Scope of Study

VCE Vocational Major Numeracy focuses on enabling students to develop and enhance their numeracy skills to make sense of their personal, public and vocational lives. Students develop mathematical skills with consideration of their local, national and global environments and contexts,

and an awareness and use of appropriate technologies.

This study allows students to explore the underpinning mathematical knowledge of number and quantity, measurement, shape, dimensions and directions, data and chance, the understanding and use of systems and processes, and mathematical relationships and thinking. This mathematical knowledge is then applied to tasks which are part of the students’ daily routines and practices, but also extends to applications outside the immediate personal environment, such as the workplace and community.

Numeracy empowers students to use mathematics to make sense of the world and apply mathematics in a context for a social purpose. Numeracy gives meaning to mathematics, where mathematics is the tool (knowledge and skills) to be applied efficiently and critically. Numeracy

involves the use and application of a range of mathematical skills and knowledge that arise in a range of different contexts and situations.

Numeracy enables students to develop logical thinking and reasoning strategies in their everyday activities. It develops students’ problem-solving skills, and allows them to make sense of numbers, time, patterns and shapes for everyday activities like cooking, gardening, sport and travel. Through the applied learning principles Numeracy students will understand the mathematical requirements for personal organisation matters involving money, time and travel. They can then apply these skills to their everyday lives to recognise monetary value, understand scheduling and timetabling, direction, planning, monetary risk and reward.

Applied Learning

VM Numeracy is based on an applied learning approach to teaching, ensuring students feel empowered to make informed choices about the next stage of their lives through experiential learning and authentic learning experiences.

Applied learning incorporates the teaching of skills and knowledge in the context of ‘real life’ experiences. Students will apply what they have learnt by doing, experiencing and relating acquired skills to the real world. Applied learning teaching and practice ensures that what is learnt in the classroom is connected to scenarios and experiences outside the classroom and makes that connection as immediate and transparent as possible.

The applied learning approach of this study is intended to meet the needs of students with a wide range of abilities and aspirations.

Aims

This study enables students to:

• develop and enhance their numeracy practices to help them make sense of their personal, public and vocational lives

• develop mathematical skills with consideration of their local, national and global environments and contexts, and an awareness and use of appropriate technologies.

In Unit 1 students will develop their numeracy practices to make sense of their personal, public and vocational lives. They will develop mathematical skills with consideration of their local, community, national and global environments and contexts, and an awareness and use of appropriate technologies.

These units provide students with the fundamental mathematical knowledge, skills, understandings and dispositions to solve problems in real contexts for a range of workplace, personal, further learning and community settings relevant to contemporary society.

There are four areas of study for Unit 1:

• Area of Study 1: Number

• Area of Study 2: Shape

• Area of Study 3: Quantity and measures

• Area of Study 4: Relationships.

The areas of study cover a range of different mathematical knowledge and skills that are expected to be used and applied across the three outcomes.

Outcome 1

On completion of this unit, the student should be able to select, interpret and use the mathematical key knowledge and key skills from the four Areas of Study 1-4, embedded in familiar, routine and some less familiar contexts across the chosen range of numeracies.

Outcome 1 is framed by six different numeracies over two units.

• Personal numeracy relates to the mathematical requirements for personal organisational matters involving numbers, data, money, time and travel.

• Civic numeracy relates to participating in civic life through knowing how to stay informed, and understanding government, political and social data, information and processes.

• Financial numeracy relates to understanding and undertaking financial transactions and making informed judgments and decisions regarding the use and management of money.

• Health numeracy relates to accessing, understanding and using mathematical information to make decisions and act in the interests of personal and community health and well-being.

• Vocational numeracy relates to effectively participating in the workplace and managing the demands of work and/or vocational training.

• Recreational numeracy relates to the mathematical aspects of recreational activities including but not limited to arts, sport and social media.

Each unit will cover three of the numeracies.

Area of Study 1: Number

In this area of study students will develop number sense through meaningful application of numeracy practices to a range of contexts where whole numbers, fractions, decimals and percentages are used. Students will select the appropriate method or approach required and communicate their ideas. They should be at ease with performing straightforward calculations both mentally, manually and using

software tools and devices.

