Planning

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 that 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.

The contexts are the starting point and the focus, and are framed in terms of personal, financial, civic, health, recreational and vocational classifications. These numeracies are developed using a problem-solving cycle with four components: formulating; acting on and using mathematics; evaluating and reflecting; and communicating and reporting.

Numeracy empowers students to use mathematics to make sense of the world and apply mathematics in a context for work, citizenship, personal or 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.

Technology is an integral part of everyday and working life in Australia. Handheld devices like tablets are used for common daily uses: connectivity, communication, sourcing information, and as a tool for carrying out a myriad of functions. Software applications are available on a range of devices. There is an expectation that our students are ready with these skills when they transition to independent living, further study or to work. The integration of digital technologies in the learning of mathematical processes is essential and is embedded throughout this study.

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.

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.

Applied learning is about nurturing and working with a student in a holistic manner, taking into account their personal strengths, interests, goals and previous experiences to ensure a flexible and independent approach to learning. Applied learning emphasises skills and knowledge that may not normally be the focus of more traditional school curriculums. It also recognises individual differences in ways of learning and post-educational experiences. Real-life application often requires a shift from a traditional focus on discrete curriculum to a more integrated and contextualised approach to learning, as students learn and apply the skills and knowledge required to solve problems, implement projects or participate in the workforce.

This study design acknowledges that part of the transition from school to further education, training and employment is the ability to participate and function in society as an adult. Moving students out of the classroom to learn allows them to make the shift to become more independent and responsible for their own learning and increase their intrinsic motivation. Best practice applied learning programs are flexible and student-centred, where learning goals and outcomes are individually designed and negotiated with students.

Applied learning may also involve students and their teachers working in partnership with external organisations and individuals to access VET and integrated work placements. These partnerships provide the necessary contexts for students to demonstrate the relevance of the skills and knowledge they have acquired in their study and training.

Outcome 1: Numeracy in context outlines the six contexts under which the eight areas of study are to be taught. The teacher selects these contexts in an order that suits the learning program. These contexts are:

• personal
• civic
  
• financial
• health
• vocational
• recreational

Once the context has been determined from the six prescribed contexts, the teacher must select one or two areas of study outlining the mathematics to be taught in context.

There are four areas of study in each unit, to a total of eight areas of study over two units.

For example: Unit 1. The context chosen is vocational numeracy.

The teacher then might select the areas of study:

• Shape
• Quantity and Measures

For more details see Planning the curriculum.

In this example the teacher may decide to plan a learning program around the real-life context of building a swimming pool. This context will then be the basis for a series of projects and activities to teach the key knowledge and skills that are in the Areas of Study 4 and 5.

The teacher has selected areas of study that will fit naturally with the context to be studied. The context of building a swimming pool involves mathematics of measurement and ideas of geometry.

Using the areas of study and the context (Outcome 1), the teacher teaches these mathematical skills and knowledge using the problem-solving cycle.

In this example, the teacher introduces the concept of building a swimming pool.

The components of the cycles may be considered as follows when planning an activity or learning sequence.

Identifying the mathematics

In outlining the problem to be studied, the mathematics can be identified. The teacher may consider questions such as:

• What mathematics is required to solve this problem?
• What knowledge do we need to learn?
• What skills do we need to learn?
• How can we apply the mathematical knowledge in context?
• How can we apply these mathematical skills in context?
• What technologies can be used to solve this problem?

Act on and use the mathematics

The maths skills and knowledge that have been identified may need to be taught and practised.

The teacher may choose to introduce a series of activities to assist students to learn and practise these skills.

The teacher may also choose to select mini contexts to develop these skills; for example, the students may examine building plans, or plan a garden bed, or calculate the amount of paint required to paint a room. These projects may be hands-on.

The mathematical knowledge and skills are applied to the problem of building a swimming pool.

Evaluate and reflect

In this phase the mathematics should mirror and reflect the real-life calculations that would occur in building a swimming pool. In real life, calculations may not have clear solutions and require interpretation, adjustments and re-calculation.

Communicate and report

Explaining and communicating mathematical results is essential in industry and trade. The teacher may choose for students to present their work using the software of trade. In this example, this might take the form of plans in a PowerPoint presentation.

To extend this further, the teacher may teach the students the mathematics behind generating quotations.

A spectrum of technologies, both digital and analogue, should be used when carrying out the mathematical processes.
In Australian workplaces many different technologies are required, and students should develop adaptability to transfer their skills from one technology to another.

In the example given above, students may learn to use a variety of measurement tools, measuring tapes, measurement apps, laser measures etc. They may need to use software applications for designing and developing plans. Additionally, they might use calculation devices and present their work digitally.

When selecting technology for use in the classroom consideration may be given to:

• availability of technology
• applications (apps or software) that are free or very low cost
• real-world applicability
• relevance to the task and context.

For example: for data collection and analysis, the teacher may consider apps or software that digitally collects and collates the data.

For trade-based measurements and calculations the teacher may consider using apps or software or laser devices for measuring, and app based calculating tools for calculations.

Please note that:

• all numeracies outlined in Outcome 1 should be covered over the two units (i.e. Units 1 and 2)
• each of the required four areas of study should be covered at least once.

The curriculum stipulates that for each numeracy:

• one or two areas of study may be selected.

This flexibility allows teachers to choose areas of study that will best serve the chosen context. Teachers should select contexts that are relevant and applicable to their students' lives and interests.

An example is shown below.

Note, in this example the teacher has chosen to take the numeracies in the following order to suit the needs of their students.

In this example, the teacher has chosen to plan a program as follows:

Unit 1: Three numeracies and five areas of study have been chosen:

• Civic numeracy
• with Area of Study 1: Number and Area of Study 4: Relationships
• Vocational numeracy
• with Area of Study 3: Quantity and measures and Area of Study 4: Relationships
• Recreational numeracy
• with Area of Study 2: Shape

Unit 2: Three numeracies and six areas of study have been chosen:

• Personal numeracy
• with Area of Study 5: Dimension and direction and Area of Study 8: Systematics
• Financial numeracy
• with Area of Study 6: Data and Area of Study 7: Uncertainty
• Health numeracy
• with Area of Study 6: Data and Area of Study 8: Systematics

Using this table, in this example the teacher has ensured that each area of study (rows) has been selected and each numeracy (columns) has been selected.

1. Place each of the six numeracies in the table.
2. Consider ideas for contexts for teaching each numeracy.
3. Select one or two areas of study (to a total of six for each unit) to teach the context you have chosen for each numeracy.

