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Understand this general capability – Numeracy

Introduction

What is numeracy?

 

Numeracy is fundamental to a student’s ability to learn at school and to engage productively in society. It involves the recognition, formulation and interpretation of mathematics, and its application to real-world problems and contexts.

 

Through the Australian Curriculum, students become numerate as they develop the knowledge and skills to use mathematics confidently across learning areas at school and in their lives more broadly.

 

What is the Numeracy general capability?

 

The Version 9.0 Australian Curriculum: Numeracy general capability is presented as a Numeracy learning progression. It describes the observable indicators of increasing complexity in students’ understanding of, and skills in, key numeracy concepts. The Numeracy learning progression includes the elements of Number sense and algebra, Measurement and geometry, and Statistics and probability.

 

The Numeracy learning progression gives a comprehensive and fine-grained description of key elements of numeracy development. It is a conceptual tool that can help teachers to develop targeted teaching and learning programs for students who are working at, above or below the year-level expectation.

 

The Numeracy learning progression complements the Australian Curriculum: Mathematics. It is designed to help teachers ascertain the stage of learning reached, identify any gaps in skills and knowledge, and plan for the next step to progress learning.

 

How can you use the Numeracy learning progression?

 

Numeracy development influences student success in many areas of learning at school. Applying mathematical skills and knowledge across the curriculum can enrich the study of other learning areas and helps to develop a broader and deeper understanding of numeracy. It is essential that the mathematical ideas with which students interact are relevant to their lives. Students need opportunities to recognise that mathematics is constantly used outside the mathematics classroom and that numerate people apply mathematical skills in a wide range of familiar and unfamiliar situations.

 

The Numeracy learning progression can be used to support students to successfully engage with the numeracy demands of the Foundation to Year 10 Australian Curriculum. Students may demonstrate different rates of progress as they develop specific elements of numeracy and may therefore need support to engage in the Australian Curriculum.

 

Teachers can use the progression to support the development of targeted teaching and learning programs and to set clear learning goals for individual students. For example, teaching decisions can be based on judgements about student capability that relate to a single indicator rather than all indicators at a level.

Structure
Elements and sub-elements
 

The Numeracy general capability is organised into 3 elements as shown in Figure 1:

  • Number sense and algebra
  • Measurement and geometry
  • Statistics and probability.
 
Figure 1: Numeracy learning progression elements

Each element includes sub-elements that represent evidence-based aspects of numeracy development.

 

The sub-elements are organised into progression levels. The number of levels in each sub-element varies, and is determined by available research and evidence. For example, the Number and place value sub-element (Number sense and algebra) has 10 levels, while the Positioning and locating sub-element (Measurement and geometry) has 5 levels. This means that students may enter and exit levels over quite different time frames.

 

Some sub-elements represent constrained skills, which are those that can be learned in a limited amount of time. Once they are achieved, they require no further teaching. These are Counting processes, Additive strategies and Interpreting fractions. Some students may require a longer period of time to achieve these skills. The other sub-elements represent unconstrained skills, which continue to develop.

 

Numeracy and the Australian Curriculum: Mathematics 

 

The content descriptions and achievement standards of the Mathematics curriculum F–10 are the reference points for the teaching and learning of all aspects of Mathematics F–10. The numeracy expectation of the Mathematics curriculum at each year level has been aligned to the Numeracy learning progression. The alignment is to a sub-element level of the progression and so it is likely that only some of the indicators will relate to a particular content description. This alignment of numeracy expectation has also been used to ensure a similar expectation applies across the other learning areas.

 

The sections that follow use a series of diagrams to explain the Numeracy sub-elements, the levels of the NLP and their relationship to the Australian Curriculum: Mathematics. For more information, see Appendix 1: Numeracy learning progression and Appendix 2: Planning for teaching Mathematics.

 

Number sense and algebra 

 

The Number sense and algebra element includes 8 sub-elements.

 

These sub-elements are:

  • Number and place value
  • Counting processes
  • Additive strategies
  • Multiplicative strategies
  • Interpreting fractions
  • Proportional thinking
  • Number patterns and algebraic thinking
  • Understanding money.

This sub-element describes how students become increasingly able to recognise, read, represent, order and interpret numbers within our place value number system, expressed in different ways. It outlines key understandings needed to process, communicate and interpret quantitative information in a variety of contexts.

This sub-element describes how students become increasingly able to count both verbally, through the stable order of a counting sequence, and perceptually through counting collections. As students make the link between counting “how many” and the quantities represented by numbers, they begin to understand cardinality and the purpose of counting.

This sub-element describes how students become increasingly able to think additively, represent a wide range of additive situations, and choose and use computational strategies for different purposes. The ability to understand the nature of change to a quantity, where numbers are treated as the sum of their parts, is essential to becoming a fluent user of number.

This sub-element describes how students become increasingly able to think multiplicatively and use multiplicative strategies in computation to solve problems related to a range of multiplicative situations. Students are introduced to division through equal sharing and equal grouping situations.