Area of Study 2: Shape

In this area of study students will learn to recognise, describe and name common two- and three-dimensional shapes. They will classify, manipulate, represent and construct common and familiar shapes in diagrammatical and concrete forms. They will also become familiar with common characteristics and properties used in classifying shapes.

Area of Study 3: Quantity and measures

In this area of study students will develop an understanding of routine and familiar metric quantities and their units of measurement applied to single- and multi-step measurement tasks. They will conduct estimations of measurements, undertake routine measurements, perform measurement calculations, and convert units within the metric system with the embedded use of different technologies.

Area of Study 4: Relationships

In this area of study students will recognise, understand and represent simple patterns of relationship and change in mathematical terms where it exists in common and familiar contexts and applications. They should be able to recognise when change is occurring, be able to identify common and simple mathematical relationships and variables, and apply the most appropriate process or processes to determine the results of change.

Outcome 2

On completion of this unit, the student should be able to select, interpret and use the four stages of the mathematical problem-solving cycle, using a range of both informal and formal mathematical processes, representations, and conventions relevant to the mathematical key knowledge and key skills specified in the Areas of Study 1-4, and across the chosen range of numeracies.

The purpose of Outcome 2 is to enable students to develop their everyday numeracy skills and practices in order to make sense of their daily personal, civic and vocational lives. Students need to develop the skills and capabilities to be able to problem-solve, and to use their skills to investigate and solve a problem where the mathematics is embedded within a real-world context.

This is achieved through completion of the problem-solving cycle. The problem-solving cycle underpinning the curriculum has four distinct components that include, in order:

• Identify the mathematics: recognise, select and interpret the mathematical information embedded in a real-world context and decide what mathematics to use.

• Act on and use mathematics: perform mathematical actions and processes in order to complete a task – this includes the use and application of a range of technologies.

• Evaluate and reflect: check and reflect on the mathematical problem-solving processes and outcomes in relation to the real-world context.

• Communicate and report: use a combination of informal and formal mathematical representations to document and report outcomes and results

Outcome 3

On completion of this unit, the student should be able to select and effectively and accurately use the appropriate mathematical tools and applications chosen from a developing mathematical toolkit relevant to the key knowledge and key skills specified in the Areas of Study 1-4, and across the chosen range of numeracies.

The purpose of Outcome 3 is for students to develop a mathematical toolkit to use where necessary as they undertake their numeracy practices, activities and tasks. At the end of Units 1 and 2, students should be developing their skills of both analogue and digital technologies with the ability to identify and use a range of appropriate mathematical tools (analogue and digital/technological) to solve and communicate mathematical problems embedded in practical contexts. A student’s toolkit should include:

• existing, traditional tools such as measuring equipment (e.g. tape measures, rulers, kitchen scales);

• software applications such as spreadsheets; and

• a range of new and emerging devices and applications from across different technologies (e.g. measurement, angle and level apps available on mobile phones or portable handheld devices).

Assessment Tasks

Assessment tasks will provide opportunities for practical application of the outcome. The structure of the Numeracy study is such that the

demonstration of achievement of Outcomes 1, 2 and 3 will be based on the student’s performance on a selection of the following assessment tasks:

• Investigations and projects.
  - For example, a diary (‘week in the life of me’), outlining budgets (pay rates and tax), travel (how do I get places), shopping (best deals).

• Multimedia presentation, poster or report.
  - For example, an outline of food requirements for an athlete preparing for their sport that includes nutrition, recipes, calories required and exerted, energy requirements, and measurements including distances.

• Portfolio.
  - For example, students may prepare job interview questions and responses to include details on scheduling an appointment, planning what resources are needed for transforming a house to renewables using data and tables, and understanding cost calculations, or unpacking statistics related to climate change.

In Unit 2 students will develop and extend their numeracy practices to make sense of their personal, public and vocational lives. They will develop mathematical skills with consideration of their local, community, national and global environments and contexts, and identification and appropriate selection and use of relevant technologies.