The outcome statements use the following terminology:

Familiar refers to situations that are either well known to the student(s) or ones they have previously experienced in their lives, either at school or outside school. Applying the key mathematical knowledge and skills in well-known situations allows student(s) to access and build strong meaningful connections between the mathematics and the real-life context.

Unfamiliar therefore refers to situations or contexts that have not previously been encountered by the student(s) and are designed to extend their conceptual and contextual experience. Extending the conceptual application of mathematical key knowledge and skills to unknown situations should strengthen the skills of the student(s) to recognise and act on their mathematical knowledge and transfer their skills to other new contexts.

Routine contexts are those that the student usually encounters in their life or work. These contexts may include regular practice or a set order in which sequences of events regularly occur.

Specialised contexts may be higher order situations where the student requires particular or distinct knowledge to apply their mathematical knowledge and skills, and to carry out the mathematical acts.

When selecting contexts:

• Consider the outcome statement requirements. Does the outcome require contexts that are familiar to the student or unfamiliar? Routine or specialised?
• Take into consideration the student's local community.
• Consider the student's interests.
• Consider the student's VET subject(s) or work/industry they are interested in.
• Ask if you can broaden their horizons (with unfamiliar contexts).
• Provide opportunities for good citizenship and participation in society.
• Incorporate employability skills.

The Vocational Major has been designed to prepare young adults to take an active approach to their personal and professional development; to make valuable contributions to their chosen vocation, family and community; and to continue learning throughout their lifetime.

Integrating studies is an effective way of developing 21st Century Capabilities and is more reflective of the 'real world'. Interdisciplinary projects and assessments encourage students to develop and apply skills and knowledge in a more authentic manner.

It is possible to deliver the units in an integrated approach with other VCE Vocational Major studies, as flexible delivery of the VCE Vocational Major units allows for integration of complementary outcomes across the studies. Where an integrated program is developed and implemented, it is important for teachers to note that:

• teachers should keep clear documentation of student achievement of individual outcomes within an integrated program
• an assessment task used to demonstrate achievement of one outcome in one VCE Vocational Major unit cannot be used to demonstrate achievement in any other VCE Vocational Major unit, Victorian Pathways Certificate unit, VET unit of competency or VCE study.

Teachers must consider the authentication strategies relevant for each assessment task. Information regarding VCAA authentication rules can be found in the VCE Administrative Handbook.

Students must observe and apply VCAA authentication rules. Students must sign an authentication record for work done outside class when they submit completed work. The VCAA authentication rules state that:

• a student must ensure that all unacknowledged work submitted is their own
• a student must acknowledge all resources used, including:
  • texts, websites and other source material
  • the name and status of any person who provided assistance and the type of assistance provided
• a student must not receive undue assistance from another person, including their teacher, in the preparation and submission of work
• acceptable levels of assistance include:
  • the incorporation of ideas or material derived from other sources (for example, by reading, viewing or note taking) but which have been transformed by the student and used in a new context
  • prompting and general advice from another person or source, which leads to refinements and/or self-correction
• unacceptable forms of assistance include:
  • use of or copying another person's work, including their teacher's work, or other resources without acknowledgement
  • use of or copying sample answers provided by their teacher or another person
  • corrections or improvements made or dictated by another person, including their teacher
• a student must not submit the same piece of work for assessment in more than one study, or more than once within a study
• a student must not circulate or publish written work that is being submitted for assessment in a study in the academic year of enrolment
• a student must not knowingly assist another student in a breach of rules
• in considering whether a student's work is their own, teachers should consider if the work:
  • is atypical of other work produced by the student
  • is inconsistent with the teacher's knowledge of the student's ability
  • contains unacknowledged material
  • has not been sighted and monitored by the teacher during its development.

Teachers are encouraged to include Aboriginal and Torres Strait Islander knowledge and perspectives in the design and delivery of teaching and learning programs related to VCE VM Numeracy. The Victorian Aboriginal Education Association Inc. (VAEAI) is the peak Koorie community organisation for education and training in Victoria. VAEAI's publication Protocols for Koorie Education in Victorian schools supports teachers and students in learning about local, regional, state, national and international Indigenous perspectives.

VAEAI's Cultural Understanding and Safety Training (CUST) professional learning resources are also available for teachers when considering how they may best include Aboriginal and Torres Strait Islander perspectives in VCE VM Numeracy.

Other resources when considering Aboriginal and Torres Strait Islander perspectives:

NAIDOC

Museums Victoria

AIATSIS

NITV

Creative Spirits

ABC Indigenous

DET

Cool Australia

Aboriginal and Torres Strait Islander Curricula (University of Melbourne)

Bring Them Home

Closing the Gap Report

National Museum of Australia

Closing the Gap events

Blak & Bright First Literary Festival

CORE

The VCE Vocational Major study provides students with the opportunity to engage in a range of learning activities. In addition to demonstrating their understanding and mastery of the content and skills specific to the study, students may also develop employability skills through their learning activities.

In Outcome 1 students should develop mastery of the key skills and knowledge of mathematics that is required in Australian workplaces. Students reinforce their base knowledge of mathematical processes, which should have transferability for future mathematics encounters.

Through Outcome 2, students develop strong problem-solving skills. In learning through the stages of the problem-solving cycle it is intended that students translate this knowledge to be able to solve real-life mathematical problems such as those found in the workplace and everyday life.

The use of technology as outlined in Outcome 3 is a key component in the world of work. Many workplaces have mathematical procedures that are undertaken with digital technologies, such as the use of drones to quote roof painting, laser measures in the construction industry, Excel spreadsheets in retail stock counting, and digital booking systems. This curriculum allows for student exposure to as many different technologies as is permissible by the constraints of the classroom or environment. Teachers are encouraged to develop transferability of technology skills in their students.

The nationally agreed employability skills* are: Communication; Planning and organising; Teamwork; Problem solving; Self-management; Initiative and enterprise; Technology; and Learning.

The table links those facets that may be understood and applied in a school or non-employment-related setting, to the types of assessment commonly undertaken within the VCE study.

*The employability skills are derived from the Employability Skills Framework (Employability Skills for the Future, 2002), developed by the Australian Chamber of Commerce and Industry and the Business Council of Australia, and published by the (former) Commonwealth Department of Education, Science and Training.

