanding that people need to give and follow directions to and from a place, and that this involves turns, direction and distance
    Literacy

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

    Word Knowledge
    • Understand learning area vocabulary

    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

  • understanding the meaning and importance of words such as ‘clockwise’, ‘anticlockwise’, ‘forward’ and ‘under’ when giving and following directions
    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

    Literacy

    Word Knowledge
    • Understand learning area vocabulary

  • interpreting and following directions around familiar locations
    Literacy

    Word Knowledge
    • Understand learning area vocabulary

    Comprehending texts through listening, reading and viewing
    • Listen and respond to learning area texts
    • 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
    • Identify and clarify information and ideas

    Numeracy

    Using spatial reasoning
    • Interpret maps and diagrams

Chance

Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024 - Scootle )
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

Grammar knowledge
  • Use knowledge of words and word groups

Word Knowledge
  • Understand learning area vocabulary

Numeracy

Interpreting statistical information
  • Interpret chance events

Critical and Creative Thinking

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

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

  • justifying that some events are certain or impossible
    Critical and Creative Thinking

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

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

    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

    Numeracy

    Interpreting statistical information
    • Interpret chance events

Data representation and interpretation

Choose simple questions and gather responses and make simple inferences (ACMSP262 - Scootle )
Literacy

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

Word Knowledge
  • Understand learning area vocabulary

  • determining which questions will gather appropriate responses for a simple investigation
    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

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

Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays (ACMSP263 - 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 data displays

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

  • understanding one-to-one correspondence
    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

    Literacy

    Comprehending texts through listening, reading and viewing
    • Comprehend texts

    Word Knowledge
    • Understand learning area vocabulary

  • describing displays by identifying categories with the greatest or least number of objects
    Literacy

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

    Word Knowledge
    • Understand learning area vocabulary

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

    Critical and Creative Thinking

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

    Numeracy

    Interpreting statistical information
    • Interpret data displays


Year 1 Achievement Standards

By the end of Year 1, students describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify representations of one half. They recognise Australian coins according to their value. Students explain time durations. They describe two-dimensional shapes and three-dimensional objects. Students describe data displays.

Students count to and from 100 and locate numbers on a number line. They carry out simple additions and subtractions using counting strategies. They partition numbers using place value. They continue simple patterns involving numbers and objects. Students order objects based on lengths and capacities using informal units. They tell time to the half-hour. They use the language of direction to move from place to place. Students classify outcomes of simple familiar events. They collect data by asking questions, draw simple data displays and make simple inferences.


Year 1 Work Sample Portfolios