These units provide students with the fundamental mathematical knowledge, skills, understandings and dispositions to solve problems in real contexts for a range of workplace, personal, further learning and community settings relevant to contemporary society.

There are four areas of study for Unit 1:

• Area of Study 5: Dimension and direction

• Area of Study 6: Data

• Area of Study 7: Uncertainty

• Area of Study 8: Systematics

The areas of study cover a range of different mathematical knowledge and skills that are expected to be used and applied across the three outcomes.

Outcome 1

On completion of this unit, the student should be able to select, interpret and use the mathematical key knowledge and key skills from the four Areas of Study 5-8, embedded in familiar, routine and some less familiar contexts across the chosen range of numeracies.

Outcome 1 is framed by six different numeracies over two units.

• Personal numeracy relates to the mathematical requirements for personal organisational matters involving numbers, data, money, time and travel.

• Civic numeracy relates to participating in civic life through knowing how to stay informed, and understanding government, political and social data, information and processes.

• Financial numeracy relates to understanding and undertaking financial transactions and making informed judgments and decisions regarding the use and management of money.

• Health numeracy relates to accessing, understanding and using mathematical information to make decisions and act in the interests of personal and community health and well-being.

• Vocational numeracy relates to effectively participating in the workplace and managing the demands of work and/or vocational training.

• Recreational numeracy relates to the mathematical aspects of recreational activities including but not limited to arts, sport and social media.

Each unit will cover three of the numeracies.

Area of Study 5: Dimension and direction

In this area of study students will develop an understanding of space, direction and location in relation to common landmarks and key compass directions. They will give and follow directions to locations based on digital and printed maps and diagrams. The study of dimension also includes common and routine angles with degrees and an awareness of the one-, two- and three-dimensions of space.

Area of Study 6: Data

Data can be found in everyday life, workplaces and society. In this area of study, students will collect, represent and undertake common analyses of data to look for patterns in data and derive meaning from data sets located within familiar and routine contexts. Data should be examined for comparison and analysis. Students should draw conclusions from the data and be confident in describing general patterns and trends.

Area of Study 7: Uncertainty

In this area of study students will explore the basic concepts and everyday language of chance. They will make mathematical predictions about the likelihood of common and familiar events occurring or not occurring. They will also consider conclusions from familiar known events or data and make very simple inferences.

Area of Study 8: Systematics

In this area of study students will understand the inputs and outputs of technology that can be used in everyday lives for the purposes of planning, collecting, sorting or categorising common and familiar quantitative or mathematical data and information. Students will choose a number of inputs of familiar data, compare the outputs and results, and understand the representations and any summary information derived

from the technology.

Outcome 2

On completion of this unit, the student should be able to select, interpret and use the four stages of the mathematical problem-solving cycle, using a range of both informal and formal mathematical processes, representations, and conventions relevant to the mathematical key knowledge and key skills specified in Areas of Study 5-8, and across the chosen range of numeracies.

This is achieved through completion of the problem-solving cycle. The problem-solving cycle underpinning the curriculum has four distinct components that include, in order:

• Identify the mathematics: recognise, select and interpret the mathematical information embedded in a real-world context and decide what mathematics to use.

• Act on and use mathematics: perform mathematical actions and processes in order to complete a task – this includes the use and application of a range of technologies.

• Evaluate and reflect: check and reflect on the mathematical problem-solving processes and outcomes in relation to the real-world context.

• Communicate and report: use a combination of informal and formal mathematical representations to document and report outcomes and results

Outcome 3

On completion of this unit, the student should be able to select and effectively and accurately use the appropriate mathematical tools and applications chosen from a developing mathematical toolkit relevant to the key knowledge and key skills specified in the Areas of Study 5-8, and across the chosen range of numeracies.

