Planning

Introduction

The Vocational Pathways Numeracy Curriculum Design (1 January 2023 – 31 December 2027) Advice for teachers provides teaching and learning advice and sample approaches to developing assessment for Units 1 and 2.

The program developed and delivered to students must be in accordance with the Vocational Pathways Numeracy Curriculum Design (1 January 2023 – 31 December 2027).

The purpose of this study is to enable students to develop their everyday numeracy practices to make sense of their personal, public, and future vocational lives. Students develop foundational mathematical skills with consideration of their personal, home, vocational and community environments and contexts, and an awareness and use of accessible and appropriate technologies.

This study focuses on providing students with the fundamental mathematical knowledge, skills, understandings and dispositions to solve problems in real life contexts for a range of workplace, personal, further learning and community settings relevant to contemporary society. The numeracies will be situated in accessible, concrete and highly familiar contexts where the mathematics content is explicit with little or no text or distracting information.

The contexts are the starting point and the focus and are framed in terms of personal, financial, civic, and health and recreational classifications. The numeracies are introduced using a problem-solving cycle with four components:

identifying the mathematics
acting on and using mathematics
evaluating and reflecting
communicating and reporting.

The mathematics includes foundational skills related to measurement, shape, numbers, and graphs applied to tasks that are part of the students’ everyday lives. At the end of the two units, students should be able to attempt structured and supported activities and tasks that require simple processes. These could be: counting, sorting, comparing and performing basic arithmetic operations with whole numbers and common, simple fractions and decimals, money, or recognising common spatial representations and measurements in highly familiar contexts.

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, and mathematics is the tool (the knowledge and skills) to be used efficiently and critically. Numeracy involves the use and application of a range of mathematical skills and knowledge which 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, allows them to make sense of numbers, time, patterns and shapes for everyday activities like cooking, gardening, sport and travel. Through numeracy, students 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 their everyday numeracy practices to make sense of their personal, public and future vocational lives
develop foundational mathematical skills with consideration of their personal, home, vocational and community environments and contexts, and an awareness and use of accessible and appropriate technologies.

Victorian Pathways Certificate Numeracy is framed around an applied learning approach to teaching ensuring that every student feels empowered to make informed choices about the next stages 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 apply what they have learnt by doing, experiencing and relating acquired skills to the real-world. Applied learning teaching 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, previous experiences and 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 curricula. 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.

The Victorian Pathways Certificate 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 can also involve students and their teachers working in partnership with external organisations to access VET and to work in integrated learning 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.

Developing a program

The Victorian Pathways Numeracy Curriculum Design outlines the nature and sequence of learning and teaching necessary for students to demonstrate achievement of the outcomes for a unit. The areas of study describe the specific knowledge and skills required to demonstrate a specific outcome. Teachers are required to develop a program for their students that meet the requirements of the curriculum design including:

eight focus areas which detail the mathematical knowledge and skills
four modules providing the contexts
the problem-solving cycle
a mathematical toolkit.

Learning should be planned according to learning goals and application specific to a module, with attention given to integrating the five applied learning principles within the program:

Motivation to engage in learning.
Applied learning practices.
Student agency in learning.
A student-centred and flexible approach.
Assessment practices which promote success.

Teachers should aim to facilitate learning through developing programs that enable students to gain an understanding of concepts and metalanguage to effectively apply and demonstrate learning goals and application in a holistic manner. Teachers should be mindful of developing programs which allow students to connect to authentic ‘real life’ knowledge, skills, environments and experiences outside the classroom. ‘Real-life’ learning experiences may include research, teamwork, verbal and written communication, incursions, excursions, simulations, inquiry approaches and project-based learning.

Attention should be given to developing a course that is;

relevant to students
contextually based
framed around the applied learning principles
employs a variety of manageable tasks
uses a variety of source material from reputable and reliable providers.

Teachers should also pay special attention to building the units of work around student interest. It is important that students engage with the topics explored and the best way to do this is to ascertain areas of student interest, expertise and common ground, and build or alter programs to reflect this.

A diagram depicting the structuring a program

These four components are intended to be taught in an integrated manner, and where possible they should not be taught in isolation.

It is helpful to view these components in relation to the analogy of baking a pie. The Numeracy in context including the focus areas represents the constituent ingredients used in the pie. The Problem-solving cycle provides the recipe to bake the pie. And the Mathematical toolkit is the equipment used in the making and baking of the pie.

Using this analogy, these components work together, and in isolation none would produce the pie. There are times where specific aspects of each component may be examined or practiced in isolation; however, where possible, the curriculum is designed so that the four components are taught together.

Numeracy in context

Numeracy in context outlines the four contexts under which the eight areas of study are to be taught. These contexts are:

Personal
Financial
Health and recreational
Civic

The mathematical knowledge and skills to be examined under each context is detailed in the curriculum.
This can be summarised as

Module	Numeracy	Focus area
Module 1	Personal numeracy	Location Systematics
Module 2	Financial numeracy	Number Change
Module 3	Health and recreational numeracy	Shape Quantity and measures
Module 4	Civic numeracy	Data Likelihood

Choosing the focus(es) of the numeracy context for study

For each module, the teacher undertakes to examine the mathematical skills and knowledge that is to be covered

For example: module is 2, financial numeracy.
The teacher undertakes to design a teaching program covering

Number learning goal: perform calculations of addition and subtraction with simple whole number amounts and familiar monetary amounts (into the 100s)
Change learning goal: repeating patterns with one element such as with shapes, or $2, $4, $6, $8, …

The teacher may decide to plan a learning program with a series of activities based around these mathematical knowledge and skills.

The contexts that they select will be the basis for a series of projects and/or activities to teach the mathematics.

In this example the teacher may choose to use play or fake money to teach money handling skills. The teacher may conduct an in-class market for students to learn about addition and subtraction, numbers of a certain magnitude, working with decimals and predicting pattern when counting money.

Overlaying the problem-solving cycle

Using the focus areas and the context, the teacher teaches these mathematical skills and knowledge using the problem-solving cycle.

In our example, the teacher introduces the concept of a market.

Identify the mathematics

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

What is the task and what is the purpose of the task?
What mathematics is required to solve this problem? Use highly explicit texts, manipulatives and/or stimuli material.
What knowledge do we need to learn?
What skills do we need to learn?

Act on and use the mathematics

The mathematical skills and knowledge that has been identified from the learning goal may need to be taught and practiced. The teacher may consider:

How can we apply the mathematical knowledge in context?
How can we apply these mathematical skills in context?
What process can be used in solving these questions
What technologies can be used to solve this problem?

The teacher may choose to introduce a series of activities to learn and practice these skills.

The teacher may also choose to select mini contexts to develop these skills. For example, the students may undertake activities around building their understanding of money. These activities may be hands-on.

The mathematics is then applied to the problem of participating in a class market.

Evaluate and reflect

Calculations should make sense and be reasonable in relation to the question. The teacher may consider:

Do the solutions make sense in relation to the context?
How can we check to see if the answer is reasonable?

In this phase the mathematics should mirror and reflect the real-life calculations that would occur. They stop, see if their answers make sense and are reasonable. They may need to adjust their thinking or calculations. In real life, calculations may not have clear solutions and they may require interpretation, adjustments and re-calculation.

Communicate and report

Students should learn to communicate mathematically, explaining the results of their mathematical processes in context. The teacher may consider:

What is the most appropriate form of communication for the task? For the context?
What mathematical language do the students need to use in communicating?
What symbols, diagrams and conventions are most relevant for this task or problem?

Explaining and communicating mathematical results is essential. Students should be able to communicate clearly with each calculation, for example they might say ‘thank you for your $20.00 note, here is your $13.40 in change.’

Developing the mathematical toolkit

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 learn to be adaptable to facilitate transferring their skills from one technology to another.

In the example given above, students may learn to use a variety of tools, such as calculators, bill splitting apps or calculation apps on their phones. Additionally, they might present their work digitally.

The Victorian Pathways Certificate 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 twenty-first 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 VPC studies, as flexible delivery of the VPC 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:

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 VPC unit cannot be used to demonstrate achievement in any other VPC unit, VCE VM 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 VPC 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.

The Victorian Pathways Certificate Work Related Skills 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.

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 study.

Assessment task	Employability skills selected facets
Practical and written investigations and projects Multimedia presentations, posters or reports Portfolios	Communication (using numeracy; persuading effectively) Problem solving (developing creative, innovative solutions; developing practical solutions; showing independence and initiative in identifying problems and solving them; solving problems; applying a range of strategies to problem solving in teams; using mathematics including budgeting and financial management to solve problems; applying problem solving strategies across a range of areas; testing assumptions taking the context of data and circumstances into account) Initiative and enterprise (adapting to new situations; being creative; identifying opportunities not obvious to others; translating ideas into action; generating a range of options; initiating innovative solutions) Planning and organising (managing time and priorities – setting timelines, coordinating tasks for self and with others; being resourceful; taking initiative and making decisions; collecting, analysing and organising information) Technology (having a range of basic IT skills; using IT to organise data; being willing to learn new IT skills)

Assessment task

Employability skills selected facets

Practical and written investigations and projects

Multimedia presentations, posters or reports

Portfolios

Communication (using numeracy; persuading effectively)

Problem solving (developing creative, innovative solutions; developing practical solutions; showing independence and initiative in identifying problems and solving them; solving problems; applying a range of strategies to problem solving in teams; using mathematics including budgeting and financial management to solve problems; applying problem solving strategies across a range of areas; testing assumptions taking the context of data and circumstances into account)

Initiative and enterprise (adapting to new situations; being creative; identifying opportunities not obvious to others; translating ideas into action; generating a range of options; initiating innovative solutions)

Planning and organising (managing time and priorities – setting timelines, coordinating tasks for self and with others; being resourceful; taking initiative and making decisions; collecting, analysing and organising information)

Technology (having a range of basic IT skills; using IT to organise data; being willing to learn new IT skills)

*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.

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 VPC 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 VPC Numeracy.

'… It is important to understand there is a distinct difference between teaching Aboriginal culture and teaching about Aboriginal culture. It is not appropriate for a non-Aboriginal person to teach Aboriginal culture, that is the traditional or sacred knowledge and systems belonging to Aboriginal people. For these kinds of teaching and learning experiences it is essential to consult and collaborate with members of your local Aboriginal or Torres Strait Islander community. It is appropriate, however, for a non-Aboriginal person to teach about Indigenous Australia, its history and its people in much the same way as a teacher of non-German heritage might teach about Germany, its history and its people … As teachers, the onus is on us to learn about Indigenous Australia, in just the same way we inform ourselves about any other subject we teach …'

Source: Victorian State Government, Education and Training

Other resources when considering Aboriginal and Torres Strait Islander perspectives:

Aboriginal and Torres Strait Islander Curricula (University of Melbourne)

Bring Them Home

Closing the Gap Report

National Museum of Australia

Closing the Gap events

CORE

Mathematics Glossary (Victorian Curriculum Foundation–10)

Department of Education and Training - Numeracy glossary

Victorian Responsible Gambling Foundation

ACCC: Scamwatch

Fairwork Australia

Consumer Affairs Victoria

Civic

Australian Red Cross

Melbourne City Mission

Disaster Resilience, Victorian Government

Recreational

AFL Victoria

Australia's official weather forecasts & weather radar - Bureau of Meteorology

Agriculture Victoria

Geoscience Australia: Community safety

Health

Healthy Schools

Department of Health

Nutrition Australia

Better Health, Victorian Government

VicRoads: Road safety

Teaching and learning sample activities

Teaching and learning activities

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

Teaching and learning activities should be designed with the learning goal in mind, and allow students to practice, apply and/or demonstrate their learning. If an activity is used for formative or summative assessment, teachers should develop a related assessment guide or rubric.

Please note: These activities must not be taught in isolation from the Problem-Solving Cycle or the Mathematical Toolkit.

Sample template for planning modules

Module	Numeracy	Focus area
Module 1	Personal numeracy	Location Systematics
Module 2	Financial numeracy	Number Change
Module 3	Health and recreational numeracy	Shape Quantity and measures
Module 4	Civic numeracy	Data Likelihood

Unit 1

Focus areas: Locations, Systematics

Module 1:

Personal numeracyrelates to the mathematical requirements for personal organisational matters involving money, time and travel, or for participation in community-based activities and events.
Personal numeracy relates to understanding, using and interpreting numerical and mathematical information presented and embedded in different formats, in order to undertake personally relevant activities in highly familiar situations.

