Mathematics

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  • Foundation to Year 10 Curriculum
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Foundation Year  

Foundation Year 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 explore

Read full 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
  • fluency includes readily counting numbers in sequences, continuing patterns and comparing the lengths of objects
  • problem-solving includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer
  • reasoning includes explaining comparisons of quantities, creating patterns and explaining processes for indirect comparison of length.

Hide full description ›

The ability to problem solve and apply mathematical knowledge and understanding within real world contexts supports students to develop 21st century numeracy skills.  Applying mathematics knowledge and understanding in the Australian Curriculum Mathematics is developed through the introduction of contexts. Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring  Catholic Perspectives and Catholic Social Teachings.

When students are asked to solve problems and understand social contexts through a mathematics lens they deepen their understanding of the world, the views of others and connect more authentically with their community and society. Developing numeracy skills provides students with the processes and skills to understand and participate in their world, justify their viewpoints and critique information.

  • Application in real world context – numeracy skills
  • Bring CONTEXT to the curriculum
  • Social context – connecting with real world

The Australian curriculum mathematical content descriptions can be taught through social contexts that connect learners to apply mathematics in order to understand their world and bring about social change.  From a Catholic perspective, contexts can be developed by teachers at different year levels depending on the relevant learning development and knowledge of students.

From the Australian Curriculum Mathematics, an understanding and application of data and statistics can be enhanced through the introduction of contexts that support a Catholic perspective.   For instance, data and statistics can be used to inform our judgement and justify how we might respond to the poor and marginalised and those in greatest need, both locally and globally.  Using data and statistics to make judgements and reason thinking strengthens students’ knowledge of their call to action, to live in the image and likeness of God.  Numeracy skills and understandings support the development of the whole learner to live with dignity with a vision for a just and fair world.

From a Catholic perspective, teachers are required to teach students the mathematical knowledge and skills that support their development as numerate learners and users who can bring a critical lens to real world contexts.  Teachers have an obligation to support students to apply their numeracy knowledge and skills in social contexts both locally and globally to enhance student capacity to improve their social and economic well-being for human flourishing.  Schools and teachers provide equitable access and opportunity for all students to learn mathematics relevant to their year level.  

Foundation Year Content Descriptions

Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring Catholic Perspectives.

In selecting authentic and relevant social contexts students move most appropriately from personal to local to global contexts.

In P-2 students can apply their numeracy knowledge to understand their place in the world, their environment, shapes and images and patterns created by nature.  Students notice and wonder at the sacramental moments of beauty and awe of the world and their environment.  They apply their numeracy knowledge to describe their understandings and reflect on their experiences.

Number and Algebra
Number and place value

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting


Connectnames, numerals and quantities, including zero, initially up to 10 and then beyond


Subitise small collections of objects


Compare, order and make correspondences between collections, initially to 20, and explain reasoning


Represent practical situations to model addition and sharing

Patterns and algebra

Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings

Measurement and Geometry
Using units of measurement

Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language


Compare and order duration of events using everyday language of time


Connect days of the week to familiar events and actions

Shape

Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment

Location and transformation

Describe position and movement

Statistics and Probability
Data representation and interpretation

Answer yes/no questions to collect information and make simple inferences

Show subject-specific achievement standard

Foundation Year Achievement Standard

By the end of the Foundation year, students make connections between number names, numerals and quantities up to 10. They compare objects using mass, length and capacity. Students connect events and the days of the week. They explain the order and duration of events. They use appropriate language to describe location.

Students count to and from 20 and order small collections. They group objects based on common characteristics and sort shapes and objects. Students answer simple questions to collect information and make simple inferences.

Show sub-strand-specific achievement standard

Foundation Year Work Sample Portfolios

 

Year 1  

Year 1 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 explore

Read full 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.

Hide full description ›

The ability to problem solve and apply mathematical knowledge and understanding within real world contexts supports students to develop 21st century numeracy skills.  Applying mathematics knowledge and understanding in the Australian Curriculum Mathematics is developed through the introduction of contexts. Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring  Catholic Perspectives and Catholic Social Teachings.

When students are asked to solve problems and understand social contexts through a mathematics lens they deepen their understanding of the world, the views of others and connect more authentically with their community and society. Developing numeracy skills provides students with the processes and skills to understand and participate in their world, justify their viewpoints and critique information.

  • Application in real world context – numeracy skills
  • Bring CONTEXT to the curriculum
  • Social context – connecting with real world

The Australian curriculum mathematical content descriptions can be taught through social contexts that connect learners to apply mathematics in order to understand their world and bring about social change.  From a Catholic perspective, contexts can be developed by teachers at different year levels depending on the relevant learning development and knowledge of students.