The purpose of Outcome 3 is for students to develop a mathematical toolkit to use where required as they undertake their numeracy practices, activities and tasks. At the end of Units 3 and 4, students should be productive, informed and efficient users of both analogue and digital technologies with the ability to select and effectively use a wide range of appropriate mathematical tools (analogue and digital/technological) to solve and communicate mathematical problems embedded in practical contexts. A student’s toolkit should include:

• existing, traditional tools such as measuring equipment (e.g. tape measures, rulers, kitchen scales);

• software applications such as spreadsheets; and

• a range of new and emerging devices and applications from across different technologies (e.g. measurement, angle and level apps available on mobile phones or portable handheld devices).

Assessment Tasks

Assessment tasks will provide opportunities for practical application of the outcome. The structure of the Numeracy study is such that the

demonstration of achievement of Outcomes 1, 2 and 3 will be based on the student’s performance on a selection of the following assessment tasks:

• Investigations and projects.
  - For example, a diary (‘week in the life of me’), outlining budgets (pay rates and tax), travel (how do I get places), shopping (best deals).

• Multimedia presentation, poster or report.
  - For example, an outline of food requirements for an athlete preparing for their sport that includes nutrition, recipes, calories required and exerted, energy requirements, and measurements including distances.

• Portfolio.
  - For example, students may prepare job interview questions and responses to include details on scheduling an appointment, planning what resources are needed for transforming a house to renewables using data and tables, and understanding cost calculations, or unpacking statistics related to climate change.

In Unit 3 students further develop and enhance their numeracy practices to make sense of their personal, public and vocational lives. Students extend their mathematical skills with consideration of their local, community, national and global environments and contexts, and the use and evaluation of appropriate technologies.

These units provide students with a broad range of mathematical knowledge, skills and understanding to solve problems in real contexts for a range of workplace, personal, further learning and community settings relevant to contemporary society.

The progression of learning is evident in Units 3 and 4 with the development of more complex numeracy and mathematical skills and knowledge, drawing on the knowledge gained from Units 1 and 2.

Outcome 1

On completion of this unit, the student should be able to extract, evaluate and apply the mathematical key knowledge and key skills from the four Areas of Study 1-4, embedded in a range of routine, non-routine, unfamiliar and some specialised contexts across the chosen range of numeracies.

Outcome 1 is framed by six different numeracies over two units.

• Personal numeracy relates to the mathematical requirements for personal organisational matters involving numbers, data, money, time and travel.

• Civic numeracy relates to participating in civic life through knowing how to stay informed, and understanding government, political and social data, information and processes.

• Financial numeracy relates to understanding and undertaking financial transactions and making informed judgments and decisions regarding the use and management of money.

• Health numeracy relates to accessing, understanding and using mathematical information to make decisions and act in the interests of personal and community health and well-being.

• Vocational numeracy relates to effectively participating in the workplace and managing the demands of work and/or vocational training.

• Recreational numeracy relates to the mathematical aspects of recreational activities including but not limited to arts, sport and social media.

Each unit will cover three of the numeracies.

Area of Study 1: Number

In this area of study students undertake single- and multi-step operations and tasks applied to a range of numbers, including positive and negative numbers, fractions, decimals and percentages and numbers expressed using familiar power notations. Students should be confident in selecting the appropriate method or approach required and communicating their ideas. They should be at ease with performing calculations

both manually and using software tools and devices.

Area of Study 2: Shape

In this area of study students learn to recognise and name a range of two-dimensional shapes and three-dimensional objects. They classify, manipulate, represent and construct a range of simple and compound shapes in diagrammatical and concrete forms. Students also become familiar with the different characteristics and properties used in classifying shapes.

Area of Study 3: Quantity and measures

In this area of study students develop an understanding of metric measurements and their units of measurement applied to multi-step measurement tasks including working with commonly used non-metric measurements and their units of measure. Students will conduct estimations of measurements, perform a range of measurement calculations, and undertake conversions with the embedded use of different

technologies.

Area of Study 4: Relationships

In this area of study students recognise, understand and represent relationship and change in more formal mathematical terms, where it exists in relevant real-life contexts and applications. Students should understand when change is occurring and be able to identify and use formal mathematical relationships, variables, and mathematical processes to determine the results of change.