Mathematics glossary

Numeracy glossary

Mathematical literacy

https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/Pages/glossary.aspx
https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/english/literacy/Pages/introduction_to_literacy_in_mathematics.aspx

Developing investigations

https://www2.census.gov/programs-surveys/sis/activities/math/mm-10_teacher.pdf
https://new.censusatschool.org.nz/
https://nrich.maths.org/

Financial

https://moneysmart.gov.au/
https://www.taxsuperandyou.gov.au/
https://responsiblegambling.vic.gov.au/reducing-harm/schools/
https://www.scamwatch.gov.au/
https://www.fairwork.gov.au/
https://www.consumer.vic.gov.au/resources-and-tools/young-consumers

Civic

https://www.redcross.org.au/emergencies/resources/resources-for-teachers/
https://www.mcm.org.au/homelessness/frontyard/community-involvement/schools
https://disasterresilience.vic.gov.au/teachers/
https://www.ga.gov.au/scientific-topics/community-safety

Recreational

https://www.aflvic.com.au/schools
http://www.bom.gov.au/
https://agriculture.vic.gov.au
https://www.melbourne.vic.gov.au/about-melbourne/melbourne-profile/Pages/city-maps.aspx

Health

https://www.achievementprogram.health.vic.gov.au/education/schools
https://www.health.vic.gov.au/
https://nutritionaustralia.org/
https://www.betterhealth.vic.gov.au/
https://www.vicroads.vic.gov.au/safety-and-road-rules/road-safety-education/secondary-schools/secondary-school-road-safety-education-resources
https://responsiblegambling.vic.gov.au/reducing-harm/schools/
https://www.scamwatch.gov.au/

Outcomes 1, 2, 3

a) Personal numeracy

Outcome 1: Areas of study

1. Number

3. Quantity and measures

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Diary or calendar
  Keep a diary or calendar keeping track of important dates and events over a designated time, such as monthly, quarterly, yearly. [AoS 3] Technology: planner/diary
• Measurement conversions
  Investigate and perform the appropriate measurement conversions to solve the problem of not having the correct measurement tool, such as grams, millilitres, cups. Practically scale up and scale down measurements. [Area of Study 3] Technology: calculator, online conversion tools
• Recipe conversions
  Perform the appropriate calculations to increase or decrease a recipe, such as double, triple, half. [Area of Study 3] Technology: calculator, online conversion tools
• Meal budget
  Select a meal or recipe to suit a specified budget and purpose, such as feeding a family of four for $30, or making mocktails for a group of two for $10, providing the source and cost of the ingredients required. [A Area of Study 1] Technology: budgeting apps, online recipes
• Pet ownership
  Create a cost analysis table to estimate the cost of owning a pet for one year, including categories such as the initial cost of the animal, equipment needed, veterinary fees and other health treatments, food etc. [Area of Study 1] Technology: spreadsheet and graphing tools/apps

Outcomes 1, 2, 3

b) Civic numeracy

Outcome 1: Areas of study

1. Number

4. Relationships

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Voting systems
  Investigate different voting systems used throughout Australia and explore mathematically how representatives are elected. [Areas of Study 1, 4] Technology: internet access, spreadsheets
• Fundraising organisations
  Look at different fundraising organisations with different types of campaigns, such as donation tins versus monthly donations or collections. Explore income and expenditure and find out how much of the donations makes up their yearly spending. [Area of Study 1]

Outcomes 1, 2, 3

c) Financial numeracy

Outcome 1: Areas of study

1. Number

2. Shape

4. Relationships

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Tax
  Explore tax-deductible items in preferred industry. Undertake calculations to identify and determine tax deductions using a stimulus such as a vehicle logbook. [Area of Study 1] Technology: tax deductions apps and digital logbooks
• Tax brackets
  Create scenario cards for students to match the workplace or industry scenario to the appropriate tax bracket.
• Bank accounts
  Explore the MoneySmart website to research different bank accounts and use a graphic organiser to show their similarities and differences. Research the requirements for opening an account at that bank. [Area of Study 2]
• Spending habits
  Explore spending habits (use banking apps or websites for financial breakdowns of income and expenditure). Separate purchases into different categories (such as food, transport, entertainment etc.). Investigate spending and/or savings goals. [Areas of Study 1, 4] Technology: banking apps
• Grocery savings
  Use online grocery advertising to calculate the percentage savings of items on sale. [Areas of Study 1, 4] Technology: shopping apps or websites
• Grocery sales
  Use regular grocery advertising over a series of a month to observe and record regular sale items trends and prepare a shopping list to help the family budget to take advantage of these sales. [Areas of Study 1, 4] Technology: shopping apps or websites
• Electronic prices
  Explore the price of an electronic item, such as a laptop or phone, from five different countries. Convert these prices to Australian dollars and investigate the price difference for the same product. Have a class discussion that investigates why these prices differ, and debate if Australians pay too much for technology items. [Area of Study 1] Technology: money conversion app
• Managing debt
  Explore the MoneySmart website to find methods to manage debt. Undertake calculations around debt and interest using an online calculator such as a loan calculator. Use a graphic organiser to accumulate research. [Area of Study 1] Technology: online loan calculators or apps

Outcomes 1, 2, 3

d) Health numeracy

Outcome 1: Areas of study

1. Number

3. Quantity and measures

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Smoking or vaping
  Use the Australian Government Department of Health website to explore the benefits of quitting smoking/vaping and create a timeline to demonstrate how quickly the body will show some benefits. [Area of Study 3] Technology: internet, spreadsheets, drawing apps
• Snack nutrition
  Explore the proportions of ingredients in favourite snack items to determine which ones offer more nutrition.
• Alcohol content
  Explore the alcoholic content and the sizes of different alcoholic drinks. Use the Better Health website to explore associated issues, such as alcohol dependence, risky situations, health effects, alcohol and the law, and reducing drinking. Create a newsletter targeted at a given audience to promote findings. [Areas of Study 1, 3]

Outcomes 1, 2, 3

e) Vocational numeracy

Outcome 1: Areas of study

1. Number

2. Shape

3. Quantity and measures

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Tiling
  Investigate tiling patterns involving different geometric shapes that could be used in different rooms in a home, business or industrial setting. Link these to tessellations. [Area of Study 2] Technology: drawing apps
• Bricklaying
  Investigate the main patterns used in bricklaying, and research the cost of cement pavers. Find or create a garden setting that needs to be paved and calculate the cost and amount of pavers needing to be ordered. [Areas of Study 1, 2, 3] Technology: laser measure, measuring apps, measuring equipment, drawing packages
• Purchase order
  Create an itemised invoice or purchase order for a service or job that highlights the cost of all materials or resources needed for the job, such as materials, labour, machine hire etc. [Area of Study 1] Technology: online templates
• Stock management
  Explore stock management in their work placement or part-time job, and the systems in place for stock management. [Area of Study 3] Technology: farming apps or online calculators
• Ratio and measurement
  Perform appropriate ratio and measurement calculations related to different scenarios in a familiar industry, such as colour pigment-developer in hairdressing, the 1-2-3 concrete mix, ratio of staff to children in childcare. [Area of Study 3]
• Medical calculations
  Undertake medical calculations, such as medicine dosages, using measuring equipment and coloured water, solid dosages, weight-based dosages, age-based dosages etc. [Area of Study 3] Technology: nursing apps