Examples of learning activities

School Garden
Investigate the requirements for setting up and maintaining a school garden. Include plant selection, location, planting times, how to plant them, how often to water etc. Create a roster assigning the tasks required to maintain the garden. Investigate how long it will take for the plants to grow and record data on a calendar. Technology: scheduling and calendar applications.
Random acts of kindness
Create a secret plan that shows three ‘random acts of kindness’. The plan needs to highlight what you are doing, when you are doing it, how you will do it and the desired outcome. The acts could include different themes such as: at school (e.g. making an effort to be polite and help in canteen or opening the door/carrying something for staff) at home (e.g. doing the dishes for the week, feeding the pet, walking the pet or making a cup of tea for someone), or for a friend (e.g. writing a nice note or text message or bringing them an extra muesli-bar). Collect evidence and create a Gantt chart to show the timeline of your plan. Create a small presentation that highlights the surprise and gratitude shown for the acts of kindness. Technology: spreadsheet or scheduling applications.
A new hobby
Choose a new sport or hobby of interest and investigate the start-up costs including any materials or equipment to purchase, uniforms, club fees and/or sign-up costs. Create a spreadsheet to show the total. Technology: spreadsheets.
Getting places
Explore the routes taken to regular destinations, such as school, part-time jobs, a regular appointment venue or a family member’s house. Compare the regular route with the new route and make note of the similarities and differences (such as major roads vs minor roads, times taken). If practical, take these new routes at the same time of day to help with comparisons and decide which route is the better. Technology: mapping applications or websites, clock/timer/stopwatch.
Lunchtime activities
As a class, organise to run a series of lunchtime activities for a target audience (such as peer group or junior year level). Create a Gantt chart to show what activity is on for the day, and who is responsible. Create newsletter articles for promotion and organise with different departments if equipment is needed to be borrowed and if rooms need to be booked. Technology: spreadsheets and scheduling or roster applications, calendar/school booking systems if applicable.
Food Drive
As a class organise a food drive for a local charity. Students use a school map to identify the best locations around the school environment for collection points. Students create a roster to regularly collect donations and, as a record for the charity, use an appropriate format for creating a stockpile inventory of the items before storing them. Students are to read labels and ensure food is stored correctly as per food labels. Technology: maps, spreadsheets and scheduling or roster applications, safe food handling procedures.
Tracking your time
Create a personal daily or weekly schedule to track how much time is spent on different activities such as school, sleep, homework/study, socialising, preparing and eating meals, sport/recreation, showering/brushing teeth/doing hair. Look ahead to include a week that includes upcoming events, activities and due dates, and adjust the schedule accordingly. Technology: scheduling or diary applications.
Using maps
Use maps or directories to locate shopping centres, zoos, aquariums and theme parks etc. Describe their location in relation to your current position or other landmarks. Give or follow directions to move between locations. Categorise the locations by 1) amenities and services (such as toilets, information services and disability service locations), and 2) places of interest. Technology: maps and directories.

Focus areas: Number, Change

Module 2:

Financial numeracy relates to undertaking basic and personal financial transactions and making straightforward decisions regarding the use and management money.

Financial numeracy involves managing relevant personal, social or work-related everyday financial costs, charges, income and expenditure.

Examples of learning activities

Payslips
Look at different payslips. Consider what is common and different about each one. Locate important information such as: the payee, the payer, the ABN, the bank account, the hours worked, the pay rate, the taxable income and rate, and superannuation contributions. If possible, have students compare their own payslips.
Calculating pay-rates
Practice calculating pay-rates using award wages from Fair Work Australia, including time-and-a-half and double-time. Use your own payslip or a sample pay slip and check the calculations are correct to ensure you have been paid correctly.
Financial Literacy glossary
Explore Fair Work Australia’s website - Pays and Wages and develop a Financial Literacy glossary focusing on terms such as minimum wage, allowances and penalty rates. Use their pay calculator to check students own wages for part-time work, apprenticeship or traineeship.
Debit vs Credit cards
Use https://moneysmart.gov.au/ to investigate the difference between debit account cards and credit cards. Create a PMI graphic organiser to collate information and write a summary that explains the positives and negatives of each type of account.
Safe online spending
Investigate the ways to safely spend money online. Investigate online scams usinghttps://www.scamwatch.gov.au/. Present findings as a newspaper article exploring famous scams, things to be careful or alert for, and how to be aware when shopping online. For an extra challenge, set audience targets for their newspaper articles, such as elderly audiences who are new to using the internet for shopping, and people who have English as a second language.
Big ticket buy
Research the cost of a big-ticket item. Create a savings plan using a spreadsheet program. Highlight current part-time job wages (if applicable) and include regular expenses. Calculate how long it would take to save for that item with a fortnightly saving schedule. Technology: spreadsheeting program.
Comparing big ticket buys
Compare the costs of a big-ticket item, such as a laptop or a refrigerator, and compare the overall costs when using different payment methods such as cash, credit cards, store lay-by, store credit programs and other ‘buy now and pay later’ programs. Identify the negatives such as hidden fees or high interest rates. Technology: spreadsheets.
Meal budget
Design a two-course meal for a group of four people on a budget of $20. List ingredients and costs using a spreadsheet program. Shop for, prepare and share the meal with invited guests at a luncheon. Technology: spreadsheets, supermarket apps/websites.
Design a uniform
Design and cost a Vocational Pathways school hoodie or t-shirt. Alternatively, you may work with the uniform department at your local club or school’s sport department to help organise the ordering of a new uniform. Collect the orders, and organise bulk order, delivery and payment. Prepare customer invoices, receipts and payments. Distribute the uniforms.
Exploring Savings
Explore the effects of regular savings and how regular contributions grow over time. Allow students to predict how much they could save over certain time periods if they made regular contributions based on different set parameters, such as a percentage from their current earnings, or a regular amount. Students could explore their own online banking services or apps and the savings goals sections. Technology: spreadsheet, savings app.
Subscription services
Investigate the current subscription services that students have access to (such as movies, music, gaming and magazines), and compare these to their ultimate subscription wish list. Students can explore the monthly costs, the yearly costs, and combined totals of the services they have access to and their wish list.
Meal voucher
Using a menu from a local restaurant, determine what you could buy with a $50 voucher to feed yourself and three friends. You are not able to get cash change from the voucher, so therefore should spend as close to $50 as possible. Discuss the positives and negatives of using vouchers over cash. Technology: menu apps, calculator.
Compare the cost
Compare the costs of the same item from different supermarkets and determine which is cheaper. Examine advertised sale items, bulk buys or bonus buys in supermarkets and determine the savings (if any) and the better option for purchases. Technology: calculator.

Unit 2

Focus areas: Shape, Quantity and measures

Module 3:

Health and recreational numeracy relates to accessing, understanding and using foundational mathematical information to be aware of issues related to health and well-being, or when engaging in different recreational activities. Recreational activities may include indoor and outdoor pursuits, arts, social media, gaming and other personal interests and hobbies.

Examples of learning activities

Sugar and salt
Explore the sugar or salt content found in snack foods or drinks. Use digital scales to accurately measure the amount of sugar/salt found in the snacks and place it in a small clear plastic bag. Create a display board that shows the empty packaging, an easy-to-read label with the sugar/salt amount and the sample bag. Draw links with health messages from trusted sources. Technology: digital scales.
Athletics carnival
Plan some novelty activities that can be completed during Athletics Carnival such as egg and spoon race, 3-legged race and thong-throw, and ask if points can be awarded and contribute to the winner of the day. Prior to the day, explore different measurements that are appropriate for the events, and practice marking them out for accuracy and authenticity of the event. On the day, set up the novelty events, highlighting the start and finish lines. Measure and record the results of the events. Technology: measuring tape, marking equipment, trundle wheel, timers.
Cookie cutters
Explore the shape of different cookies or cookie cutters and predict which shapes are the best to use for: the strongest biscuit shape, the least crumbling biscuit and the easiest biscuit to eat. Follow a recipe and accurately measure ingredients to make a range of cookie shapes. Review the final cookie shape products and compare with your predictions. Technology: kitchen scales and measuring cups.
Drinking glasses
Explore the shape of different drinking glasses and identify the equivalent 2D and 3D shapes. Discuss the purposes of drink glasses being different shapes in the hospitality industry. Estimate and measure the capacity of each glass by filling each with coloured water then pouring into a measuring jug. Review your estimations and check if you ordered the glasses correctly. Technology: measuring cups and jugs.
Sports equipment
Examine a selection of different balls used across different sports such as netball, basketball, football, rugby, cricket, hockey etc. Discuss the size and shape of each ball, and the difference between their sizes, shapes and weights in light of their use. Investigate the official sizing for sports and their recommendations, and accurately measure and record the size and weight of the balls examined to see if they compare true. Technology: measuring tape, scales.
Road signs
Examine the shape of common road signs. Discuss the properties of the shapes and why certain shapes and colours may be used for different signs. Estimate then measure (where safe to do so) the height and size of road signs. Technology: measuring tapes, apps.
Participate in a scavenger hunt
Conduct a scavenger hunt around the school looking for specific shaped items and ask students to take photos of them. On the photos label the shape and its common properties such as side lengths, 90° angles and parallel sides. Technology: camera, editing software.
Create a scavenger hunt
Have students create a scavenger hunt around school or the local community using orienteering and navigating with a directional compass. Students will have check-in points or clues at each station about the next point. Technology: directional compass.
Estimating time & distance
Estimate the distance between two locations around the school using informal and formal units, e.g. number of steps vs. metres. Estimate the time it would take to move between the two locations. Accurately measure the distances and times and compare with initial estimates. Technology: tape measures, laser measures, trundle wheel, pedometer, stopwatch, timer.
Timetables
Explore a variety of timetables, identifying the time format used. Interpret the information provided on the timetable which may include converting 24-hour time to 12-hour time for understanding.
Scheduling
Examine upcoming important dates, such as public holidays, schoolwork due dates, work schedule or other appointments and accurately record them on a diary or calendar app. Create notes in organisers to check-in with dates coming up as tracking tools to completing any set work or completing any requirements prior to the dates set.
Veggie soup
Find a vegetable soup recipe and guess the total weight of vegetables in the soup before finding the total. Explore the percentage of each individual vegetable within the soup. Have students repeat the task with another recipe (e.g. pizza and toppings, hamburger and ingredients, rocky road and ingredients).
Healthy Food Pyramid
Read the Healthy Food Pyramid and Australian Dietary Guidelines on Nutrition Australia and make a table that highlights the daily food recommendations for adolescents. Create some simple and healthy food suggestions for breakfasts and lunches that can be displayed around the senior area to highlight the importance of eating well and participating in exercise.
Packaging
Explore a series of different sized boxes and unfold them to explore the net shapes. Resize the packaging to see if it can be can reduced but maintain the same volume.

Focus areas: Data, Likelihood

Module 4:

Civic numeracy refers to activities related to participating in the student’s community and social life through being aware of and knowing about government and societal data, information and related processes.

Examples of learning activities

Daily specials
Record the daily specials at the school canteen over a one- or two-week period. Interview other students and ask about the canteen specials and how frequently they occur. Use this combined data to make predictions on when and how frequently different canteen specials will occur. Technology: spreadsheets and data collection tools.
Rainfall patterns
Examine rainfall patterns in your local area. Use data from http://www.bom.gov.au/. Explore probabilities and percentages regarding likelihood of rain and discuss changing weather patterns over time.
School bins
Conduct a feasibility survey to see if there are enough bins within the school environment. Prepare and produce a report for the school management. Technology: spreadsheets, survey tools such as Google survey.
Class Survey
Conduct a class survey to get to know each other, such as number of siblings, favourite food, part-time job and future career choice, and use different visual data methods to display the results. Technology: spreadsheets, survey tools such as Google survey.
Weather data
Explore upcoming weather data, and compare the information given from different websites or apps. Determine the likelihood of different weather events happening over the next week based on the weather predictions. Technology: weather apps.
Music charts
Examine different music charts and identify any patterns in the top artists. Discuss the likelihood of artists becoming chart toppers.
Litter survey
Conduct a quadrant or zone survey of the litter in the school yard or local park, recording the amount and type of litter found in different areas. The survey can also be repeated at different times of the day to explore any patterns in the amount of litter found. Use this information to suggest strategies to reduce the likelihood of littering. Technology: cameras, spreadsheets.
Vic Roads data
Examine graphs and infographics that show differences in crash risks for Learner (L) and Provisional (P) drivers. Use Vic Roads data and discuss when you are most at risk of having a road accident.

Unit 3

Personal numeracy relates to the mathematical requirements for personal organisational matters involving money, time and travel, or for participation in community-based activities and events. Personal numeracy relates to understanding, using and interpreting numerical and mathematical information presented and embedded in different formats, in order to undertake personally relevant activities in familiar situations.