From the Australian Curriculum Mathematics, an understanding and application of data and statistics can be enhanced through the introduction of contexts that support a Catholic perspective.   For instance, data and statistics can be used to inform our judgement and justify how we might respond to the poor and marginalised and those in greatest need, both locally and globally.  Using data and statistics to make judgements and reason thinking strengthens students’ knowledge of their call to action, to live in the image and likeness of God.  Numeracy skills and understandings support the development of the whole learner to live with dignity with a vision for a just and fair world.

From a Catholic perspective, teachers are required to teach students the mathematical knowledge and skills that support their development as numerate learners and users who can bring a critical lens to real world contexts.  Teachers have an obligation to support students to apply their numeracy knowledge and skills in social contexts both locally and globally to enhance student capacity to improve their social and economic well-being for human flourishing.  Schools and teachers provide equitable access and opportunity for all students to learn mathematics relevant to their year level.  

Year 1 Content Descriptions

Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring Catholic Perspectives.

In selecting authentic and relevant social contexts students move most appropriately from personal to local to global contexts.

In P-2 students can apply their numeracy knowledge to understand their place in the world, their environment, shapes and images and patterns created by nature.  Students notice and wonder at the sacramental moments of beauty and awe of the world and their environment.  They apply their numeracy knowledge to describe their understandings and reflect on their experiences.

Number and Algebra
Number and place value

Develop confidence withsequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero


Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a


Count collections to 100 bynumbers using


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

Fractions and decimals

Recognise and describe one-half as one of two equal parts of a whole.

Money and financial mathematics

Recognise, describe and order Australian coins according to their value

Patterns and algebra

Investigate and describepatterns formed by skip-counting and patterns with objects

Measurement and Geometry
Using units of measurement

Measure and compare the lengths and capacities of pairs of objects using uniform informal units


Tell time to the half-hour


Describe duration using months, weeks, days and hours

Shape

Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features

Location and transformation

Give and follow directions to familiar locations

Statistics and Probability
Chance

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

Data representation and interpretation

Choose simple questions and gather responses and make simple inferences


Representwith objects and drawings where one object or drawing represents onevalue. Describe the displays

Show subject-specific achievement standard

Year 1 Achievement Standard

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.

Show sub-strand-specific achievement standard

Year 1 Work Sample Portfolios

 

Year 2  

Year 2 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 explore

Read full 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.

Hide full description ›

The ability to problem solve and apply mathematical knowledge and understanding within real world contexts supports students to develop 21st century numeracy skills.  Applying mathematics knowledge and understanding in the Australian Curriculum Mathematics is developed through the introduction of contexts. Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring  Catholic Perspectives and Catholic Social Teachings.

When students are asked to solve problems and understand social contexts through a mathematics lens they deepen their understanding of the world, the views of others and connect more authentically with their community and society. Developing numeracy skills provides students with the processes and skills to understand and participate in their world, justify their viewpoints and critique information.

  • Application in real world context – numeracy skills
  • Bring CONTEXT to the curriculum
  • Social context – connecting with real world

The Australian curriculum mathematical content descriptions can be taught through social contexts that connect learners to apply mathematics in order to understand their world and bring about social change.  From a Catholic perspective, contexts can be developed by teachers at different year levels depending on the relevant learning development and knowledge of students.

From the Australian Curriculum Mathematics, an understanding and application of data and statistics can be enhanced through the introduction of contexts that support a Catholic perspective.   For instance, data and statistics can be used to inform our judgement and justify how we might respond to the poor and marginalised and those in greatest need, both locally and globally.  Using data and statistics to make judgements and reason thinking strengthens students’ knowledge of their call to action, to live in the image and likeness of God.  Numeracy skills and understandings support the development of the whole learner to live with dignity with a vision for a just and fair world.

From a Catholic perspective, teachers are required to teach students the mathematical knowledge and skills that support their development as numerate learners and users who can bring a critical lens to real world contexts.  Teachers have an obligation to support students to apply their numeracy knowledge and skills in social contexts both locally and globally to enhance student capacity to improve their social and economic well-being for human flourishing.  Schools and teachers provide equitable access and opportunity for all students to learn mathematics relevant to their year level.  

Year 2 Content Descriptions

Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring Catholic Perspectives.

In selecting authentic and relevant social contexts students move most appropriately from personal to local to global contexts.

In P-2 students can apply their numeracy knowledge to understand their place in the world, their environment, shapes and images and patterns created by nature.  Students notice and wonder at the sacramental moments of beauty and awe of the world and their environment.  They apply their numeracy knowledge to describe their understandings and reflect on their experiences.