Outcome 2

On completion of this unit, the student should be able to select, evaluate and apply the four stages of the mathematical problem-solving cycle, using an expanding range of both informal and formal mathematical processes, representations, and conventions relevant to the mathematical key knowledge and key skills specified in the Areas of Study 1-4, and across the chosen range of numeracies.

This is achieved through completion of the problem-solving cycle. The problem-solving cycle underpinning the curriculum has four distinct components that include, in order:

• Identify the mathematics: recognise, select and interpret the mathematical information embedded in a real-world context and decide what mathematics to use.

• Act on and use mathematics: perform mathematical actions and processes in order to complete a task – this includes the use and application of a range of technologies.

• Evaluate and reflect: check and reflect on the mathematical problem-solving processes and outcomes in relation to the real-world context.

• Communicate and report: use a combination of informal and formal mathematical representations to document and report outcomes and results

Outcome 3

On completion of this unit, the student should be able to flexibly, effectively and accurately use a range of appropriate tools and applications chosen from an extensive mathematical toolkit relevant to the key knowledge and key skills specified in the Areas of Study 1-4, and across the chosen range of numeracies.

The purpose of Outcome 3 is for students to apply and use an extensive mathematical toolkit to use where required as they undertake their numeracy practices, activities and tasks. At the end of Units 3 and 4, students should be productive, informed and efficient users of both analogue and digital technologies with the ability to select and effectively use a wide range of appropriate mathematical tools (analogue and digital/technological) to solve and communicate mathematical problems embedded in practical contexts. A student’s toolkit should include:

• existing, traditional tools such as measuring equipment (e.g. tape measures, rulers, kitchen scales);

• software applications such as spreadsheets; and

• a range of new and emerging devices and applications from across different technologies (e.g. measurement, angle and level apps available on mobile phones or portable handheld devices).

Assessment Tasks

Assessment tasks will provide opportunities for practical application of the outcome. The structure of the Numeracy study is such that the

demonstration of achievement of Outcomes 1, 2 and 3 will be based on the student’s performance on a selection of the following assessment tasks:

• Investigations and projects.
  - For example, students may undertake the costings of a project, including budgeting, invoices, receipts and money handling, or consider loans or mortgages including interest and repayments for buying a car or a house.

• Multimedia presentation, poster or report.
  - For example, students may consider the materials needed for painting a house, including measurement, cost and labour.

• Portfolio.
  - For example, students may plan design and run an event for the community, taking into consideration factors such as budgeting, measuring, time and travel.

In Unit 4 students further develop, enhance and extend their numeracy practices to make sense of their personal, public and vocational lives. Students extend their mathematical skills with consideration of their local, community, national and global environments and contexts, and use of, evaluation and justification of appropriate technologies.

These units provide students with a broad range of mathematical knowledge, skills and understanding to solve problems in real contexts for a range of workplace, personal, further learning and community settings relevant to contemporary society.

The progression of learning is evident in Units 3 and 4 with the development of more complex numeracy and mathematical skills and knowledge, drawing on the knowledge gained from Units 1 and 2.

Outcome 1

On completion of this unit, the student should be able to extract, evaluate and apply the mathematical key knowledge and key skills from the four Areas of Study 5-8, embedded in a range of routine, non-routine, unfamiliar and some specialised contexts across the chosen range of numeracies.

Outcome 1 is framed by six different numeracies over two units.

• Personal numeracy relates to the mathematical requirements for personal organisational matters involving numbers, data, money, time and travel.

• Civic numeracy relates to participating in civic life through knowing how to stay informed, and understanding government, political and social data, information and processes.

• Financial numeracy relates to understanding and undertaking financial transactions and making informed judgments and decisions regarding the use and management of money.

• Health numeracy relates to accessing, understanding and using mathematical information to make decisions and act in the interests of personal and community health and well-being.

• Vocational numeracy relates to effectively participating in the workplace and managing the demands of work and/or vocational training.

• Recreational numeracy relates to the mathematical aspects of recreational activities including but not limited to arts, sport and social media.