Examples of learning activities	Learning goals	Application
Getting places Use the school map to create instructions to get from one school building/location to another. The student reads their instructions out loud for a partner to follow, and check if they lead to the intended building. Feedback on the instructions is given using graphic organisers using the ‘plus, minus, interesting’ (PMI) technique. Repeat the task switching partners. Extension task: Take students out to a local area, such as a park or shopping centre and complete the task. Technology: Maps, mapping apps and directories.	Location: find locations and give directions in relation to everyday, familiar places within their extended vicinity.	Location: provide oral and written instructions to describe the location of familiar, local places and landmarks.
Amazing scavenger race Provide a paper copy of a map taken from an interactive map. Students use the maps to create their own amazing race or scavenger hunt. They then complete each other tasks using the interactive map. Extension task: Compare and contrast the accessibility and usability of paper vs digital maps. Technology: Maps, mapping applications.	Location: find locations and give directions using simple navigation with everyday, familiar maps and technologies.	Location: use interactive, digital technologies and paper maps to locate familiar places or landmarks and places of significance, and describe suitable routes.
Food glorious food Use an online food ordering application (app) to plan a family meal. Explore the app for special offers, delivery costs, opening hours or other features, then simulate the input of an order. Extension task: Using different food ordering apps, compare costs to find the best deal. Compare these apps to ordering direct from restaurants. Consider discount codes and undertake calculations to compare costs. Technology: Food ordering applications, restaurant websites, search engines.	Systematics: read and interpret data inputs and outputs summarise information plan and schedule.	Systematics: input data into familiar apps read input and output data interpret simple output data plan and schedule with common and familiar data.
Sporting warmups Examine the lines on a sports field or a sports court such as for basketball or netball. Develop warm-up routines for athletes of the sport and shout out instructions from the sidelines using directional language. Technology: timing devices such as stopwatch.	Location: use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.	Location: give and follow simple oral and written directions to familiar locations use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.
Fictional maps Create a map that relates to a fairytale or to a story that has a journey. Include compass directions with the map. Use directional language and compass directions to describe the different characters’ journeys. Technology: Map making apps such as fictional map making apps.	Location: find locations and give directions using simple navigation with everyday, familiar maps and technologies use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.	Location: provide oral and written instructions to describe location of familiar, local places and landmarks give and follow simple oral and written directions to familiar locations use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.
Finding recipes Consider an interactive recipe or cooking applications and websites. Choose a recipe and explore what happens when you choose different inputs, such as specific ingredients (chicken, cheese etc.), dietary requirements (vegetarian or allergy-specific etc.), specific timeframes (less than 15-minute prep time, less than 20-minute cook time etc.). Investigate how changing certain parameters, such as the number of servings or units of measurement, alters the recipe information. Technology: Cooking or recipe applications and websites.	Systematics: use common and familiar information including data read and interpret data inputs and outputs summarise information plan and schedule.	Systematics: input data into familiar apps read input and output data interpret simple output data plan and schedule with common and familiar data.
A big cook-up Plan the kitchen schedule for preparing and cooking a two-course meal for a group of ten people that will sit down to eat at 1 pm. The plan should include a list of necessary ingredients, a plan for preparation, the cooking order for the ingredients, and a menu. Technology: Spreadsheet for scheduling, supermarket websites.	Systematics: use common and familiar information including data read and interpret data inputs and outputs summarise information plan and schedule.	Systematics: read input and output data plan and schedule with common and familiar data.
Treasure map Create a treasure map for the local primary school or for younger siblings. Write clues for them to follow and find the hidden treasure. The clues should include the language of direction, simple angle measures, and simple compass directions. The clues should include the language of direction, simple angle measures and simple compass directions Technology: Maps	Location: find locations and give directions in relation to everyday, familiar places within their extended vicinity use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.	Location: provide oral and written instructions to describe the location of familiar, local places and landmarks give and follow simple oral and written directions to familiar locations use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.
Geocaching Explore the worldwide recreational activity of Geocaching and use geocaching websites to explore the location of caches near the school or other familiar locations. Create Geocaches within the school grounds (or in nearby appropriate locations) and record the GPS location of the caches and write directions to find the caches. Use appropriate directional language. In groups, students use GPS technology and written clues to find the hidden caches. Extension: Use official geocaching websites or applications to locate caches in the local area beyond the school grounds. Technology: GPS and geocaching applications.	Location: find locations and give directions in relation to everyday, familiar places within their extended vicinity find locations and give directions using simple navigation with everyday, familiar maps and technologies use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.	Location: use interactive, digital technologies and paper maps to locate familiar places or landmarks and places of significance, and describe suitable routes use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.

Examples of learning activities

Learning goals

Application

Getting places

Use the school map to create instructions to get from one school building/location to another. The student reads their instructions out loud for a partner to follow, and check if they lead to the intended building. Feedback on the instructions is given using graphic organisers using the ‘plus, minus, interesting’ (PMI) technique.

Repeat the task switching partners.

Extension task: Take students out to a local area, such as a park or shopping centre and complete the task.

Technology: Maps, mapping apps and directories.

Location:

find locations and give directions in relation to everyday, familiar places within their extended vicinity.

Location:

provide oral and written instructions to describe the location of familiar, local places and landmarks.

Amazing scavenger race

Provide a paper copy of a map taken from an interactive map. Students use the maps to create their own amazing race or scavenger hunt. They then complete each other tasks using the interactive map.
Extension task: Compare and contrast the accessibility and usability of paper vs digital maps.

Technology: Maps, mapping applications.

Location:

find locations and give directions using simple navigation with everyday, familiar maps and technologies.

Location:

use interactive, digital technologies and paper maps to locate familiar places or landmarks and places of significance, and describe suitable routes.

Food glorious food

Use an online food ordering application (app) to plan a family meal. Explore the app for special offers, delivery costs, opening hours or other features, then simulate the input of an order.

Extension task: Using different food ordering apps, compare costs to find the best deal. Compare these apps to ordering direct from restaurants. Consider discount codes and undertake calculations to compare costs.

Technology: Food ordering applications, restaurant websites, search engines.

Systematics:

read and interpret data inputs and outputs
summarise information
plan and schedule.

Systematics:

input data into familiar apps
read input and output data
interpret simple output data
plan and schedule with common and familiar data.

Sporting warmups

Examine the lines on a sports field or a sports court such as for basketball or netball. Develop warm-up routines for athletes of the sport and shout out instructions from the sidelines using directional language.

Technology: timing devices such as stopwatch.

Location:

use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.

Location:

give and follow simple oral and written directions to familiar locations
use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.

Fictional maps

Create a map that relates to a fairytale or to a story that has a journey. Include compass directions with the map. Use directional language and compass directions to describe the different characters’ journeys.

Technology: Map making apps such as fictional map making apps.

Location:

find locations and give directions using simple navigation with everyday, familiar maps and technologies
use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.

Location:

provide oral and written instructions to describe location of familiar, local places and landmarks
give and follow simple oral and written directions to familiar locations
use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.

Finding recipes

Consider an interactive recipe or cooking applications and websites. Choose a recipe and explore what happens when you choose different inputs, such as specific ingredients (chicken, cheese etc.), dietary requirements (vegetarian or allergy-specific etc.), specific timeframes (less than 15-minute prep time, less than 20-minute cook time etc.).

Investigate how changing certain parameters, such as the number of servings or units of measurement, alters the recipe information.

Technology: Cooking or recipe applications and websites.

Systematics:

use common and familiar information including data
read and interpret data inputs and outputs
summarise information
plan and schedule.

Systematics:

input data into familiar apps
read input and output data
interpret simple output data
plan and schedule with common and familiar data.

A big cook-up

Plan the kitchen schedule for preparing and cooking a two-course meal for a group of ten people that will sit down to eat at 1 pm. The plan should include a list of necessary ingredients, a plan for preparation, the cooking order for the ingredients, and a menu.

Technology: Spreadsheet for scheduling, supermarket websites.

Systematics:

use common and familiar information including data
read and interpret data inputs and outputs
summarise information
plan and schedule.

Systematics:

read input and output data
plan and schedule with common and familiar data.

Treasure map

Create a treasure map for the local primary school or for younger siblings. Write clues for them to follow and find the hidden treasure. The clues should include the language of direction, simple angle measures, and simple compass directions. The clues should include the language of direction, simple angle measures and simple compass directions

Technology: Maps

Location:

find locations and give directions in relation to everyday, familiar places within their extended vicinity
use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.

Location:

provide oral and written instructions to describe the location of familiar, local places and landmarks
give and follow simple oral and written directions to familiar locations
use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.

Geocaching

Explore the worldwide recreational activity of Geocaching and use geocaching websites to explore the location of caches near the school or other familiar locations.

Create Geocaches within the school grounds (or in nearby appropriate locations) and record the GPS location of the caches and write directions to find the caches. Use appropriate directional language. In groups, students use GPS technology and written clues to find the hidden caches.

Extension: Use official geocaching websites or applications to locate caches in the local area beyond the school grounds.

Technology: GPS and geocaching applications.

Location:

find locations and give directions in relation to everyday, familiar places within their extended vicinity
find locations and give directions using simple navigation with everyday, familiar maps and technologies
use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E.

Location:

use interactive, digital technologies and paper maps to locate familiar places or landmarks and places of significance, and describe suitable routes
use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn.

Financial numeracy relates to undertaking basic and personal financial transactions and making straightforward decisions regarding the use and management of money. Financial numeracy involves managing relevant personal, social or work-related everyday financial costs, charges, income and expenditure.

Examples of learning activities	Learning goals	Application
Streaming services Research which streaming services students use at home or on their own devices. Calculate total monthly costs for each service and for each student. Determine how much a year is spent on each streaming service and total costs. Research alternative options or recommendations to help reduce this cost. Students present the findings to their families. Technology: Calculation app or calculator.	Number: whole numbers and monetary amounts up to $10 000 common decimals and fractions and percentages such as 1/4, 1/10, 50%, 0.25, 0.75 and other common decimals up to two decimal places, such as money and time addition and subtraction with borrowing and decomposition the order of the four arithmetical operations.	Number: perform calculations of addition and subtraction with numbers up to 10 000 recognise and use common decimals, fractions, and percentages such as and other common decimals up to two decimal places.
Earning the dollars Explore online examples of different pay slips. Locate and discuss the key features legally required to appear on a payslip, such as: employee’s name, company details, hours worked, hourly rate, superannuation contribution, gross wage, net wage etc. Extension task: Use payslips to calculate expected gross pay. Calculate the net wage when given the superannuation and tax amounts. Have students compare results in a class discussion. Technology: Spreadsheets, calculator, online payslips.	Number: place value and reading numbers up to 10 000 whole numbers and monetary amounts up to $10 000 addition and subtraction with borrowing and decomposition the order of the four arithmetical operations.	Number: recognise and use common decimals, fractions, and percentages such as and other common decimals up to two decimal places calculate simple problems using the order of the four arithmetical operations with whole-value numbers only.
Meal planning for the family Explore different apps and websites that support meal planning and discuss the benefits. Create a weekly meal plan. Consider the number of people to cater for and any special requirements. Create a shopping list for the weekly meal plans. Extension task: Use the meal plan to make a price comparison using a supermarket app or website. Extension task: Introduce discounts that the students need to respond to reduce the overall total of their shopping lists. Technology: Supermarket apps or websites.	Number: whole numbers and monetary amounts up to $10 000 common decimals and fractions and percentages such as 1/4, 1/10, 50%, 0.25, 0.75 and other common decimals up to two decimal places such as money and time the order of the four arithmetical operations.	Number: perform calculations of addition and subtraction with numbers up to 10 000 recognise and use common decimals, fractions, and percentages such as 3/4, 10%, 75% or 0.75, and other common decimals up to two decimal places calculate simple problems using the order of the four arithmetical operations with whole value numbers only.
Splitting the bill Explore different bill-sharing or bill-splitting apps that housemates or friends can use to keep track of shared costs. Provide different menus that replicates restaurants. Provide students with a notepad to write down the orders. Students visit all menus and write down an order for each. Students then total the orders, finding the total cost for each order. Teachers provide reasonable (play money) cash amounts that are used to pay the bill (e.g. a $153.45 bill is paid with $200). Students calculate the cost per person if the cost is evenly shared. Students calculate the change given and explore if it can be evenly split amongst those at the table. At the end of the task, all amounts (total bill, total change, total split amount) will be broken down into Australian notes and coins place value. Technology: Bill splitting apps, restaurant websites, food ordering apps, calculator or calculating app.	Number: place value and reading numbers up to 10 000 whole numbers and monetary amounts up to $10 000 addition and subtraction with borrowing and decomposition the order of the four arithmetical operations.	Number: identify place value and read whole numbers up to 10 000 perform calculations of addition and subtraction with numbers up to 10 000 find and use multiplication and division facts related to small whole-value number values only calculate simple problems using the order of the four arithmetical operations with whole-value numbers only.
Shopping madness Choose a popular retail store and ask students to imagine they have a voucher to spend, e.g. $100 or $2,000. Ask students to choose five items they would buy from that store. The sum of the five items should be as close to the target value as possible. Technology: Retail websites and apps.	Number: whole numbers and monetary amounts up to $10 000 addition and subtraction with borrowing and decomposition.	Number: identify place value and read whole numbers up to 10 000 perform calculations of addition and subtraction with numbers up to 10 000.
Counting notes Use an Australian coin resource kit or play money. Have students separate the notes into their values, and look at patterns that include: How many $5 notes make $100? How many $10 notes make $100? How many $50 notes make $1000? Place random piles of notes around different stations, and have students add up each pile. Extension: Use a timer to replicate a ‘close shift’ at work. Replicate a template that is used in workplaces to record how many of each note, total of each note type, and grand total of each till.	Number: place value and reading numbers up to 10 000 whole numbers and monetary amounts up to $10 000 Change: familiar and simple patterns or sequences in patterns and in a series of numbers familiar mathematical language and terms used in numerical pattern prediction changes and reconciliation in sets of numbers into the 1000s	Number: identify place value and read whole numbers up to 10 000 perform calculations of addition and subtraction with numbers up to 10 000. Change: identify and describe relationships and patterns of change in sets of simple numerical values demonstrate repeating patterns with one element, e.g. $2, $4, $8, $16, … reconcile and compare of simple numbers in context, e.g. prices, warehouse stock levels.
Garden patterns Explore tiling patterns found in gardens, bathrooms and fabric patterns. Find a local garden and take photos/make sketches of the patterns used and take measurements of the area. Look online for similar pavers and estimate the cost of the pavers. Technology: Retail websites and apps, area/space apps to calculate space.	Number: whole numbers and monetary amounts up to $10 000 multiplication and division related to small whole- value numbers the order of the four arithmetical operations. Change: familiar and simple patterns or sequences in patterns and in a series of numbers repeating patterns with two or more elements such as simple pricing structures.	Number: find and use multiplication and division facts related to small whole-value number values only calculate simple problems using the order of the four arithmetical operations with whole-value numbers only. Change: predict simple pattern continuation using familiar mathematical terms demonstrate repeating arithmetical and spatial patterns of familiar and simple numbers with more than one element.