Outcomes 1, 2, 3

f) Recreational numeracy

Outcome 1: Areas of study

1. Number

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Starting a hobby
  Brainstorm the equipment needed to start a new hobby or sport, and compare two stores/online vendors to find which outlet would be cheaper, which would be quicker to deliver, and which has the product in stock etc. [Area of Study 1]
• Comparing tickets
  Compare the cost of tickets to different events (festivals, sports, concerts etc.). [Area of Study 1] Technology: ticketing websites

Outcomes 1, 2, 3

a) Personal numeracy

Outcome 1: Areas of study

5. Dimension and direction

6. Data

8. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Planning a trip to the supermarket
  Use appropriate maps and technologies to plan a trip to the supermarket or local market to purchase the required ingredients, and provide appropriate directions for the journey. [Areas of Study 5, 8] Technology: online map tools/apps
• Planning a journey 1
  Use the PTV website or app to explore the different input and output options when planning a journey, such as location/destination, departure/arrival time, transport preference. Follow up with the journey planner function to respond to a set of different scenarios; for example, planning a journey to the local shopping complex to meet friends on Saturday at 2 pm, or determining how you can get to school using public transport if your parents are unable to drive you there next week. [Areas of Study 5, 8] Technology: online map tools/apps
• Planning a journey 2
  Use an online map website or app to explore the different input and output options when planning a journey such as location/destination, departure/arrival time, route options, nearby amenities or services Then use the website or app to respond to a set of different scenarios, such as determining the best route to drive to the beach from your house or meeting friends at a local park, and explore the facilities at a nearby park, such as playgrounds, toilets, restaurants or parking. [Areas of Study 5, 8] Technology: online map tools/apps
• Personal or wellness goals
  Identify a personal or wellness goal to plan, implement, monitor and evaluate. These plans might include drinking more water, walking each day, improving school attendance, choosing mindfulness. Discuss how to make measurable goals and the data and information that can be collected to measure change. [Area of Study 6] Technology: health apps on mobile devices
• Goal timeline
  Create a timeline and schedule to support the achievement of a set goal. At the end of the designated time frame, collate and organise the data and information collected in a visual display and interpret the results to describe the overall experience. [Area of Study 6] Technology: planner/diary, spreadsheets, graphing tools
• Animal shelters
  Examine data from animal shelters (e.g. the RSPCA) to explore the number of animals surrendered and/or adopted, arranging and sorting the appropriate information and data. Create appropriate tables and graphs to display the information. [Area of Study 6] Technology: spreadsheet, graphing tools/apps
• Pet cost
  Create a time 'cost' analysis table to estimate how much time it takes to look after a pet daily, weekly and yearly, including items such as feeding, cleaning up after the pet, grooming, play, walk/exercise, vet visits and pet/obedience training. [Area of Study 6] Technology: spreadsheet, graphing tools/apps

Outcomes 1, 2, 3

b) Civic numeracy

Outcome 1: Areas of study

6. Data

7. Uncertainty

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Voting systems
  Investigate different voting systems used throughout Australia and explore mathematically how representatives are elected. [Area of Study 7] Technology: internet access, spreadsheets
• Class election
  Explore the voting systems (local, state, federal) and conduct an election in the class to understand the numbers and processes. [Areas of Study 6, 7] Technology: internet access, spreadsheets
• First Nations health data
  Investigate First Nations peoples' health data, including information in the Closing the Gap report and using this as a resource. Compare data from the report with wider data in the Australian population. [Areas of Study 6, 7] Technology: internet access, spreadsheets
• Charities and fundraising organisations
  Explore different charities and fundraising organisations to identify their sources of revenue and the distribution of funds. Use this information to make choices about which organisations you would prefer to support. Create a costings sheet that shows how much you would pay over a fortnight, one-month, six-month or yearly period. Investigate the personal tax benefits and business tax benefits to making charitable donations. [Area of Study 6] Technology: online tax calculators, budgets/costing spreadsheets
• News and media data
  Explore data presented in news or media reports on a controversial topic and identify how the data has been presented, why it is presented in this way, and possible ways the information could be misleading or used to sway popular opinion. [Area of Study 6]

Outcomes 1, 2, 3

c) Financial numeracy

Outcome 1: Areas of study

8. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Tax deductibles
  Explore tax-deductible items in a preferred industry. Undertake calculations to identify and determine tax deductions using a stimulus such as a vehicle logbook. [Area of Study 8] Technology: tax deductions apps, digital logbooks

Outcomes 1, 2, 3

d) Health numeracy

Outcome 1: Areas of study

6. Data

7. Uncertainty

Outcome 2: Problem- solving cycle

Examples of learning activities

• Sporting activities
  Survey peers about their after-school sporting activities and compare against the recommended guidelines. [Area of Study 6] Technology: digital survey tools, spreadsheets
• Counting steps
  Count steps for a 24-hour period using smart phone/pedometer. Look for simple strategies to increase the number of steps in a day. Create projections using percentage increases to complete over a fortnight, such as 2%, 5% and up to 10% over a period of time. Choose appropriate methods to summarise and present data. [Area of Study 6] Technology: pedometer, health apps, spreadsheets
• Screen time
  Discuss the ideas around recommended amounts of screen time. Consider what constitutes screen time, and estimate and record daily screen time over a set period of time. Compare student data to research recommendations from Australian health guidelines for children-and young people aged five to 17 years. [Area of Study 6] Technology: screen time apps
• Gaming addiction
  Research gaming addiction and strategies to decrease computer addiction. Produce information in the form of a public campaign, newsletter article, or social media advertisement. [Areas of Study 6, 7] Technology: screen time apps

Outcomes 1, 2, 3

e) Vocational numeracy

Outcome 1: Areas of study

5. Dimension and direction

6. Data

8. Systematics

Outcome 2: Problem- solving cycle

Examples of learning activities

• Salon schedule
  Create a daily or weekly schedule for a hairdressing or beauty salon, taking into consideration the time each service requires. Use set parameters to plan and schedule key actions. [Area of Study 8] Technology: scheduling apps or calendars
• Evacuation
  Discuss with your employer the emergency management protocols when there is an evacuation at work. Create a plan or map that highlights these steps. [Area of Study 5] Technology: drawing apps
• Work placement calendar
  Track work placements and organise these over different calendars: a daily one showing work/jobs from start to finish over an entire day; weekly one tracking movements and jobs/activities. [Areas of Study 5, 8] Technology: online personal organiser
• Stock management
  Explore stock management at a work placement or part-time job, as well as the systems in place for stock management. [Areas of Study 6, 8] Technology: farming apps or online calculators
• Job sheet
  Provide students with a job sheet including at least five addresses. They create a schedule for the day including directions, distances travelled (logbook), approximate times, and estimated time for the job. [Area of Study 5, 8]