Each unit will cover three of the numeracies.

Area of Study 5: Dimension and direction

In this area of study students develop an understanding of the use of space, direction and location in relation to landmarks and compass directions. Students should be able to accurately give and follow complex directions to multiple locations based on digital and printed maps and diagrams. The study of dimension also includes angles with degrees and spatial awareness.

Area of Study 6: Data

Data can be found in everyday life, workplaces and society. In this area of study, students collect, represent and undertake different analyses of data to discover patterns in data, undertake summary statistics, and derive meaning from data located within relevant but possibly unfamiliar or non-routine contexts. Data should be examined for comparison and analysis. Students should draw conclusions from the data and their analysis and be confident to represent, describe and reflect on any patterns, outcomes and trends.

Area of Study 7: Uncertainty

In this area of study students use concepts of randomness, chance and probability. Students should be able to make mathematical predictions about the likelihood of events occurring or not occurring. They should be able to consider and make conclusions about likelihood based on the data and make straightforward inferences. Students should be familiar with the concept of risk and apply the idea of uncertainty to risk.

Area of Study 8: Systematics

In this area of study students develop an understanding of inputs and outputs of technology, including emerging technologies, that can be used for the purposes of planning, collecting, sorting or categorising a range of quantitative or mathematical data and information. Students should be confident in choosing multiple inputs of data, compare the outputs and results, and analyse, review and make decisions and conclusions based on the representations and any summary information derived from the technology.

Outcome 2

On completion of this unit, the student should be able to select, evaluate and apply the four stages of the mathematical problem-solving cycle, using an expanding range of both informal and formal mathematical processes, representations, and conventions relevant to the mathematical key knowledge and key skills specified in the Areas of Study 1-4, and across the chosen range of numeracies.

This is achieved through completion of the problem-solving cycle. The problem-solving cycle underpinning the curriculum has four distinct components that include, in order:

• Identify the mathematics: recognise, select and interpret the mathematical information embedded in a real-world context and decide what mathematics to use.

• Act on and use mathematics: perform mathematical actions and processes in order to complete a task – this includes the use and application of a range of technologies.

• Evaluate and reflect: check and reflect on the mathematical problem-solving processes and outcomes in relation to the real-world context.

• Communicate and report: use a combination of informal and formal mathematical representations to document and report outcomes and results

Outcome 3

On completion of this unit, the student should be able to flexibly, effectively and accurately use a range of appropriate tools and applications chosen from an extensive mathematical toolkit relevant to the key knowledge and key skills specified in the Areas of Study 5-8, and across the chosen range of numeracies.

The purpose of Outcome 3 is for students to apply and use an extensive mathematical toolkit to use where required as they undertake their numeracy practices, activities and tasks. At the end of Units 3 and 4, students should be productive, informed and efficient users of both analogue and digital technologies with the ability to select and effectively use a wide range of appropriate mathematical tools (analogue and digital/technological) to solve and communicate mathematical problems embedded in practical contexts. A student’s toolkit should include:

• existing, traditional tools such as measuring equipment (e.g. tape measures, rulers, kitchen scales);

• software applications such as spreadsheets; and

• a range of new and emerging devices and applications from across different technologies (e.g. measurement, angle and level apps available on mobile phones or portable handheld devices).

Assessment Tasks

Assessment tasks will provide opportunities for practical application of the outcome. The structure of the Numeracy study is such that the

demonstration of achievement of Outcomes 1, 2 and 3 will be based on the student’s performance on a selection of the following assessment tasks:

• Investigations and projects.
  - For example, students may undertake the costings of a project, including budgeting, invoices, receipts and money handling, or consider loans or mortgages including interest and repayments for buying a car or a house.

• Multimedia presentation, poster or report.
  - For example, students may consider the materials needed for painting a house, including measurement, cost and labour.

• Portfolio.
  - For example, students may plan design and run an event for the community, taking into consideration factors such as budgeting, measuring, time and travel.

For more information about the VCE Vocational Major, see Adrian Panckhurst