Examples of learning activities

Learning goals

Application

Streaming services

Research which streaming services students use at home or on their own devices. Calculate total monthly costs for each service and for each student. Determine how much a year is spent on each streaming service and total costs. Research alternative options or recommendations to help reduce this cost. Students present the findings to their families.

Technology: Calculation app or calculator.

Number:

whole numbers and monetary amounts up to $10 000
common decimals and fractions and percentages such as 1/4, 1/10, 50%, 0.25, 0.75 and other common decimals up to two decimal places, such as money and time
addition and subtraction with borrowing and decomposition
the order of the four arithmetical operations.

Number:

perform calculations of addition and subtraction with numbers up to 10 000
recognise and use common decimals, fractions, and percentages such as and other common decimals up to two decimal places.

Earning the dollars

Explore online examples of different pay slips. Locate and discuss the key features legally required to appear on a payslip, such as: employee’s name, company details, hours worked, hourly rate, superannuation contribution, gross wage, net wage etc.

Extension task: Use payslips to calculate expected gross pay. Calculate the net wage when given the superannuation and tax amounts. Have students compare results in a class discussion.

Technology: Spreadsheets, calculator, online payslips.

Number:

place value and reading numbers up to 10 000 whole numbers and monetary amounts up to $10 000
addition and subtraction with borrowing and decomposition
the order of the four arithmetical operations.

Number:

recognise and use common decimals, fractions, and percentages such as and other common decimals up to two decimal places
calculate simple problems using the order of the four arithmetical operations with whole-value numbers only.

Meal planning for the family

Explore different apps and websites that support meal planning and discuss the benefits. Create a weekly meal plan. Consider the number of people to cater for and any special requirements. Create a shopping list for the weekly meal plans.

Extension task: Use the meal plan to make a price comparison using a supermarket app or website.

Extension task: Introduce discounts that the students need to respond to reduce the overall total of their shopping lists.

Technology: Supermarket apps or websites.

Number:

whole numbers and monetary amounts up to $10 000
common decimals and fractions and percentages such as 1/4, 1/10, 50%, 0.25, 0.75 and other common decimals up to two decimal places such as money and time
the order of the four arithmetical operations.

Number:

perform calculations of addition and subtraction with numbers up to 10 000
recognise and use common decimals, fractions, and percentages such as 3/4, 10%, 75% or 0.75, and other common decimals up to two decimal places
calculate simple problems using the order of the four arithmetical operations with whole value numbers only.

Splitting the bill

Explore different bill-sharing or bill-splitting apps that housemates or friends can use to keep track of shared costs.

Provide different menus that replicates restaurants. Provide students with a notepad to write down the orders. Students visit all menus and write down an order for each. Students then total the orders, finding the total cost for each order. Teachers provide reasonable (play money) cash amounts that are used to pay the bill (e.g. a $153.45 bill is paid with $200). Students calculate the cost per person if the cost is evenly shared. Students calculate the change given and explore if it can be evenly split amongst those at the table.

At the end of the task, all amounts (total bill, total change, total split amount) will be broken down into Australian notes and coins place value.

Technology: Bill splitting apps, restaurant websites, food ordering apps, calculator or calculating app.

Number:

place value and reading numbers up to 10 000
whole numbers and monetary amounts up to $10 000
addition and subtraction with borrowing and decomposition
the order of the four arithmetical operations.

Number:

identify place value and read whole numbers up to 10 000
perform calculations of addition and subtraction with numbers up to 10 000
find and use multiplication and division facts related to small whole-value number values only
calculate simple problems using the order of the four arithmetical operations with whole-value numbers only.

Shopping madness

Choose a popular retail store and ask students to imagine they have a voucher to spend, e.g. $100 or $2,000. Ask students to choose five items they would buy from that store. The sum of the five items should be as close to the target value as possible.

Technology: Retail websites and apps.

Number:

whole numbers and monetary amounts up to $10 000
addition and subtraction with borrowing and decomposition.

Number:

identify place value and read whole numbers up to 10 000
perform calculations of addition and subtraction with numbers up to 10 000.

Counting notes

Use an Australian coin resource kit or play money. Have students separate the notes into their values, and look at patterns that include:

How many $5 notes make $100?
How many $10 notes make $100?
How many $50 notes make $1000?

Place random piles of notes around different stations, and have students add up each pile.

Extension: Use a timer to replicate a ‘close shift’ at work. Replicate a template that is used in workplaces to record how many of each note, total of each note type, and grand total of each till.

Number:

place value and reading numbers up to 10 000
whole numbers and monetary amounts up to $10 000

Change:

familiar and simple patterns or sequences in patterns and in a series of numbers
familiar mathematical language and terms used in numerical pattern prediction
changes and reconciliation in sets of numbers into the 1000s

Number:

identify place value and read whole numbers up to 10 000
perform calculations of addition and subtraction with numbers up to 10 000.

Change:

identify and describe relationships and patterns of change in sets of simple numerical values
demonstrate repeating patterns with one element, e.g. $2, $4, $8, $16, …
reconcile and compare of simple numbers in context, e.g. prices, warehouse stock levels.

Garden patterns

Explore tiling patterns found in gardens, bathrooms and fabric patterns.
Find a local garden and take photos/make sketches of the patterns used and take measurements of the area. Look online for similar pavers and estimate the cost of the pavers.

Technology: Retail websites and apps, area/space apps to calculate space.

Number:

whole numbers and monetary amounts up to $10 000
multiplication and division related to small whole- value numbers
the order of the four arithmetical operations.

Change:

familiar and simple patterns or sequences in patterns and in a series of numbers
repeating patterns with two or more elements such as simple pricing structures.

Number:

find and use multiplication and division facts related to small whole-value number values only
calculate simple problems using the order of the four arithmetical operations with whole-value numbers only.

Change:

predict simple pattern continuation using familiar mathematical terms
demonstrate repeating arithmetical and spatial patterns of familiar and simple numbers with more than one element.

Unit 4

Health and recreational numeracy involves accessing, understanding and using foundational mathematical information to raise awareness of issues related to health and wellbeing. This can include engaging in different recreational activities such as indoor and outdoor pursuits, arts, social media, gaming and other personal interests and hobbies.

Examples of learning activities	Learning goals	Application
Stride to measure Walk the perimeter of a commonly used sporting court. Use stride length to estimate the length walked. Estimate the perimeter. Measure with a trundle wheel or measuring device and compare your estimates with the actual measurement. Technology: Trundle wheel, measuring devices.	Quantity & measures: common metric distance and length measurements and quantities.	Quantity & measures: estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.
Look, measure, compare Look at two different sporting fields or courts, e.g. football and cricket. Make predictions about which court will have the bigger length, width, perimeter and area. Measure and perform calculations to compare the fields or courts. Technology: Trundle wheel, measuring tape, digital measuring devices.	Shape: common two-dimensional shapes such as circles, triangles, quadrilaterals. Quantity & measures: common metric distance and length measurements and quantities.	Shape: recognise and name common two-dimensional shapes and simple three-dimensional objects Quantity & measures: estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.
A measured estimate Estimate the number of steps used when walking around school on a routine day, such as from the front gate to the classroom, classroom to toilets, canteen to back oval etc. Use a measuring tool to calculate and compare to your estimate. Technology: Step-counter, step-counter app.	Quantity & measures: common metric distance and length measurements and quantities.	Quantity & measures: estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.
Weigh up the options Bring in common items from daily life – such as filled water bottle, loaf of bread, block of butter, bottle of shampoo, a book, a gaming controller, a shoe, a hat, a calculator etc. For the first challenge, each student sorts the items from the lightest to the heaviest in front of the class – based on their own knowledge. Record results on the board. For the second challenge, one student takes a leader role and feels the weight of the items.The student leader responds to class questions and moves the items around. Record results on the board. In the third challenge, all students feel the weights of the items and as a class, they agree on the order. Record results on the board. In the final challenge, students weigh items and list all the weights on the board. The students compare the estimates to the actual weights. Technology: Digital and analogue scales.	Quantity & measures: common metric distance and length measurements and quantities.	Quantity & measures: estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities.
Cups to measure Collect different size bottles, such as 250ml, 600ml, 1L, 2L, 3L. Fill each bottle with water. For each bottle, estimate the number of standard cups. Measure and check estimates. Compare the quantity found versus the quantity shown on the label. Technology: measuring cups.	Quantity & measures: simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml.	Quantity & measures: make simple conversions between commonly used units, e.g. one cup is 250 ml.
Play and compare Investigate and play a traditional Aboriginal or Torres Strait Islander game. Compare the rules, equipment (size, weight) or playing spaces (perimeter, area) with popular games played in your schools. Technology: Trundle wheel, measuring tape, digital measuring device, scales.	Quantity & measures: common metric distance and length measurements and quantities simple perimeter and area measurements such as measuring area by squares. Shape: common two-dimensional shapes such as circles, triangles, quadrilaterals.	Quantity & measures: estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius. Shape: recognise and name common two-dimensional shapes and simple three-dimensional objects.
Shape in the community Take a walk around the neighbourhood and take photos of the street signs and road signs in use. Explore and discuss the messages being communicated by the signs and the shapes being used. Students to consider if common shapes are used to communicate similar messages? Technology: Recording device such as a phone camera.	Shape: common two-dimensional shapes such as circles, triangles, quadrilaterals.	Shape: recognise and name common two-dimensional shapes and simple three-dimensional objects.
Food packaging Provide different food containers to illustrate common three-dimensional shapes such as cylinder, cube, rectangular prism etc. Identify and explore the common properties of the objects. Explore the different shapes used within the packaging and how the packaging works (strong base, easy to re-fold top to secure after use, falls apart after opening etc). Unfold the packaging into its net and get students to draw the nets onto graph paper to examine the shapes and area being used. To explore the object in detail, create a table for students to fill out about each piece of packaging, e.g. how many different shapes are being used? How many edges, faces, corners etc. are there? Extension: Provide printable net templates for students to build different objects.	Shape: common two-dimensional shapes such as circles, triangles, quadrilaterals simple three-dimensional objects such as cube, cylinder, simple prisms common properties and language of two-dimensional shapes and three-dimensional objects (such as edges, faces, corners) and making connections between nets and three-dimensional objects, e.g. matching solids and nets.	Shape: recognise and name common two-dimensional shapes and simple three-dimensional objects construct common two-dimensional shapes and simple three-dimensional objects categorise common two-dimensional shapes and simple three-dimensional objects and shapes according to different common classifications match common and familiar three-dimensional solids and their nets.
Kitchen measuring Use the school kitchens to explore measuring cups and spoons. Make a comparison table to show the capacity of each, e.g. millilitres/grams. Estimate volumes and masses of water or rice. Students measure the water and rice using the measuring tools. Students discuss how to accurately measure with the product and scales. Technology: Measuring cups, measuring spoons, digital or analogue scales, measuring jug.	Quantity & measures: simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml.	Quantity & measures: estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities make simple conversions between commonly used units, e.g. one cup is 250 ml.
Cookbook Collate students favourite family recipes to make a class cookbook. Each recipe should include: an ingredients list, preparation tips, cooking instructions and cooking time. Students should ensure their recipe uses metric measurements and if not, make the appropriate changes. Extension: Choose and make a recipe. Technology: Measuring cups, measuring spoons, digital scales, analogue scales, measuring jug.	Quantity & measures: simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml common units of quantities, such as mass (g, Kg) and volume (ml, L) and temperature in degrees Celsius.	Quantity & measures: estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius make simple conversions between commonly used units, e.g. one cup is 250 ml.
Calendars Students estimate how many days and weeks they are at school for in the school year. Use student organisers/planners to calculate, remembering not to count the school holidays. Students estimate how many days and weeks before another event, such as the next school holidays or end of the year. Students use their organisers to work it out. Use an online calendar function to plan and schedule. Extension one: Calculate age in weeks and days instead of years. Extension two: Students identify a future event that they are looking forward to, for example their next big birthday (18th or 21st, starting their apprenticeship, a holiday planned etc). Students make a countdown of days and weeks. Technology: Student organiser, online calendar	Quantity & measures: digital and analogue calendars.	Quantity & measures: read and interpret common and familiar dates and times using digital and analogue clocks and calendars.