This sub-element emphasises the development of fraction sense, which is foundational to learning how to reason proportionally. Students become increasingly able to recognise the part-whole description of a fraction. They also recognise and use fractions as numbers, measures, operators, ratios and as a division.

This sub-element addresses the proportional relationships between quantities. The ability to reason proportionally requires students to think multiplicatively and work with percentages, rates and ratios, and proportions.

This sub-element describes how students become increasingly able to identify and describe repeating and growing patterns in the environment and other everyday contexts. Students develop the capacity to generalise as they learn to recognise, represent, describe and use patterns for prediction and decision-making.

This sub-element addresses the financial numeracy skills that support students to become financially literate members of society. Financial decisions require the capacity to carry out calculations with money and apply their knowledge to purchasing, budgeting and justification for the use of money.

Figure 2 represents the alignment of the Number sense and algebra sub-elements with the Australian Curriculum: Mathematics Years F–2 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

 

Note: *The sub-element of Interpreting fractions does not apply to the Foundation and Year 1 curriculum. The sub-element Proportional thinking does not apply to the Foundation, Year 1 or Year 2 curriculum.

Figure 2: Number sense and algebra F–2

 

Figures 3a and 3b represent the alignment of the Number sense and algebra sub-elements with the Australian Curriculum: Mathematics Years 3–6 levels. There are often multiple Numeracy progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

 

Note: *The sub-element of Proportional thinking does not apply to the Year 3 or Year 4 curriculum.

Figure 3a: Number sense and algebra Years 3–5
Figure 3b: Number sense and algebra Year 6

 

Figures 4a and 4b represent the alignment of the Number sense and algebra sub-elements with the Australian Curriculum: Mathematics Years 7–10 levels. There are often multiple Numeracy progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

 

Note: *The sub-element levels for Counting processes, Additive strategies and Interpreting fractions do not apply to the curriculum beyond Year 7, Year 8 and Year 9 respectively.

Figure 4a: Number sense and algebra Year 7
Figure 4b: Number sense and algebra Years 8–10
 
Measurement and geometry
 

The Measurement and geometry element includes 4 sub-elements.

 

These sub-elements are:

  • Understanding units of measurement
  • Understanding geometric properties
  • Positioning and locating
  • Measuring time.

 

Understanding units of measurement

 

This sub-element describes how students become increasingly able to identify attributes that can be measured and the units by which they are measured. They initially use direct comparison to recognise and understand what it means to have more or less of a particular attribute. Then they progress to using informal units, and then metric and other formal units.

 

Understanding geometric properties

 

This sub-element describes how students become increasingly able to identify the properties of shapes and objects, and how they can be combined or transformed. They develop an understanding of how objects are represented using a combination of shapes. Knowledge of angle properties and line and rotational symmetry helps students to recognise how shapes are used to create patterns.

 

Positioning and locating

 

This sub-element describes how students become increasingly able to recognise the attributes of position and location. They learn to use positional language to describe themselves and objects in the environment using maps, plans and coordinates. Students learn to reason with representations of shapes and objects regarding position and location. They learn to visualise and orientate objects to solve problems in spatial contexts.

 

Measuring time

 

This sub-element describes how students become increasingly aware of reading and describing the passage of time and how elapsed time or duration can be measured. They learn to apply units and conventions associated with measuring and recording the sequencing and duration of time.

 

Figure 5 represents the alignment of the Measurement and geometry sub-elements with the Australian Curriculum: Mathematics Years F–2 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

Figure 5: Measurement and geometry F–2

 

Figure 6 represents the alignment of the Measurement and geometry sub-elements with the Australian Curriculum: Mathematics Years 3–6 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

Figure 6: Measurement and geometry Years 3–6

 

Figure 7 represents the alignment of the Measurement and geometry sub-elements with the Australian Curriculum: Mathematics Years 7–10 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

Figure 7: Measurement and geometry Years 7–10
 
Statistics and probability
 

The Statistics and probability element includes 2 sub-elements.

 

These sub-elements are:

  • Understanding chance
  • Interpreting and representing data.

 

Understanding chance

 

This sub-element describes how students become increasingly able to use the language of chance and the numerical values of probabilities when determining the likelihood of an event. They learn to compare chance events in relation to variation and expectation. Students recognise that events may or may not happen and describe familiar events that involve chance. They progress to describe outcomes of chance experiments, develop an understanding of randomness and recognise bias. Students make predictions and explain why expected results may differ from the actual results of chance events.

 

Interpreting and representing data

 

This sub-element describes how students become increasingly able to recognise, use and interpret visual and numerical displays to describe data associated with statistical investigations. They also develop the ability to critically evaluate investigations by others. Students learn to employ the sequence of steps involved in a statistical investigation: posing questions, collecting and analysing data, and drawing conclusions.

 

Figure 8 represents the alignment of the Statistics and probability sub-elements with the Australian Curriculum: Mathematics Years F–2 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

 

Note: *The sub-element of Understanding chance does not apply to the F–2 curriculum.