Outcomes 1, 2, 3

f) Recreational numeracy

Outcome 1: Areas of study

5. Dimension and direction

6. Data

7. Uncertainty

8. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Interstate trip
  Plan a two-week interstate trip. Determine the full itinerary including the route and times, costs (fuel, toll fees etc.), meals (meal planning for some take away options and some cooked meals and cost both), accommodation, activities (including some free ones). [Areas of Study 5, 8] Technology: travel; apps and websites, fuel calculator apps
• Online hours
  Estimate how long students spend online in a day. Compare their usage data from apps with recommended guidelines. Extrapolate calculations to determine time spent online over the period of a week, month or year. [Area of Study 6] Technology: Smart devices
• Medal tallies
  Use a world-wide event, such as an Olympic Games, Commonwealth Games, World Cup Sporting Event, and compare previous results or medal tallies to predict the results of the current event. [Area of Study 6]
• Weather predictions
  Use seasonal weather patterns of the previous year to make predictions for the year ahead. Investigate trends goods or services based on seasonal sales, such as ski equipment or beach umbrellas. Use your weather trends to predict future sales. [Area sof Study 6, 7] Technology: weather apps and websites

Outcomes 1, 2, 3

a) Personal numeracy

Outcome 1: Areas of study

1. Number

2. Shape

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Pet carriers
  Investigate the shape and size of a variety of different pet carriers. Explore why certain shapes are more commonly used for different species of pet; for example, horse float, cat carrier, fish aqua transport. Use algebraic formulae to calculate the perimeter and area of the floor space (base) and carrying capacity of the carrier. [Area of Study 2] Technology: internet access
• Online gifts
  Investigate the costs of sending an online gift such as flowers, a hamper etc. Find the best option to fit your set budget for a range of scenarios, such as 'thank you', 'get well', birthday etc. Compare deals and make recommendations for best buys. [Area of Study 1] Technology: shopping apps
• Streaming TV
  Compare the costs of streaming TV services. Consider factors such as how many movies, shows each member of the family prefers on which service. Make a table comparing monthly and yearly costs. Make recommendations based on research for the family to save money on streaming services. [Area of Study 1] Technology: streaming apps and websites
• Buying a car
  Undertake an investigation into the costs of buying a first car. Use the VicRoads website as a resource. Consider all the costs involved, such as vehicle inspection, registration, insurance, mileage, etc. Investigate car loans and interest repayments for this type of personal loan. [Area of Study 1]

Outcomes 1, 2, 3

b) Civic numeracy

Outcome 1: Areas of study

1. Number

3. Quantity and measures

4. Relationships

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Charity budgets
  Examine the published budgets of selected charity organisations and identify the sources of revenue they receive. Display the data in the most appropriate format. Determine how the revenue and donations are used by the charity organisation. Calculate the percentage of donations that are directly used to support the charity and its relief efforts compared with administration, employment and other costs. [Area of Study 1] Technology: spreadsheet, graphing applications
• Reaction times
  Use the 'ruler drop test' to measure reaction times under different conditions, such as looking at the ruler, having a conversation with someone, listening to music or changing the radio station, talking on the phone, sending a text message etc. Record the results in a table and work out the average reaction time for each condition. Link this data to average reaction times for braking when driving a car. Calculate how far a car would travel before starting to brake when driving at speeds such as 40km/h, 50km/h, 60km/h, 80km/h and 100km/h. Discuss the impact different conditions have on reaction times, and hence the distance travelled before stopping. [Areas of Study 3, 4] Technology: spreadsheets, online reaction-time tests

Outcomes 1, 2, 3

c) Financial numeracy

Outcome 1: Areas of study

1. Number

4. Relationships

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Tax
  Undertake a series of taxation-related activities. Use the Australian Government Tax, Super, You website for resources. Investigate the reasons for paying tax and classify which of the three levels of government are responsible for community services. Determine the appropriate tax bracket when given different scenarios and calculate the amount that employees will be required to pay. [Area of Study 1] Technology: online tax calculators, pay-slips
• Paying fines
  Undertake activities to investigate the costs and issues encountered with paying fines, such as vehicle fines, public transport, driving with a phone, driving with more people than allowed in a vehicle etc. Make a spreadsheet detailing the costs involved and strategies to avoid debt. Present work as an information poster or social media post. [Area of Study 1, 4] Technology: online interest calculators
• Celebration costs
  Determine the cost of supplies for a celebration using two online supermarkets. Compare and contrast the costings and find ways to make savings (i.e. brand versus generic products and loyalty programs). Provide a detailed breakdown using spreadsheets and make recommendations based on the research. [Area of Study 1] Technology: online shopping apps
• Buying a big-ticket item
  Research the cost of a big-ticket item, such as a washing machine, and then cost the purchase using the different methods, such as savings, credit cards and 'buy now, pay later' platforms. Create a spreadsheet that explores using these buying options to find the total costs. [Area of Study 1] Technology: spreadsheets
• Buy now, pay later
  Research articles on 'buy now, pay later' platforms and credit cards, and the debt issues they bring. Discuss the advantages and disadvantages of these services. Consider why these services use high-profile people as brand ambassadors, and then debate when there could be an appropriate time to use them. Undertake interest calculations and compare services. Discuss the debt trap. [Area of Study 1] Technology: interest calculators
• Moving out
  Investigate costs associated with moving out of home. Consider budgeting for utilities and undertake calculations around paying household bills. Consider furnishing a new property and take into consideration wants versus needs. Investigate savings schedules to ensure weekly, monthly and annual bills are taken care of. [Area of Study 1] Technology: spreadsheets

Outcomes 1, 2, 3

d) Health numeracy

Outcome 1: Areas of study

1. Number

4. Relationships

5. Dimensions and direction

6. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Smoking cost analysis
  Undertake a cost analysis associated with smoking, and examine how much it costs over a week, month, and year. Investigate the ingredients found in cigarettes and vape pens, and create a percentage total of the different ingredients to explore the toxins found and explore the health impact of each. [Area of Study 1] Technology: calculating apps
• Health care
  Undertake a series of calculations related to health care. Include calculating and measuring dosage of medications, and scheduling of medications and care. [Area of Study 5] Technology: nursing apps
• Private health care
  Investigate costs associated with private health care. Compare different providers and make a comparative cost chart of services offered. Consider the different costs for different stages of life and factor in the Medicare levy. [Areas of Study 1, 6] Technology: calculating apps
• Medical aids
  Examine the shape and design of medical aids such as walking frames, wall handles, shower seats etc. Undertake a mathematical program to design your own aids for someone in need. Include all measurements, scale drawings and plans. [Areas of Study 4, 5] Technology: drawing apps