Examples of learning activities

Learning goals

Application

Stride to measure

Walk the perimeter of a commonly used sporting court. Use stride length to estimate the length walked.

Estimate the perimeter. Measure with a trundle wheel or measuring device and compare your estimates with the actual measurement.

Technology: Trundle wheel, measuring devices.

Quantity & measures:

common metric distance and length measurements and quantities.

Quantity & measures:

estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.

Look, measure, compare

Look at two different sporting fields or courts, e.g. football and cricket. Make predictions about which court will have the bigger length, width, perimeter and area. Measure and perform calculations to compare the fields or courts.

Technology: Trundle wheel, measuring tape, digital measuring devices.

Shape:

common two-dimensional shapes such as circles, triangles, quadrilaterals.

Quantity & measures:

common metric distance and length measurements and quantities.

Shape:

recognise and name common two-dimensional shapes and simple three-dimensional objects

Quantity & measures:

estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities
estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.

A measured estimate

Estimate the number of steps used when walking around school on a routine day, such as from the front gate to the classroom, classroom to toilets, canteen to back oval etc. Use a measuring tool to calculate and compare to your estimate.

Technology: Step-counter, step-counter app.

Quantity & measures:

common metric distance and length measurements and quantities.

Quantity & measures:

estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.

Weigh up the options

Bring in common items from daily life – such as filled water bottle, loaf of bread, block of butter, bottle of shampoo, a book, a gaming controller, a shoe, a hat, a calculator etc.

For the first challenge, each student sorts the items from the lightest to the heaviest in front of the class – based on their own knowledge. Record results on the board.

For the second challenge, one student takes a leader role and feels the weight of the items.The student leader responds to class questions and moves the items around. Record results on the board.

In the third challenge, all students feel the weights of the items and as a class, they agree on the order. Record results on the board.

In the final challenge, students weigh items and list all the weights on the board. The students compare the estimates to the actual weights.

Technology: Digital and analogue scales.

Quantity & measures:

common metric distance and length measurements and quantities.

Quantity & measures:

estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities.

Cups to measure

Collect different size bottles, such as 250ml, 600ml, 1L, 2L, 3L. Fill each bottle with water. For each bottle, estimate the number of standard cups. Measure and check estimates.

Compare the quantity found versus the quantity shown on the label.

Technology: measuring cups.

Quantity & measures:

simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml.

Quantity & measures:

make simple conversions between commonly used units, e.g. one cup is 250 ml.

Play and compare

Investigate and play a traditional Aboriginal or Torres Strait Islander game. Compare the rules, equipment (size, weight) or playing spaces (perimeter, area) with popular games played in your schools.

Technology: Trundle wheel, measuring tape, digital measuring device, scales.

Quantity & measures:

common metric distance and length measurements and quantities
simple perimeter and area measurements such as measuring area by squares.

Shape:

common two-dimensional shapes such as circles, triangles, quadrilaterals.

Quantity & measures:

estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities
estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius.

Shape:

recognise and name common two-dimensional shapes and simple three-dimensional objects.

Shape in the community

Take a walk around the neighbourhood and take photos of the street signs and road signs in use. Explore and discuss the messages being communicated by the signs and the shapes being used. Students to consider if common shapes are used to communicate similar messages?

Technology: Recording device such as a phone camera.

Shape:

common two-dimensional shapes such as circles, triangles, quadrilaterals.

Shape:

recognise and name common two-dimensional shapes and simple three-dimensional objects.

Food packaging

Provide different food containers to illustrate common three-dimensional shapes such as cylinder, cube, rectangular prism etc.

Identify and explore the common properties of the objects. Explore the different shapes used within the packaging and how the packaging works (strong base, easy to re-fold top to secure after use, falls apart after opening etc). Unfold the packaging into its net and get students to draw the nets onto graph paper to examine the shapes and area being used.

To explore the object in detail, create a table for students to fill out about each piece of packaging, e.g. how many different shapes are being used? How many edges, faces, corners etc. are there?

Extension: Provide printable net templates for students to build different objects.

Shape:

common two-dimensional shapes such as circles, triangles, quadrilaterals
simple three-dimensional objects such as cube, cylinder, simple prisms
common properties and language of two-dimensional shapes and three-dimensional objects (such as edges, faces, corners) and making connections between nets and three-dimensional objects, e.g. matching solids and nets.

Shape:
recognise and name common two-dimensional shapes and simple three-dimensional objects

construct common two-dimensional shapes and simple three-dimensional objects
categorise common two-dimensional shapes and simple three-dimensional objects and shapes according to different common classifications
match common and familiar three-dimensional solids and their nets.

Kitchen measuring

Use the school kitchens to explore measuring cups and spoons. Make a comparison table to show the capacity of each, e.g. millilitres/grams. Estimate volumes and masses of water or rice. Students measure the water and rice using the measuring tools. Students discuss how to accurately measure with the product and scales.

Technology: Measuring cups, measuring spoons, digital or analogue scales, measuring jug.

Quantity & measures:

simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml.

Quantity & measures:

estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities
make simple conversions between commonly used units, e.g. one cup is 250 ml.

Cookbook

Collate students favourite family recipes to make a class cookbook. Each recipe should include: an ingredients list, preparation tips, cooking instructions and cooking time. Students should ensure their recipe uses metric measurements and if not, make the appropriate changes.

Extension: Choose and make a recipe.

Technology: Measuring cups, measuring spoons, digital scales, analogue scales, measuring jug.

Quantity & measures:

simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml
common units of quantities, such as mass (g, Kg) and volume (ml, L) and temperature in degrees Celsius.

Quantity & measures:

estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities
estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius
make simple conversions between commonly used units, e.g. one cup is 250 ml.

Calendars

Students estimate how many days and weeks they are at school for in the school year. Use student organisers/planners to calculate, remembering not to count the school holidays.

Students estimate how many days and weeks before another event, such as the next school holidays or end of the year. Students use their organisers to work it out.

Use an online calendar function to plan and schedule.

Extension one: Calculate age in weeks and days instead of years.

Extension two: Students identify a future event that they are looking forward to, for example their next big birthday (18th or 21st, starting their apprenticeship, a holiday planned etc). Students make a countdown of days and weeks.

Technology: Student organiser, online calendar

Quantity & measures:

digital and analogue calendars.

Quantity & measures:

read and interpret common and familiar dates and times using digital and analogue clocks and calendars.

Civic numeracy refers to activities where students participate in their community and social life through being aware of government and societal data, information and related processes.

Examples of learning activities	Learning goals	Application
Streaming services Consider some interesting questions about the class use of streaming services. Use these questions to collect some simple data from the class. Using software, sort the data into a table or spreadsheet. Use a graphing or display functions to display the data. Draw some conclusions from your tables and graphs. Technology: Spreadsheets.	Data: simple data collection methods including use of tables, spreadsheets and tallies display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.	Data: collect, collate, sort and order data sets, e.g. use survey to collect data, use tallies to collate data and insert set of data into a table/spreadsheet, sort from lowest to highest construct simple charts or graphs using familiar data with simple scales, e.g. in 1’s, 5’s or 10’s read, identify and interpret familiar information and facts from simple tables, graphs and infographics make simple comparisons and interpretations between provided simple data sets and their representations.
School expenses Consider the cost of the items needed to get ready for the start of the school year. Collect your data using an online table or spreadsheet. Display your data as a graph or infographic. Using your displays, compare the costs from the booklist to online ordering. Interpret the information you have collected to make a recommendation about where to purchase different items. Technology: Retail outlets online or apps, catalogues.	Data: display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.	Data: construct simple charts or graphs using familiar data with simple scales, e.g. in 1’s, 5’s or 10’s read, identify and interpret familiar information and facts from simple tables, graphs and infographics make simple comparisons and interpretations between provided simple data sets and their representations.
Weather patterns Consider a country with different weather to Australia. For the previous month find their monthly average temperature (maximum temperature). Repeat for the weather in your area, nearest town or city. As a travel writer, write a summary of the data presented, making predictions for readers when is the best time to travel and what to pack, and when are the times to avoid. Technology: Weather apps or websites, ‘what to pack’ apps, travel blogs.	Data: simple data collection methods including use of tables, spreadsheets and tallies. Likelihood: likelihood of familiar events or occurrences happening using everyday language of chance common likelihoods and chance events such as weather predictions, dice or spinner success rates language and relative magnitude of the risk of common or familiar events of chance.	Data: collect, collate, sort and order data sets, e.g. use survey to collect data, use tallies to collate data and insert set of data into a table/spreadsheet, sort from lowest to highest read, identify and interpret familiar information and facts from simple tables, graphs and infographics make simple comparisons and interpretations between provided simple data sets and their representations. Likelihood: order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’ read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure order and compare the relative magnitude of the risk of common and familiar events of chance use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.
Say it aloud Create a set of examples that examine risk, such as ‘what is the chance that all students will be in correct uniform today?’ or ‘what is the chance there will be a female prime minister in Australia within the next ten years?’ or ‘what is the chance Melbourne CBD will experience snow?’. Examine the statements and compile a list of the language students are using to examine chance and risk. Students submit two statements they create into a spin-generator. Compile suggested responses and complete the task together as a class. Technology: Spin generator.	Likelihood: likelihood of familiar events or occurrences happening using everyday language of chance common likelihoods and chance events such as weather predictions, dice or spinner success rates language and relative magnitude of the risk of common or familiar events of chance.	Likelihood: order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’ read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure order and compare the relative magnitude of the risk of common and familiar events of chance use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.
Likelihood Create a list of events for students to question the likelihood of their occurrence, e.g. one in a hundred year floods, earthquakes in Victoria, volcanoes erupting in Australia, election forecasts, winning the Lotto. Students look into the likelihood of events occurring and connect their research with the language list they have been compiling. Technology: Internet.	Likelihood: likelihood of familiar events or occurrences happening using everyday language of chance common likelihoods and chance events such as weather predictions, dice or spinner success rates language and relative magnitude of the risk of common or familiar events of chance.	Likelihood: order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’ read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure order and compare the relative magnitude of the risk of common and familiar events of chance use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.
Data in the media Present different tables, charts, infographics and graphs found in the news media. Highlight key features that students should be looking for to understand the information, such as titles, axes labels, legends etc. Present a graph or chart that has misinformation or is misleading. Discuss how the data has been presented to tell a particular story or point of view. Technology: News media websites.	Data: display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.	Data: read, identify and interpret familiar information and facts from simple tables, graphs and infographics make simple comparisons and interpretations between provided simple data sets and their representations.
Data in advertising – how it’s used to persuade us! Consider examples of targeted advertising on social media. Identify the data found in the advertising such as: 4 out 5 women recommend or 70% more effective than other brands. Discuss how the advertisers can make these claims and decide whether they may be correct or not.	Data: display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.	Data: read, identify and interpret familiar information and facts from simple tables, graphs and infographics.

Examples of learning activities

Learning goals

Application

Streaming services

Consider some interesting questions about the class use of streaming services. Use these questions to collect some simple data from the class. Using software, sort the data into a table or spreadsheet. Use a graphing or display functions to display the data. Draw some conclusions from your tables and graphs.

Technology: Spreadsheets.

Data:

simple data collection methods including use of tables, spreadsheets and tallies
display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.

Data:

collect, collate, sort and order data sets, e.g. use survey to collect data, use tallies to collate data and insert set of data into a table/spreadsheet, sort from lowest to highest
construct simple charts or graphs using familiar data with simple scales, e.g. in 1’s, 5’s or 10’s
read, identify and interpret familiar information and facts from simple tables, graphs and infographics
make simple comparisons and interpretations between provided simple data sets and their representations.

School expenses

Consider the cost of the items needed to get ready for the start of the school year. Collect your data using an online table or spreadsheet. Display your data as a graph or infographic. Using your displays, compare the costs from the booklist to online ordering. Interpret the information you have collected to make a recommendation about where to purchase different items.

Technology: Retail outlets online or apps, catalogues.

Data:

display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.

Data:

construct simple charts or graphs using familiar data with simple scales, e.g. in 1’s, 5’s or 10’s
read, identify and interpret familiar information and facts from simple tables, graphs and infographics
make simple comparisons and interpretations between provided simple data sets and their representations.

Weather patterns

Consider a country with different weather to Australia. For the previous month find their monthly average temperature (maximum temperature). Repeat for the weather in your area, nearest town or city. As a travel writer, write a summary of the data presented, making predictions for readers when is the best time to travel and what to pack, and when are the times to avoid.

Technology: Weather apps or websites, ‘what to pack’ apps, travel blogs.

Data:

simple data collection methods including use of tables, spreadsheets and tallies.

Likelihood:

likelihood of familiar events or occurrences happening using everyday language of chance
common likelihoods and chance events such as weather predictions, dice or spinner success rates
language and relative magnitude of the risk of common or familiar events of chance.