Figure 8: Statistics and probability F–2

 

Figure 9 represents the alignment of the Statistics and probability sub-elements with the Australian Curriculum: Mathematics Years 3–6 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

Figure 9: Statistics and probability Years 3–6

 

Figure 10 represents the alignment of the Statistics and probability sub-elements with the Australian Curriculum: Mathematics Years 7–10 levels. There are often multiple Numeracy learning progression levels within a Mathematics curriculum year level. The progression levels may span across year levels of the curriculum. The number of progression levels is determined by the research evidence and is not the same for each sub-element.

Figure 10: Statistics and probability Years 7–10
Key connections

General capabilities support and deepen student engagement with learning area content and are best developed within the context of the learning area.

In English, students use numeracy skills to communicate, read and evaluate information that includes quantities, statistics and patterns. They use numeracy skills to understand and present evidence and substantiate ideas. They determine, examine and comment on any possible bias that is present in numerical data and quantitative sources. 

In Humanities and Social Sciences, students develop the numeracy capability as they apply numeracy skills in relation to historical, geographical, civic, economic and business inquiries. Students count and measure data and information, construct and interpret tables and graphs, and calculate and interpret statistics in their investigations. Students learn to use scaled timelines, including those involving negative and positive numbers, as well as calendars and dates, to recall information on topics of historical significance and to illustrate the passing of time. They collect data through methods such as surveys and field tests. They construct and interpret maps, models, diagrams, and remotely sensed and satellite images, working with numerical concepts of grids, scale, distance, area and projections.  

 

Students learn to analyse numerical data to make meaning of the past, to test relationships in patterns and between variables, such as the effects of location and distance, and to draw conclusions. They make predictions and forecast outcomes based on civic, economic and business data, and environmental and historical information, and represent their findings in numerical and graphical form. Students use numeracy to understand the principles of financial management, and to make informed consumer, financial, and business decisions. They appreciate the ways numeracy knowledge and skills are used in society, and apply these to hypothetical and/or real-life experiences.

As students engage with learning experiences in Health and Physical Education, they select and apply relevant numeracy knowledge and skills. Students use calculation, estimation and measurement to collect and interpret information related to nutrition, fitness, navigation or skill performances. They use spatial reasoning in movement activities and in developing concepts and strategies for individual and team sports or recreational pursuits. Students interpret and analyse health and physical activity information using statistical reasoning. They identify patterns and relationships in data to consider trends, draw conclusions, make predictions and inform health behaviour and practices.  

Languages develops students’ numeracy capability as they communicate in real or simulated real-life situations. Students use numbers in the target language to share information (time, directions, etc.)  and understand how these might be represented in diverse languages and cultures. They use aspects of measurement in the language of transaction when using money, and units of measurement in the number, volume and weight of items. Students use number patterns and algebraic thinking when they recognise and apply the patterns of grammatical and syntactical rules to respond to and create text. 

Mathematics has a more fundamental role in the development of numeracy compared to other learning areas. The Mathematics curriculum provides opportunities to apply mathematical understanding and skills in other learning areas and to real-world contexts. Financial mathematics, health and well-being are important contexts for the application of number, algebra, measurement and probability. In measurement and space, there is also an opportunity to apply understanding to design and construction. Today’s world is information driven; through statistics and probability, students can interpret and critically analyse data, and make informed judgements about events involving uncertainty.

Students use and develop numeracy through investigation of Science understanding concepts and application of Science inquiry practices. The key ideas of science which underpin Science understanding and Science as a human endeavour are closely linked to Numeracy through their focus on scale and measurement, and patterns, order and organisation. 

 

Through inquiry practices, students develop numeracy through a focus on measurement and data collection. They identify patterns in data and use mathematical relationships to represent those patterns. They represent observed and secondary data using tables, displays and visualisations and interpret data to construct evidence-based conclusions and arguments. In later years, they engage in statistical analysis of data and consider issues of validity and reliability of data. 

Students develop the capacity to interpret and use mathematical knowledge and skills in a range of real-life situations. They use number to calculate, measure and estimate; interpret and draw conclusions from statistics; measure and record throughout the process of generating and iterating ideas; develop, refine and test concepts; and cost and sequence when making products and managing projects. In using software, materials, tools and equipment, students work with the concepts of number, geometry, scale, proportion, measurement and volume. They use 3-dimensional models, create accurate technical drawings, work with digital models and use computational thinking in decision-making processes when designing and creating bestfit solutions.

In The Arts, students select and use relevant numeracy knowledge and skills to plan, design, make, interpret, analyse and evaluate arts works. Across The Arts subjects, students recognise and use: number to calculate and estimate; spatial reasoning to solve problems involving space, patterns, symmetry, 2D shapes and 3D objects; scale and proportion to show and describe positions, pathways and movements; and measurement to explore length, area, volume, capacity, time, mass and angles. Students work with a range of numerical concepts to organise, analyse and create representations of data such as diagrams, charts, tables, graphs and motion capture, relevant to their own or others’ arts works.

Downloads

General capabilities documents and glossaries are available on the downloads page.

General capability downloads