Outcomes 1, 2, 3

e) Vocational numeracy

Outcome 1: Areas of study

1. Number

2. Shape

3. Quantity and measures

4. Relationships

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Flooding
  Whenever there is flooding in Southeast Queensland, engineers at a rock quarry face the same exact problem – pit flooding. If the flood is 5m deep, and the floor area is 700 square metres, and the pump will operate at 60L/s, how long, in hours, will it take for the pit to be emptied? [Areas of Study 1, 4] Technology: calculator apps
• Paving materials
  Research the costs of using two different materials (such as pavers versus bricks) when paving a back garden area. Determine the amount of material needed to pave the area and hence the total cost for each material. Compare the costs and discuss the pros and cons of each. [Areas of Study 1, 3] Technology: calculating apps
• Uniform costs
  Investigate uniform companies and compare the costs of different uniform types. Design a new uniform for the business you are currently working in and prepare a cost sheet that shows the cost of providing new uniforms for all staff. Design an order form to give to employees. Create an appropriate method of recording employee uniform requests, such as a spreadsheet with embedded formulas. [Areas of Study 1, 2, 3] Technology: spreadsheets, invoice or order form applications
• PPE requirements
  Review your school environment and estimate the amount of PPE needed for certain situations; for example, to provide masks to staff and students for a week, term, and whole year; the purchase of safety glasses and lab coats for science classes; or hearing protection, gloves, aprons, breathing apparatus for woodwork. Investigate school PPE suppliers and determine the cost of providing the necessary PPE. Prepare an invoice or quote that you would submit, outlining the items needing to be purchased, the costs and included GST. [Areas of Study 1, 4] Technology: spreadsheets, invoice or order form applications
• Trade tools
  Make a list of the essential tools needed for starting out in your specific trade of choice. Research and compare the cost of buying a pre-made kit with purchasing the individual tools separately. Investigate the deductions that can be claimed for purchasing tools for work on the Australian Taxation Office website and calculate how much you can claim for setting up your tool kit. [Area of Study 1] Technology: online tax claim and allowances tools

Outcomes 1, 2, 3

f) Recreational numeracy

Outcome 1: Areas of study

1. Number

2. Shape

3. Quantity and measures

4. Relationships

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• International holiday
  Plan a two-week international holiday. Include a full itinerary with flights, connecting transport and accommodation. Consider additional information such as finding the closest embassy, hospital, local rules to respect. Include both local and Australian times on the itinerary. Undertake activities related to conversion of Australian dollars to the local currency and provide a run-down of the major costs of the holiday alongside the itinerary. [Areas of Study 1, 3, 4] Technology: flight apps and websites, travel and accommodation apps and websites
• Community event
  Plan a community event. Choose an event for the class to run for the local community such as a community gathering or a religious celebration. Find a community venue and calculate the costs of hire and cleaning. Create planning documents for the event, including a full budget that includes food, entertainment, furniture hire, security, decorations etc. [Areas of Study 1, 4] Technology: budgeting apps
• Feeding a family
  Investigate the costs of feeding an average family for a week. Create an online shopping list for seven days of home-cooked meals and cost the weekly shop. Compare with online delivery options, such as pre-packaged meal kits or takeaway options. Provide a cost analysis of both options and a mixture of options. Provide advice based on your calculations for the best way to feed a family. [Areas of Study 1, 4] Technology: food apps
• End-of-year celebration
  Investigate the costs of the work 'end-of-year' celebration party. Cost and plan for three options including: a sit-down meal, an activity that everyone participates in, and a surprise event. Options must suit the audience and meet a set budget. [Area of Study 1] Technology: spreadsheets, invoices
• Kites
  Explore the origins of kites and how they fly, and redesign them using different shapes and/or different materials. Find an appropriate day to test them all, and film this to allow discussion and feedback. Apply adjustments, and re-test. Present a poster with original diagrams and measurements, feedback, adjustments, and results. [Areas of Study 1, 2, 3] Technology: measuring tools and equipment
• Board games and card names
  Revisit favourite board games and card games and complete a positive-negative analysis. Use the feedback to design a numbers and maths skills board game. Include rules and an explanation guide, playing pieces, playing board, etc. [Areas of Study 1, 2, 3, 4]

Outcomes 1, 2, 3

a) Personal numeracy

Outcome 1: Areas of study

5. Dimensions and direction

6. Data

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Sleep
  Investigate the optimum amount of sleep teenagers should get each night and compare it with students' current sleep patterns. Undertake a statistical analysis of sleep data. Consider using data from New Zealand's Census at School website for comparisons. Use this data and students' conclusions form the data to make recommendations for optimum sleep hours. [Area of Study 6] Technology: spreadsheets, graphing software
• Plan a journey
  Use an online map, website or app to plan a journey or class excursion. Include the location/destination, departure and arrival times, route options, nearby amenities, or services. Use websites or apps to compare different routes to a chosen destination and provide clear directions, including a comparison of different routes and a recommendation for the best route. [Area of Study 5] Technology: online map tools/apps

Outcomes 1, 2, 3

b) Civic numeracy

Outcome 1: Areas of study

6. Data

7. Uncertainty

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Global data
  Investigate data reported on a global issue that affects developing countries; for example, disease, food production, water pollution, education, poverty. Compare the information with that from developed countries. Use the Gapminder website as a resource. Choose the most appropriate methods to display the information. Calculate the relevant measures of centre and spread. [Area of Study 6] Technology: spreadsheets, graphing applications
• Win the lottery
  Investigate what it takes to win some of the most popular lotteries and research the odds of winning different prize divisions. Comment on which division you would be more likely to win. Investigate if the number of people entering the lottery changes these odds. Explore how the prize money is shared between the prize divisions and the potential winners. Make a decision as to whether you think it is worth buying a lottery ticket, giving mathematical reasons for your choice. [Area of Study 7] technology: calculator apps
• Road statistics
  Examine the data presented on Australia's road statistics on the Australian Government's National Road Safety Data Hub. Read and interpret the information presented to make conclusions about road safety in Australia, such as which age groups are more likely to be involved fatal collisions, effects of speed on the number of fatalities, and types of vehicles more likely to be involved in incidents. Explore how fatalities on the road have changed over recent years. Use research to make conclusions about the safety of Australian roads and to make recommendations. [Area of Study 6] technology; online interactive data displays