Data:

collect, collate, sort and order data sets, e.g. use survey to collect data, use tallies to collate data and insert set of data into a table/spreadsheet, sort from lowest to highest
read, identify and interpret familiar information and facts from simple tables, graphs and infographics
make simple comparisons and interpretations between provided simple data sets and their representations.

Likelihood:

order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’
read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure
order and compare the relative magnitude of the risk of common and familiar events of chance
use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.

Say it aloud

Create a set of examples that examine risk, such as ‘what is the chance that all students will be in correct uniform today?’ or ‘what is the chance there will be a female prime minister in Australia within the next ten years?’ or ‘what is the chance Melbourne CBD will experience snow?’. Examine the statements and compile a list of the language students are using to examine chance and risk. Students submit two statements they create into a spin-generator. Compile suggested responses and complete the task together as a class.

Technology: Spin generator.

Likelihood:

likelihood of familiar events or occurrences happening using everyday language of chance
common likelihoods and chance events such as weather predictions, dice or spinner success rates
language and relative magnitude of the risk of common or familiar events of chance.

Likelihood:

order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’
read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure
order and compare the relative magnitude of the risk of common and familiar events of chance
use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.

Likelihood

Create a list of events for students to question the likelihood of their occurrence, e.g. one in a hundred year floods, earthquakes in Victoria, volcanoes erupting in Australia, election forecasts, winning the Lotto.

Students look into the likelihood of events occurring and connect their research with the language list they have been compiling.

Technology: Internet.

Likelihood:

likelihood of familiar events or occurrences happening using everyday language of chance
common likelihoods and chance events such as weather predictions, dice or spinner success rates
language and relative magnitude of the risk of common or familiar events of chance.

Likelihood:

order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’
read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure
order and compare the relative magnitude of the risk of common and familiar events of chance
use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.

Data in the media

Present different tables, charts, infographics and graphs found in the news media. Highlight key features that students should be looking for to understand the information, such as titles, axes labels, legends etc. Present a graph or chart that has misinformation or is misleading. Discuss how the data has been presented to tell a particular story or point of view.

Technology: News media websites.

Data:

display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.

Data:

read, identify and interpret familiar information and facts from simple tables, graphs and infographics
make simple comparisons and interpretations between provided simple data sets and their representations.

Data in advertising – how it’s used to persuade us!

Consider examples of targeted advertising on social media. Identify the data found in the advertising such as: 4 out 5 women recommend or 70% more effective than other brands. Discuss how the advertisers can make these claims and decide whether they may be correct or not.

Data:

display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics.

Data:

read, identify and interpret familiar information and facts from simple tables, graphs and infographics.

Sample approaches to developing assessment

Assessment

Assessment must be a part of the regular teaching and learning program and should be completed mainly in the classroom within a predetermined timeframe. Assessment is to be undertaken as an ongoing process which integrates knowledge and skills with practical applications over a period of time. It will require a combination of evidence collected through teacher observations along with the collection of records of student work.

When developing assessment tasks, teachers should refer to the VCAA policies and school assessment procedures as specified in the VPC Administrative Handbook.
The studies in a VPC program must be assessed in accordance with the requirements and guidelines outlined in the curriculum designs for the studies delivered in the learning program.

The assessment should be:

Valid and reliable

Assessment tasks/activities should be designed to reflect the nature of the outcomes/elements of the study.
Students should be assessed across a range of different tasks/activities and contexts.
Assessment should be conducted on a number of occasions.

Fair

Assessment tasks/activities should be grounded in a relevant context and be sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location.
Instructions for assessment tasks should be clear and explicit.

Flexible

Assessment should be open ended and flexible to meet the specific needs of students.
Students should have the opportunity to demonstrate achievement at their own level and pace.

Efficient

Assessment instruments that provide evidence of achievement across a range of outcomes/studies should be used.

The assessment tools used to collect evidence of student achievement (performance descriptors, rubrics and/or marking guide) should reflect the Modules, Learning Goals and Application 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 a unit and/or module. 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 VPC 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.

Vocational Pathways – Numeracy SCHOOL-ASSESSED COURSEWORK
Performance descriptors
Unit: Module:	DESCRIPTOR: typical performance in each range
Unit: Module:	Very low	Low	Medium	High	Very high
Learning goals and applications Students should be able to apply the mathematical knowledge and skills from the learning goals and applications across the specified numeracy context.	Limited or no use of mathematical conventions, symbols and language	Some use of mathematical conventions, symbols and language	Correct use of mathematical conventions, symbols and language	Correct and consistent use of mathematical conventions, symbols and language	Comprehensive and consistent use of mathematical conventions, symbols and language
	Limited or no use of key concepts	Some use of key concepts	Adequate use of key concepts	Detailed use of key concepts	Thorough use of key concepts
	Little or no use of mathematical skills to obtain solutions	Some use of accurate mathematical skills to obtain solutions	Correct use of accurate mathematical skills to obtain solutions	Correct and consistent use of accurate mathematical skills to obtain solutions	Comprehensive and consistent use to obtain solutions
Problem solving Students should be able to use the problem-solving cycle in an applied learning context, relevant to the mathematics that is reflected in the learning goals and applications, and across the specified numeracy context.	Limited or no identification of the mathematics relevant to the task and context	Some identification of the mathematics relevant to the task and context	Adequate identification of the mathematics relevant to the task and context	Detailed identification of the mathematics relevant to the task and context	Comprehensive identification of the mathematics relevant to the task and context
	Very limited or no use of mathematical procedures to solve problems	Limited use of key mathematical procedures to solve problems	Sound use of key mathematical procedures to solve problems	Clear use of key mathematical procedures to solve problems	Insightful use of key mathematical procedures to solve problems
	Very limited or no communication of results	Limited communication of results	Satisfactory communication of results	Careful communication of results	Thorough communication of results
Mathematical toolkit Students should develop a mathematical toolkit and be able to select and apply the appropriate mathematical tool to undertake the numeracy tasks.	Very limited or inappropriate use of technology	Limited use of technology	Satisfactory use of technology	Careful use of technology	Comprehensive use of technology
	Very limited or inappropriate use of the conventions of different technologies	Limited use of the conventions of different technologies	Satisfactory use of the conventions of different technologies	Careful use of the conventions of different technologies	Comprehensive use of the conventions of different technologies
	Very limited or no interpretation of the results of technology	Limited interpretation of the results of technology	Satisfactory interpretation of the results of technology	Clear interpretation of the results of technology	Insightful interpretation of the results of technology

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

Unit 1:

Module 1: Personal numeracy

Focus areas: Location, Systematics

Detailed example – RACE IN THIS SPACE

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Personal numeracy, and students use their mathematical toolkit to support Personal numeracy.

Task – Students will plan an amazing race around the Melbourne CBD and visit five landmarks.

Introduce the context and focus areas

The context is Personal numeracy and the two focus areas are Location and Systematics.

The following learning goals will be considered:

find location and direction in relation to everyday, familiar places within the vicinity
find location and direction with everyday, simple and familiar maps and technologies
use everyday oral directions using informal language such as left/right, up/down, front/back, under/beside/over
find common and familiar information and data inputs
read data outputs
summarise information.

Application:

orally describe location of familiar, local places
use interactive and paper maps to locate highly familiar places or objects
give and follow simple oral directions to highly familiar locations
input simple data into familiar apps
read simple output data
interpret simple output data.

Identify the context

The context to be considered in this example activity will be students planning an amazing race type activity in the Melbourne CBD. Students use maps to plan challenges and complete each other’s challenges to provide feedback and test their navigational skills.

Students use the problem-solving cycle to undertake a series of activities related to reading maps, using grids and writing their own grids, so they can have a successful day out in the CBD.

Provide stimulus material such as:

City of Melbourne Maps website keeps up-to-date information on the maps, boundaries and information for Melbournians and tourists.

Step 1: Identify the mathematics

Discuss with students how the city looks – pointing out the grid formation. Ask why they think it is like this and the benefits this might offer. Ask students their experiences of being in the city, what the city is famous for, why do they think tourists come and visit, what streets they know etc.

Present the students with a map of the Melbourne CBD and ask them to point to the north and discuss. Place this compass direction on the map.

Ask them to highlight some key features such as:

Train stations: Flinders St Station, Southern Cross, Flagstaff, Melbourne Central and Parliament
Famous Meeting Places: The State Library, Federation Square, St Paul’s Cathedral

Have students research famous landmarks in the Melbourne CBD and list them under these categories:

The Arts

Landmark

Address

Grid Reference

Historic Buildings

Landmark

Address

Grid Reference

Shopping

Landmark

Address

Grid Reference

Food/Restaurants

Landmark

Address

Grid Reference

Sports

Landmark

Address

Grid Reference

Step 2: Act on and use the mathematics

Maps and grids – you may choose to print your own CBD map and draw your own grid reference for student use.

Show the students a short clip of ‘The Amazing Race’ – a reality television show based on pairs working together, completing challenges, and racing around the world. Introduce the students to the idea that they will be creating a similar style of race, where they will need to give directions to three landmarks and the first group back in the quickest time wins.

Ask students to work in groups. Present the challenge of making an Amazing Race within the boundary of the map that you present them.

Each group must:

make directions that start and finish at Federation Square
visit one of example landmarks in each categories listed above
write clear instructions for the teams to follow
provide two printouts of all instructions to the teacher.

On the day – when students are completing their tasks – make sure they take photos of each site they visit for proof of completion of the tasks. If you feel adventurous, have students complete different activities at each task – such as a dance, singing a song and playing a game of scissors/paper/rock.

Students writing instructions:

Examples of written language for instructions includes left/right, up/down, north/south/east/west, etc.

Starting at Federation Square cross over at the lights and stand in front of the Church St Paul’s Cathedral and continue walking north up Swanston Street. Continue until you find the State Library of Victoria, this is your historic building. Take a photo out the front as your evidence.

At the Corner of the State Library and Latrobe Street, turn right and start walking up Latrobe Street in an easterly direction. You will be walking up to Spring Street, which is at the top of the grid. Then turn right and walk down to the Windsor Hotel and take a photo showing the hotel sign. This is your famous food site.

Class Meeting Time in the City

As a class, work together to use the PTV app or website to determine how to plan the journey so that everyone will be at the meeting point before the time required. Discuss morning travel peak times, possible lates or no-shows on the network and what the student procedure is if they are running late on the day.

Allow students to choose five landmarks within the city boundaries and use a table as above to store their data. Discuss the idea of how to order the five landmarks in the challenge, with a recommendation of having the further distances to travel first so that the closest ones are last (this will allow the teacher to call students back quickly if there is an emergency or if groups are taking too long). Present students with a new copy of the map so they can map their five landmarks to determine the visiting order and highlight the walking trail to help write their directions.

Step 3: Evaluate and reflect

Students are to submit their plans and highlighted map to the teacher for feedback. This is necessary to ensure that the walking trail chosen will work and the instructions are clear and have enough detail. Teachers should ensure the instructions are clear and easily understood.

Students swap their plans with another group who will complete the task via Google Maps and provide feedback.

Discuss or present students with a template to use that will have the instructions for each visiting landmark.

Class Meeting Time in theCity

Students write up the two plans to get into the city and meeting place and share them in a public space so all students can see it. Teacher to read before it is shared publicly to ensure the instructions are clear and easy to read.

Step 4: Communicate and report

Students transfer their instructions into the template and print two copies before they leave school for the excursion. On the day of the excursion, bring enough copies for the students to each have their own map.

Teams swap their races and time each group, setting off with a staggered start (1 to 2 minute intervals and record the times in your own notebook). Remind students they need to complete the race, visit each landmark, take photos of the group (minus the photographer/selfies) and of the landmarks. Students need to complete a peer-review template for the individual task and the overall day. Reinforce that the winner is the group who completes the challenges in the quickest time you can make other competitions if your class is competitive. Have a safety talk before starting the race.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 1: Personal numeracy
it is part of a range of activities for Module 1: Personal Numeracy

This task is fair because

it allows students and teachers to work together to build the activity around landmarks and modes of travel that a relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location.
It allows students to work together in groups and support one another.
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Module 2: Financial numeracy

Focus areas: Number, Change

Detailed example – FOODS UP

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Financial numeracy, and students use their mathematical toolkit to support Financial numeracy.

Introduce the context and focus areas

The context is Financial numeracy and the two focus areas are Number and Change.

The following learning goals will be considered:

place value and numbers up to 1000
whole numbers and monetary amounts up to $1000
addition and subtraction (with no borrowing or decomposition) of whole numbers and familiar monetary amounts into the 100s
common, simple unit fractions such as 1/2, 1/4 and 1/10
changes and number matching with simple numbers, for example prices increasing or decreasing, matching corresponding numbers.