Number and Algebra
Number and place value

Investigatesequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences


Recognise, model, represent and order numbers to at least 1000


Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting


Explore the connection between addition and subtraction


Solve simple addition and subtraction problems using a range of efficient mental and written strategies


Recognise and represent multiplication as repeated addition, groups and arrays


Recognise and represent division as grouping into equal sets and solve simple problems using these representations

Fractions and decimals

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

Money and financial mathematics

Count and order small collections of Australian coins and notes according to their value

Patterns and algebra

Describe patterns with numbers and identify missing elements


Solve problems by usingsentences for addition or subtraction

Measurement and Geometry
Using units of measurement

Compare and order several shapes and objects based on length, area,andusing appropriate uniform informal units


Compare masses of objects using balance scales


Tell time to the quarter-hour, using the language of 'past' and 'to'


Name and order months and seasons


Use a calendar to identify the date and determine theof days in each month

Shape

Describe and draw two-dimensional shapes, with and without digital technologies


Describe the features of three-dimensional objects

Location and transformation

Interpret simple maps of familiar locations and identify the relative positions of key features


Investigate the effect of one-step slides and flips with and without digital technologies


Identify and describe half and quarter turns

Statistics and Probability
Chance

Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’

Data representation and interpretation

Identify a question of interest based on one categorical variable. Gatherrelevant to the question


Collect, check and classify


Create displays ofusing lists, table andand interpret them

Show subject-specific achievement standard

Year 2 Achievement Standard

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.

Show sub-strand-specific achievement standard

Year 2 Work Sample Portfolios

 

Year 3  

Year 3 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 explore

Read full 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.

Hide full description ›

The ability to problem solve and apply mathematical knowledge and understanding within real world contexts supports students to develop 21st century numeracy skills.  Applying mathematics knowledge and understanding in the Australian Curriculum Mathematics is developed through the introduction of contexts. Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring  Catholic Perspectives and Catholic Social Teachings.

When students are asked to solve problems and understand social contexts through a mathematics lens they deepen their understanding of the world, the views of others and connect more authentically with their community and society. Developing numeracy skills provides students with the processes and skills to understand and participate in their world, justify their viewpoints and critique information.

  • Application in real world context – numeracy skills
  • Bring CONTEXT to the curriculum
  • Social context – connecting with real world

The Australian curriculum mathematical content descriptions can be taught through social contexts that connect learners to apply mathematics in order to understand their world and bring about social change.  From a Catholic perspective, contexts can be developed by teachers at different year levels depending on the relevant learning development and knowledge of students.

From the Australian Curriculum Mathematics, an understanding and application of data and statistics can be enhanced through the introduction of contexts that support a Catholic perspective.   For instance, data and statistics can be used to inform our judgement and justify how we might respond to the poor and marginalised and those in greatest need, both locally and globally.  Using data and statistics to make judgements and reason thinking strengthens students’ knowledge of their call to action, to live in the image and likeness of God.  Numeracy skills and understandings support the development of the whole learner to live with dignity with a vision for a just and fair world.

From a Catholic perspective, teachers are required to teach students the mathematical knowledge and skills that support their development as numerate learners and users who can bring a critical lens to real world contexts.  Teachers have an obligation to support students to apply their numeracy knowledge and skills in social contexts both locally and globally to enhance student capacity to improve their social and economic well-being for human flourishing.  Schools and teachers provide equitable access and opportunity for all students to learn mathematics relevant to their year level.  

Year 3 Content Descriptions

Authentic contexts can also be located in other areas of the curriculum by connecting the mathematical content to be applied across the curriculum. Numeracy is the application of mathematical knowledge and skills in real world contexts. The general capability of numeracy provides a pathway for exploring Catholic Perspectives.

In selecting authentic and relevant social contexts students move most appropriately from personal to local to global contexts.

In 3-6 students can apply their numeracy knowledge and skills to explore social issues within their local community and make connections to global needs.  Students can collect and analyse their own data to understand to make a difference in their school or local contexts. 

Number and Algebra
Number and place value

Investigate the conditions required for ato be odd or even and identify odd and even numbers


Recognise, model, represent and order numbers to at least 10 000


Applyto partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems


Recognise and explain the connection between addition and subtraction


Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation


Recall multiplication facts of two, three, five and ten and related division facts


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

Fractions and decimals

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole

Money and financial mathematics

Represent money values inways and count the change required for simple transactions to the nearest five cents

Patterns and algebra

Describe, continue, and createpatterns resulting from performing addition or subtraction

Measurement and Geometry
Using units of measurement

Measure, order and compare objects using familiar metric units of length, mass and


Tell time to the minute and investigate the relationship between units of time

Shape

Make models of three-dimensional objects and describe key features

Location and transformation

Create and interpret simple grid maps to show position and pathways


Identify symmetry in the environment

Geometric reasoning

Identify angles as measures of turn and comparesizes in everyday situations

Statistics and Probability
Chance

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results

Data representation and interpretation

Identify questions or issues for categorical variables. Identifysources and plan methods ofcollection and recording