Outcomes 1, 2, 3

c) Financial numeracy

Outcome 1: Areas of study

7. Uncertainty

8. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Gambling
  Investigate the issue of problem gambling and debt in Victoria. Use the numeracy resources developed by the Victorian Responsible Gambling Foundation. Investigate notions of chance and probability with gambling. Consider the idea of risk and evaluate scenarios that have an element of risk. [Area of Study 7] Technology: online calculators, spreadsheets
• Planning a celebration
  Determine the cost of supplies for a celebration using two online supermarkets. Compare and contrast the costings and find ways to make savings (i.e. brand versus generic products and loyalty programs). Provide a detailed breakdown using spreadsheets and make recommendations based on the research. [Area of Study 8] Technology: online shopping apps
• Big-ticket item
  Research the cost of a big-ticket item, such as a washing machine, and then cost the purchase using the different methods, such as saving, credit cards and 'buy now, pay later' platforms. Create a spreadsheet that explores using these buying options to find the total costs. [Area of Study 8] Technology: spreadsheets
• Moving out
  Investigate costs associated with moving out of home. Consider budgeting for utilities and undertake calculations around paying household bills. Consider furnishing a new property and take into consideration wants versus needs. Investigate savings schedules to ensure weekly, monthly, and annual bills are taken care of. [Area of Study 8] Technology: spreadsheets

Outcomes 1, 2, 3

d) Health numeracy

Outcome 1: Areas of study

1. Number

5. Dimension and direction

6. Data

7. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Eating habits
  Conduct a survey about typical eating habits. Consider data collection and collation. Compare results of data collection and analysis against the Australian daily recommendations. Create a public campaign to increase awareness based on results. [Area of Study 6] Technology: data collection and presentation apps
• Sport supplements
  Investigate the use of supplements and drugs among sports players, and the effects they have on the body. Find recent examples to create a digital portfolio that highlights athletes who have been involved in controversies, the supplements and drugs associated, and the health effects. [Area of Study 6] Technology: data presentation apps
• Local community issues
  Investigate an issue in the local community, such as drugs and alcohol, mental health, violence, low education rates, unemployment. Consider reliable sources of secondary data for analysis. Compare data and analysis with published Australia-wide statistics. Draft a letter to a local MP with the findings and offer solutions to the problem investigated, including data as back-up. [Areas of Study 6, 7]
  Technology: spreadsheets
• Health care
  Undertake a series of calculations related to health care. Include calculating and measuring dosage of medications, and scheduling of medications and care. [Area of Study 5] Technology: nursing apps
• Private health care
  Investigate costs associated with private health care. Compare different providers and make a comparative cost chart with services offered. Consider the different costs for different stages of life and factor in the Medicare levy. [Areas of Study 1, 6] Technology: calculating apps

Outcomes 1, 2, 3

e) Vocational numeracy

Outcome 1: Areas of study

6. Data

8. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• Weekly schedule
  Create a weekly schedule for a work setting such as a fitness centre. Take into consideration the time each participant or class requires. Create a weekly timetable. Consider the number of employees that will be required for the roster and include their work times and breaks as designated by their award. [Areas of Study 6, 8] Technology: scheduling apps
• Healthy lunches
  Investigate the different healthy lunches that can be brought to a job site when working on mobile jobs, such as the ones occupied by 'tradies'. Create a chart that compares the nutrition value of the lunch options and the recommended daily requirements. Investigate safe food storage temperatures. Research and select appropriate containers, coolers and thermos options. Use the dimensions of the containers to determine the volume and storage capacity. Report on the key features of the different food storage options, making appropriate comparisons and recommending the best option. [Area of Study 6] Technology: calculator, spreadsheet or graphing applications

Outcomes 1, 2, 3

f) Recreational numeracy

Outcome 1: Areas of study

5. Dimension and direction

6. Data

8. Systematics

Outcome 2: Problem- solving cycle

Outcomes 3: Mathematical toolkit

Examples of learning activities

• International holiday
  Plan a two-week international holiday. Include a full itinerary with flights, connecting transport and accommodation. Consider additional information such as finding the closest embassy, hospital, local rules to respect. Include both local and Australian times on their itinerary. Undertake activities related to conversion of Australian dollars to the local currency and provide a run-down of the major costs of the holiday alongside the itinerary. [Areas of Study 5, 8] Technology: flight apps and websites, travel and accommodation apps and websites
• AFL statistics
  Compare the statistics of a first-year AFL player to a consistent and well-known player over the course of a season. Choose different visual methods to communicate the data. [Area of Study 6] Technology: spreadsheets
• Prize money
  Explore the prize money at the four Tennis Grand Slams: the amounts of prize money won by able-bodied singles players compared to the money won by the wheelchair singles players; and compare the singles prize amounts across all four Grand slams. Convert all monies into Australian dollars. Undertake a comparison of the costs involved with attending an event. Explore how the prize money has changed historically (and in which year each Grand Slam took on price parity). To extend this task, students may investigate the costs of hosting an event and analyse these alongside the benefits to the host city. [Areas of Study 6, 8] Technology: calculators, spreadsheets

The assessment tools used to collect evidence of student achievement (performance descriptors, rubrics and/or marking guide) should reflect the Outcomes, Key Knowledge and Key Skills of the unit.

Assessment tasks should be developed within the specific context of the setting and related to applied learning principles by being designed with authentic purposes and practical outcomes.

Teachers should develop a range of assessment activities in order to collect specific evidence of student learning in an outcome. Teachers should develop an assessment guide or rubric to make decisions about the evidence of student learning.

The assessment task and assessment tools should be explained to students before they commence the task.

When developing assessment tasks, teachers should refer to the VCAA policies and school assessment procedures as specified in the VCE Administrative Handbook.

Schools may determine the conditions for assessment tasks. Assessment tasks should be a part of the regular teaching and learning program and should not add unduly to student workload. Students should be advised of the timeline and conditions under which the task is to be completed. It is recommended that assessment tasks be completed in class under supervision within a limited timeframe.

The overall assessment program for the unit should include a variety of activities, include provision for authentication of student work and take into consideration the overall workload for students.

The assessment task and assessment tools should be explained to students before they commence the task.

The following sample performance descriptors may be used or modified for in-school assessment purposes.

The following advice is intended to support teachers by outlining sample approaches to developing an assessment task in Units 3 and 4.

Unit 3: Developing an assessment task

1. Identify the Numeracy that has been selected from Outcome 1, and the key knowledge and key skills from the chosen area(s) of study. 

The VCE Vocational Major Numeracy Study Design outlines the outcomes and areas of study. 