Application:

perform calculations of addition and subtraction with simple whole number amounts and familiar monetary amounts (into the 100s)
recognise and understand very common simple unit fractions, decimals and percentages.
number matching and comparison of simple numbers in context such as matching prices from receipts to on-the-shelf items
demonstrate repeating patterns with one element, for example $2, $4, $6, $8, …

Identify the context

Students use the problem-solving cycle to undertake a series of activities related to issues found in the costs of meal planning for their home situation. They compare the costs of home cooked meals with a pre-packed food delivery service that includes all ingredients and recipes. Students explore budgeting for food costs, as well as the value of family time and ask if there is a cost of convenience.

Step 1: Identify the mathematics

Discuss with students the organisation of meals in the home. Consider how meals are organised, where the shopping is done, who in the household shops, who cooks, who helps etc.

Ask students to complete a Plus Minus, Interesting (PMI) graphic organiser to compare home cooked meals to food delivery service meals, where they deliver pre-portioned ingredients with recipe cards.

Home cooked meals			Pre-prepared food delivery kits
Plus	Minus	Interesting	Plus	Minus	Interesting

Challenge the students to compare the costs of four home cooked meals vs the cost of four from a food delivery service where they deliver pre-portioned ingredients with recipe cards.

Step 2: Act on and use the mathematics

Students are to compare the cost of a home cooked meal with that from a pre-prepared or pre-packaged meal delivery service.

Students should choose a recipe from a pre-prepared or pre-packaged delivery service. Using an online shopping app or website, ask students to do a cost analysis of the ingredients.

Repeat this for four meals.

Use spreadsheets for all calculations and to collate information.

Display the totals for each as a side-by-side comparison bar chart.

Step 3: Evaluate and reflect

Students check their calculations and look for errors in the decision making. Students may consider issues such as costing salt or taking a portion of the cost as this is a staple pantry item.

Step 4: Communicate and report

Students should communicate clearly which is better, a home cooked meal or a pre-packaged or prepared meal. They should be able to use their mathematical calculations as evidence for their assertions.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 2: Financial numeracy
it is part of a range of activities for Module 2: Financial numeracy.

This task is fair because

it allows students to plan a meal for the activity that is relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
it allows students to use familiar information from their personal lives to complete the task
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Unit 2:

Module 3: Health and recreational numeracy

Focus areas: Shape, Quantity and measures

Detailed example – THE GREAT MARBLE RUN

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Health and recreational numeracy and students use their mathematical toolkit to support Shape and Quantity and measures.

Introduce the context and focus areas

The context is Health and recreational numeracy and the two focus areas are: Shape and Quantity and measures.

The following learning goals will be considered:

common and familiar one- and two-dimensional shapes such as lines, triangles, circles and squares
common properties of different one- and two-dimensional shapes such as size, colour, number and type of sides (straight/curved)
use common and familiar basic metric measurements and quantities such as length, mass, capacity/volume, time and temperature in everyday ways such as personal height and weight, door height, liquid measurement, temperatures
recognise common and familiar units such as m, cm, Kg, L, degrees C.

Application:

recognise common and familiar one- and two-dimensional shapes
name common and familiar one- and two-dimensional shapes
construct common and familiar two-dimensional shapes
categorise similar shapes according to common classifications
estimate lengths of highly familiar objects or items
order and compare simple everyday measures and quantities
recognise familiar and commonly used units of metric measurement.

Identify the context

Students use the problem-solving cycle to undertake a series of activities related to issues found in exploring, designing and testing their own marble run.

A marble run is a popular toy created by children where they connect many different pipes and attachments, watching the marbles filter down, e.g. water slides for marbles. Students use recycled materials from home to make their own marble runs and then have a class competition.

Step 1: Identify the mathematics

Challenge students to work in teams to make a marble run. Use recycled materials such as cardboard tubes from foil and wrapping paper or postage packs, different size and types of boxes.
Students must design their Marble Run with the following parameters:

be at least 80 cm in height
be free standing
include at least two ‘uphill’ sections
a straight run of at least 10 cm
include at least two more bends/turns
have both closed and open sections.

Students should discuss and consider how to

construct the base
construct the leg supports
make the twists and turns using straight cardboard
reinforce joints and connections.

Students should make some initial sketches as they consider these requirements before starting their construction.

Step 2: Act on and use the mathematics

Students construct their marble run. Students submit a list of materials they need and use a spreadsheet for record keeping.
Students estimate then calculate the length of their marble run.

Students identify the two-dimensional and three-dimensional shapes that form their build, name the shapes and make scale drawings of the build. Students calculate lengths, area and volume where possible.

Step 3: Evaluate and reflect

The teams trial their marble runs and see if they need to make modifications. Students list the modifications they are making, so they can report on the decisions and the effect of the decisions on the run.

Students check on their estimations and formulas. Are their answers reasonable? What does their gut say? Students use an online calculator to check their calculations.

Step 4: Communicate and report

Students film their marble run before and after the modifications. Students create a video to show their teacher and families what they have created and the mathematics behind it. Students discuss their marble run this can include: what modifications were made, and how they improved the build etc.

The class competition should have different criteria for successful marble runs. This could include: whose ran the fastest, who had the most creative run, whose run had the most twist/turn etc.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 3: Health and recreational numeracy
it is part of a range of activities for Module 3: Health and recreational numeracy.

This task is fair because

it allows teachers to develop instructions, tools and activities that are relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
it allows students to work in groups to support one another
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Module 4: Civic numeracy

Focus areas: Data, Likelihood

FEELING THIRSTY?

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Civic numeracy and students use their mathematical toolkit to support Data and Likelihood.

Introduce the context and focus areas

The context is Civic numeracy and the two focus areas are Data and Likelihood.

The following learning goals will be considered:

simple data collection by hand or with tables
simple cases of data, graphs and infographics
use everyday language to talk about the likelihood of an event occurring such as possible, impossible, unlikely, likely, certain, ‘Buckley’s chance’, ‘pigs might fly’, ‘dead-set’
understand language and relative magnitude of simple and highly familiar chance events.

Application:

collect and display simple data
read simple graphs such as bar or pie graphs
read simple tables
identify and locate key facts from simple data
recognise and use the everyday language of chance and likelihood
use everyday language to compare and order different and simple magnitudes of chance.

Identify the context

Students use the problem-solving cycle to undertake a series of activities related to issues found when exploring the weather and the impact of droughts. Students use previous data to track weather patterns and make predictions for the future.

The Bureau of Meteorology is a useful resource for this activity.

Step 1: Identify the mathematics

Discuss the impact of weather on farming food supplies/production and how farmers are relying more on science to help them out.

Watch ‘Understanding Droughts’ to learn how science is helping mitigate the impact of drought on farms.

Use the Bureau of Meteorology (BOM) app or website and look at the 7-day weather forecast.

Consider the terminology used with weather: temperature, high, low, pollen count, humidity, degrees, millimeters and time.

Step 2: Act on and use the mathematics

Ask students to survey the class about how often they check the weather forecast. Collect, collate and display the data.

Discuss the language of probability used in weather forecasts: certain, highly likely, likely equal chance, unlikely, highly unlikely, impossible. Ask students to arrange these words in order along a line. Provide scenarios such as the chances of winning a lottery and ask them to place the scenario on the line.

Examine the probability of rain given in weather forecasts. Using 100 charts (10-by-10 grid with the numbers one to one hundred printed in the squares). Shade the percentages to match, i.e. 10%, 70% etc., and discuss what percentage chance of rain means.

Conduct a short experiment with 100 different coloured blocks or lollies to demonstrate ideas of percentage and relate these to the chances of rain.

Step 3: Evaluate and reflect

Reflect on the 100 charts and explain how a 100 chart relates to a percentage. Relate this knowledge to the current weekly weather forecast and explain the current weather forecast.

Step 4: Communicate and report

The class survey and graphs should be presented to the class using either a poster or PowerPoint presentation. Students should present the current weather forecast and talk knowledgably about the data that informs the forecast.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 4: Civic numeracy
it is part of a range of activities for Module 4: Civic numeracy

This task is fair because

it allows teachers to develop instructions, tools and activities that are relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Unit 3:

Module 1: Personal numeracy

Focus areas: Location, Systematics

Detailed example – Using Technology for Planning and Organising – Plan a day trip.

Task – Students are to plan a day trip at a place of interest such as Melbourne Zoo, Melbourne Aquarium, ScienceWorks, Luna Park etc.

The context is personal numeracy, and the two focus areas mandated for this numeracy are location and systematics.

Learning goals:

find locations and give directions in relation to everyday, familiar places within the vicinity
find locations and give directions with everyday, simple and familiar maps and technologies
use informal, and some formal, language of location and direction, including simple angle measures and representations such as: quarter and half turns, left and right, N, S, W, E
use common and familiar information including data
read and interpret data inputs and outputs
summarise information
plan and schedule.

Application:

provide oral and written instructions to describe the location of familiar, local places and landmarks
use interactive, digital technologies and paper maps to locate familiar places or landmarks and places of significance, and describe suitable routes
give and follow simple oral and written directions to familiar locations
use everyday language of angles and compass directions (N, S, W, E) to describe familiar locations and directions such as half turn, U-turn
input data into familiar apps
read input and output data
interpret simple output data
plan and schedule with common and familiar data.

Introduce the context

Introduce the context of personal numeracy, the mathematical requirements for personal organisation involving transport and travel and planning a day trip.

To complete the tasks, students must:

Choose a place of interest and decide on a day, date and time for the visit. Students decide who they will go with, such as friends, family, siblings etc. Students go through the process of ‘mock’ booking tickets.
Determine how they will get to their chosen place of interest. Students choose an appropriate mode of transport, route to take and appropriate departure and arrival times.
Plan out a schedule for the day, making sure they can visit all the attractions they want to see as well as leaving time for eating.
Use the venue map to find specific locations and describe their location, such as information booth, food court, toilets, first aid, souvenir shop etc.

Step 1: Identify the mathematics

As a class, share strategies for trip planning. Generate a list of the technology used for the purposes of planning and scheduling such as maps, PTV, venue websites etc.

Discuss what information might be entered into websites/applications when planning day trips, such as booking tickets. Identify expected information to be shown after booking.

Review the terms: inputs (information that goes into the technology) and outputs(information that comes out of the technology). Share ideas and create a combined class list of inputs and outputs.

Choose a place of interest such as the zoo, Melbourne Aquarium, ScienceWorks, Luna Park etc. for the day trip and outline the requirements of the task.

Identify the following:

the purpose of the task
any specific mathematical skills, knowledge or technologies needed to complete the task (as outlined in the learning goals and application statements)
information needed to plan the day out, such as
- when and where they will be going and who they will be going with
- what they want to do once they are there, including any specific attractions or activities they want to see or do
- any other input information that may be needed.

Step 2: Act on and use the mathematics

Consider which technologies (analogue and digital) are readily available and will help support and examine the mathematics.

Choose the place of interest to visit for a day trip. Find the opening hours and decide on a day, date and time for their day out. Mimic the booking process for entry tickets and any other activities or events that need to be pre-booked. Write down the details of their day out, including location, day, date and arrival time, and take screenshots of any booking details.
Research at least two travel or transport options to reach the destination starting from school. Select the most appropriate mode of transport, route to take, appropriate departure and arrival times, giving reasons for their choice.

Describe the planned route using directional language. Include screenshots of the planned journey such as online maps or the PTV app.
Plan a general schedule for the day, including travel, attractions, rest breaks and meals.
Use a locations map to find specific locations and describe their location in relation to other key features or locations on the map, such as help desk/information centre, food court/kiosk, toilets, first aid and souvenir shop. Plan the directions they would give a friend who is lost, telling them how to get from one location to another designated spot, where they will meet them. Read out their directions to someone else, who needs to follow the directions by drawing them on a paper copy of the location’s map.

Step 3: Evaluate and reflect

Review plans to make sure they are reasonable and appropriate and make any changes if required. Consider the mathematics and check that estimates make sense and that solutions are mathematically reasonable.

Step 4: Communicate and report

Create an itinerary that explains the details of their day out. Use both formal and informal mathematical language to communicate. Where appropriate, use visualisations and representations, including mathematical symbols and notation.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 1: Personal numeracy.
it is part of a range of activities for Module 1: Personal numeracy.

This task is fair because

it allows students choice to plan their day out around locations and modes of transport that are relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
it can provide opportunities for students to work together to support one another
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Module 2: Financial numeracy

Focus areas: Number, Change

Detailed example – Supermarket investigation

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Financial numeracy, and students use their mathematical toolkit to support Financial numeracy.

Task – To determine which supermarket is cheapest, students investigate how much it costs to buy branded and unbranded items at Coles, Woolworths and Aldi.

The context is financial numeracy, and the two focus areas mandated for this numeracy are number and change.

Learning goals:

place value and reading numbers up to 10 000
whole numbers and monetary amounts up to $10 000
common decimals and fractions and percentages such as and other common decimals up to two decimal places, such as money and time
the order of the four arithmetical operations
familiar mathematical language and terms used in numerical pattern prediction
changes and reconciliation in sets of numbers into the 1000s
repeating patterns with two or more elements such as simple pricing structures.

Application:

identify place value and read whole numbers up to 10 000
perform calculations of addition and subtraction with numbers up to 10 000
recognise and use common decimals, fractions, and percentages such as and other common decimals up to two decimal places
find and use multiplication and division facts related to small whole-value number values only
calculate simple problems using the order of the four arithmetical operations with whole-value numbers only
familiar and simple patterns or sequences in patterns and in a series of numbers
familiar mathematical language and terms used in numerical pattern prediction
changes and reconciliation in sets of numbers into the 1000s
repeating patterns with two or more elements such as simple pricing structures.

Identify the context

Introduce the context of financial numeracy, exploring money management and becoming financially responsible.

A popular Australian supermarket’s biggest advertising campaign is that they are ‘nice, distinct’ and that families can save up to $2500 a year on groceries by shopping at this store. When it comes to grocery shopping, everyone has their preferences, but are the claims of this popular supermarket true?

Step 1: Identify the mathematics

Share supermarket shopping preferences as a class. Discuss which supermarkets are considered cheaper.

Discuss the costs of branded and unbranded items at Australian supermarkets.

Support students to identify the following:

The information they need to complete the task.
The mathematical calculations they will need to perform.
How they will make decisions about which supermarket is cheaper.

Step 2: Act on and use the mathematics

Consider which technologies (analogue and digital) are readily available and will help support and examine the mathematics.

Provide a ‘shopping cart’ of items to investigate, which may include:

Loaf of sliced white bread.
Block of chocolate.
Bottle of milk.
Tub of butter/margarine.
Box of breakfast cereal.
Bag of frozen vegetables.
Carton of eggs.
Frozen meal, e.g. Family Pizza or Lasagne.

Use websites for Australian supermarkets to select ‘branded’ items for the shopping cart. Note the numerical information given for each item, such as the item price, size or weight, unit price, and any discounts or sale price. Prompt students to try and select the same brand item at each supermarket or items that are the same product and size.
Repeat for ‘unbranded’ items.
Calculate the total cost of each of the shopping carts.

Step 3: Evaluate and reflect

Review the shopping carts and decide if the costs seem mathematically reasonable. Use the following questions as a guide:

Do your choices seem reasonable?
Are the totals correct?
What conclusions can you make about which supermarket is cheapest?
What other factors should you consider when deciding which supermarket is cheapest?

Step 4: Communicate and report

Explain which supermarket is cheapest and give reasons for this choice. Use both formal and informal mathematical language to communicate. Where appropriate, use visualisations and representations, including mathematical symbols and notation.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 2: Financial numeracy
it is part of a range of activities for Module 2: Financial numeracy.

This task is fair because

it allows teachers to develop instructions, tools and activities that are relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
it can provide opportunities for students to work together to support one another
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels

Unit 4:

Teachers can use the following sample tasks as formative assessment or summative assessment for learning goals in each module.

Teachers are encouraged to develop assessment tasks specifically suited to the needs of their students and context. Teachers should assess the learning goals and applications using the problem-solving cycle and appropriate technologies (analogue and/or digital).

Module 3: Health and recreational numeracy

Focus areas: Shape, Quantity & measures

Detailed example – Bake and create

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Health & recreational numeracy, and students use their mathematical toolkit to support Health & recreational numeracy.

Task – Students use recipes to accurately measure ingredients and investigate the shape and design of different baking trays and storage containers.

The context is Health and recreational numeracy, and the two focus areas mandated for this numeracy are shape, and quantity & measures.

Learning goals:

common two-dimensional shapes such as circles, triangles, quadrilaterals
simple three-dimensional objects such as cube, cylinder, simple prisms
common properties and language of two-dimensional shapes and three-dimensional objects (such as edges, faces, corners) and making connections between nets and three-dimensional objects, e.g. matching solids and nets.
simple perimeter and area measurements such as measuring area by squares
simple conversions between common and familiar metric units or common measures such as one teaspoon is 5 ml, one cup is 250 ml
common units of quantities, such as mass (g, Kg) and volume (ml, L) and temperature in degrees Celsius
analogue and digital times, including 12-hour time in hours (AM and PM), minutes and seconds on digital clocks, and hours, quarters, and halves, 10 and 5 to/from on analogue clocks.

Application:

recognise and name common two-dimensional shapes and simple three-dimensional objects
construct common two-dimensional shapes and simple three-dimensional objects
match common and familiar three-dimensional solids and their nets.
estimate, measure and compare distance and length, mass (g, Kg) and volume (ml, L) of familiar items and quantities
estimate, measure and compare simple quantity and measures such as perimeter, area and temperatures in degrees Celsius
make simple conversions between commonly used units, e.g. one cup is 250 ml
read and interpret common and familiar dates and times using digital and analogue clocks and calendars.

Introduce the context

Introduce the contexts of home baking using recipes. Consider store bought baking and the packaging used for these products.

Step 1: Identify the mathematics

Share experiences of cooking and baking in a home environment, in particular baking cakes, cupcakes or muffins. Generate a list of mathematical skills, knowledge and tools involved when cooking. These can include measuring cups, measuring spoons, scales, cooking time, temperature, knowing the dimensions of baking trays and cake tins, converting between measurements, etc.

Part A: Baking

Provide a cake or baking recipe to use. Identify the quantity and measures included in the recipe, discussing what it means when two different measurements or quantities are given for a single ingredient, e.g. 1 cup (250ml) milk.

Provide a variety of baking pans and trays of different sizes and shapes. Ask students to identify the different two-dimensional and three-dimensional shapes they can see. Support students to identify and determine strategies for selecting the most appropriate baking pan for the recipe. Encourage different groups of students to choose pans of different shapes and sizes.

Part B: Packaging

Challenge students to design a box or packaging for their baking. Students should consider:

the shape and size of their packaging. How can they ensure their cake or cupcakes will fit?
the construction of their packaging. Linking the three-dimensional shape of their packaging to its net.

Step 2: Act on and use the mathematics

Consider which technologies (analogue and digital) are readily available and will help support and examine the mathematics.

Students prepare an ingredient and equipment request list, which includes:

the quantity of each ingredient required
measuring equipment (and other cooking equipment)
an estimation of the time to complete the baking, including prep time, cooking time, cooling, decorating (if needed) and packaging
a design for packaging, including its dimensions and justification of its size using basic perimeter and area measurements.

Accurately follow the recipe to demonstrate the required quantity and measurement skills and knowledge to make the recipe.

Create a packaging box using measurement, by first constructing a template (net) and then constructing a three-dimensional product.

Step 3: Evaluate and reflect

Evaluate and reflect on the accuracy of measurements and the success (or not) of the recipe. Identify any measuring challenges or difficulties encountered and strategies used to overcome them.

Review the packaging to see if it is a suitable size and shape for the baking and make any modifications if required.

Consider the mathematics and check that estimates make sense and that solutions are mathematically reasonable.

Step 4: Communicate and report

Share baking and packaging with the class. Explain and justify the choices made.

Use both formal and informal mathematical language to communicate. Where appropriate, use visualisations and representations, including mathematical symbols and notation.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 3: Health and recreational numeracy
it is part of a range of activities for Module 3: Health and recreational numeracy.

This task is fair because

it allows teachers to develop instructions, tools and activities that are relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
it allows students to work together to support one another
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Module 4: Civic numeracy

Focus areas: Data, Likelihood

Detailed example – Is it worth the gamble?

This example demonstrates teaching the three components: Numeracy in context, Problem-solving cycle and Mathematical toolkit cohesively as per the curriculum guidelines. Students use the problem-solving cycle within the context and skills outlined in Civic numeracy, and students use their mathematical toolkit to support Civic numeracy.

Task – Students use data and statistics to make judgements about the likelihood of their favourite sports team or athlete winning.

The context is Civic numeracy, and the two focus areas mandated for this numeracy are data and likelihood.

Learning goals:

simple data collection methods including use of tables, spreadsheets and tallies
display of data with commonly used tables and graphs with scale of 1’s, 5’s or 10’s including familiar and simple cases of data, graphs and infographics
likelihood of familiar events or occurrences happening, using everyday language of chance
common likelihoods and chance events such as weather predictions, dice or spinner success rates
language and relative magnitude of the risk of common or familiar events of chance.

Application:

collect, collate, sort and order data sets, e.g. use survey to collect data, use tallies to collate data and insert sets of data into a table/spreadsheet, sort from lowest to highest
construct simple charts or graphs using familiar data with simple scales, e.g. in 1’s, 5’s or 10’s
read, identify and interpret familiar information and facts from simple tables, graphs and infographics
make simple comparisons and interpretations between provided simple data sets and their representations
order and compare simple familiar likelihood events and statements such as ‘evens’, ‘for sure’, ‘Buckley’s chance’, ‘impossible’
read, interpret and make decisions about likelihood statements based on their chance of occurrence or success/failure
order and compare the relative magnitude of the risk of common and familiar events of chance
use the language of likelihood such as chance, possibility, highly likely, certain, risk, success/failure, predict.

Identify the context

Introduce the context of Civic numeracy and the concept of ‘taking a chance’ or having a bet.

Consider the idea that as people, we are taking chances or making decisions about the likelihood of something happening all the time. Discuss chance in relation to sporting teams and events such as footy tipping, fantasy leagues, Melbourne Cup sweep, etc.

Step 1: Identify the mathematics

Select a sporting event, athlete or team. Research data and information that might be used to make judgements about the likelihood of their chosen team or athlete winning and whether it is worth the ‘gamble’.

Consider the following:

The data and information that might be useful.
How to find, collate, present and interpret the data and information.
Which language of likelihood and chance might be used.

Step 2: Act on and use the mathematics

Consider which technologies (analogue and digital) are readily available and will help support and examine the mathematics.

Find and collect appropriate data and information relevant to the chosen sports team or athlete and event. For example, if determining who to ‘tip’ for the next AFL round, the data and information might include current ladder positions, wins and losses for the previous five games, previous results when playing that team, wins and losses at home vs away games etc.

Present graphs from the research or create a graph. Write a brief summary interpreting the information in terms of the likelihood of success.

Decide whether or not to ‘bet’ on the success of the chosen sports team, athlete or event, using the data and information to justify the choice.

Step 3: Evaluate and reflect

Consider the following:

Does the data and information presented make sense?
Have you correctly interpreted the data and information you collected?
Is your description of likelihood and justification reasonable?
Do you need to make any changes to your work?

Consider the mathematics and check that estimates make sense and that solutions are mathematically reasonable.

Step 4: Communicate and report

Explain how the data and information was used to make decisions about the likelihood of success of their chosen sports team, athlete or event.

Use both formal and informal mathematical language to communicate. Where appropriate, use visualisations and representations, including mathematical symbols and notation.

Curriculum and assessment principles

This task is valid and reasonable and efficient because

it assesses multiple learning goals and applications in Module 4: Civic numeracy.

This task is fair because

it allows students to investigate data and information that are relevant and sensitive to gender, culture, linguistic background, disability, socioeconomic status and geographic location
it can provide opportunities for students to work together to support one another
the teacher will provide clear and explicit instructions, templates, feedback, support and assessment details to students.

This task is flexible because

it allows students to demonstrate understanding throughout the activity
it can be assessed at a range of levels.

Planning

Introduction

Scope of study

Rationale

Aims

Applied Learning

Developing a program

Structuring a program

Numeracy in context

Choosing the focus(es) of the numeracy context for study

Overlaying the problem-solving cycle

Identify the mathematics

Act on and use the mathematics

Evaluate and reflect

Communicate and report

Developing the mathematical toolkit

Integration of studies

Authentication

Employability skills

Aboriginal and Torres Strait Islander knowledge, culture and histories

Glossary

Further resources

Mathematical literacy

Developing investigations

Financial

Civic

Recreational

Health

Teaching and learning sample activities

Teaching and learning activities

Sample template for planning modules

Unit 1

Module 1: Personal numeracy

Module 1:

Examples of learning activities

Module 2: Financial numeracy

Module 2:

Examples of learning activities

Unit 2

Module 3: Health and recreational numeracy

Module 3:

Examples of learning activities

Module 4: Civic numeracy

Module 4:

Examples of learning activities

Unit 3

Module 1 – Personal numeracy (Location and Systematics)

Module 2 – Financial Numeracy (Number and Change)

Unit 4

Module 3 – Health and Recreational numeracy (Shape and Quantities & measures)

Module 4 – Civic Numeracy (Data and Likelihood)

Sample approaches to developing assessment

Assessment

Assessing the task

Conditions of task

Performance descriptors

Sample approaches to assessment

Unit 1:

Module 1: Personal numeracy

Detailed example – RACE IN THIS SPACE

Step 1: Identify the mathematics

Step 2: Act on and use the mathematics

Step 3: Evaluate and reflect

Step 4: Communicate and report

Curriculum and assessment principles

Module 2: Financial numeracy

Detailed example – FOODS UP

Step 1: Identify the mathematics

Step 2: Act on and use the mathematics

Step 3: Evaluate and reflect

Step 4: Communicate and report

Curriculum and assessment principles

Unit 2:

Module 3: Health and recreational numeracy

Detailed example – THE GREAT MARBLE RUN

Step 1: Identify the mathematics

Step 2: Act on and use the mathematics

Step 3: Evaluate and reflect

Step 4: Communicate and report

Curriculum and assessment principles