2. Choose the assessment task type from the range of options listed in the study design. 

In this example the students will undertake an investigation into Outcome 1: Numeracy in context, f) Recreational numeracy with Area of Study 2: Shape. 

This investigation will incorporate an excursion to the city to look at the shapes in Federation Square. From the assessment table this topic lends itself to an investigation. 

3. Identify the issues around the topic and develop a research question to be investigated.   

The key knowledge and skills for Area of Study 5: Dimension and direction are also addressed. The study design indicates that this topic is about space, direction and location in relation to landmarks and compass directions. Students should give and follow directions to landmarks using maps. This excursion will also encompass Area of Study 2: Shape by engaging with a range of two-dimensional shapes and three-dimensional objects.

In this task students create a treasure map with mathematical clues in and around Federation Square.

4. Identify the nature and sequence of teaching and learning activities to cover the key knowledge and key skills that are outlined in the area of study and provide for different learning styles.

This example requires students to demonstrate their knowledge in:

• Area of Study 2: Shape by addressing the three outcomes
• the context of f) Recreational numeracy
• applicable technologies.

In this example the teacher has chosen the Investigation to suit the type of mathematics that is being studied. 

• Students will follow the problem-solving cycle in their investigation of the issue, thereby satisfying the demands of the assessment outlined in the VCE Vocational Major Numeracy Study Design. 
• Students may work individually, in pairs or small groups to create a treasure hunt map for each other in and around Federation Square in the City of Melbourne. This treasure map must contain clues about the shape of buildings, objects or landmarks, using the formal language of mathematics and the key ideas of the properties of shape. Students must use compass points in their clues and on their corresponding map.
• Students undertake a research phase where they seek to identify the mathematical skills they will need to identify the mathematical processes that will be required to investigate in order to provide possible solutions or results to the problem.
• For this example, teachers might ask students to undertake some pre-activities in the classroom based on shape and dimension. In addition, they might teach their students the conventions of maps and map-making.
• Students are communicating mathematically as they create and use their treasure maps.
• Students should be able to evaluate their activity and clues, based on feedback from peers. Students should be encouraged to reflect back on the question or problem.
• Students should then report back on their work, communicating the key ideas with mathematical language and results.

5. Decide which technologies – analogue and/or digital – will be required to complete this task. 

Teachers may wish to introduce students to online drawing packages to create their maps. They may wish to use interactive or digitalised maps in both their research and creation phase.

6. Determine the length of time required for students to complete the task type.

In this example students might have 1–2 weeks to undertake the task. They may use both in-class and out-of-class time, especially in the data collection phase.

Students must have access to the performance descriptors and/or assessment criteria. Students should keep copies of all their notes, surveys, calculations and workings, which the teacher may collect and use to help monitor student progress through the task.

Ideally students will have completed a similar task in class prior to the assessment, as this will provide opportunities for students to fully understand the processes involved, and examples for use in class during the assessment.

7. Feedback should periodically be provided by the teacher to ensure students are on task and able to move through the cycle to completion. Peer feedback may be helpful in assessing a student's progress.

Unit 4: Developing an assessment task

1. Identify the Numeracy that has been selected from Outcome 1, and the key knowledge and key skills from the chosen area(s) of study.

The VCE Vocational Major Numeracy Study Design outlines the outcomes and areas of study.

2. Choose the assessment task type from the range of options listed in the Study Design.

In this example the students will undertake an investigation into Outcome 1: Numeracy in context, d) Health numeracy with Area of Study 6: Data.

This investigation might examine the issue of young adults and exercise. From the assessment table this topic lends itself to an investigation.

3. Identify the issues around the topic and develop a research question to be investigated. 

The key knowledge and skills for Area of Study 6: Data are focused on identifying the issue, collecting, sorting and displaying the data, as well as data analysis.

For this example, teachers may develop questions such as: How much, or what types of exercise do young people engage in? Or they may consider what sports students in this school play and how many hours they spend on sport each week.

4. Identify the nature and sequence of teaching and learning activities to cover the key knowledge and key skills that are outlined in the area of study and provide for different learning styles.

This example requires students to demonstrate their knowledge in:

• Area of study 6: Data by addressing the three outcomes
• the context of d) Health numeracy
• the problem-solving cycle
• applicable technologies.

In this example the teacher has chosen an investigation to suit the type of mathematics that is being studied.

• Students will follow the problem-solving cycle in their investigation of the issue, thereby satisfying the demands of the assessment outlined in the VCE Vocational Major Numeracy Study Design.
• Students may work individually, in pairs or small groups to identify a research question. The question(s) should reflect real-life, and be realistic and manageable within the confines of the task and the classroom. The question(s) must relate to the topic that has been selected, which in this example is young adults and exercise.
• With teacher assistance students might choose the variables to investigate and decide on the best method of data collection.
• Students will undertake a research phase where they seek to understand the issue and identify the mathematical processes that will be required to investigate and provide possible solutions or results to the problem.
• Students might undertake data collection or, where this is not possible, they may choose to source data online from reputable sources such as the Australian Bureau of Statistics or New Zealand's Census at School website.
• Data collection activities should occur, and the students should choose the most appropriate form of data display relevant to the data that they have collected.
• Appropriate analysis of the data should reflect the data that has been collected and displayed, and students should be able to relate the type of display back to the original question.
• Students should then be able to evaluate their data and reflect back on the question or problem. Further analysis or re-evaluation of the display or analysis may occur. Students should be able to draw meaningful conclusions to the data.
• Students should then present their work, communicating the key ideas with mathematical language and results.

5. Decide which technologies – analogue and/or digital – will be required to complete this task.

In this example students may wish to survey their peers using an online survey tool such as Google Trends or Survey Monkey. They may need access to graphing software such as Excel or Google Sheets. Additionally, they might use a calculator.

6. Determine the likely length of time required for students to complete the task type.

In this example students might have 1–2 weeks to undertake the task. They may use both in-class and out-of-class time, especially in the data collection phase.

Students must have access to the performance descriptors and/or assessment criteria. Students should keep copies of all their notes, surveys, calculations and workings, which the teacher may collect and use to help monitor student progress through the task.

Ideally students will have completed a similar task in class prior to the assessment, as this will provide opportunities for students to fully understand the processes involved, and examples for use in class during the assessment.

7. Feedback should periodically be provided by the teacher to ensure students are on task and able to move through the cycle to completion. Peer feedback may be helpful in assessing a student's progress.

The following sample tasks represent a range of sample assessments teachers can choose to use as formative assessment or summative assessment for outcomes in each unit. It should be noted that teachers are encouraged to develop assessment tasks specifically suited to the needs of their students and context.