Accreditation period Units 1-4: 2023-2027
Developing a program and weekly planner
The areas of study in the VCE Foundation Mathematics Study Design describe the specific key knowledge and key skills required for students to demonstrate achievement of the outcomes for a unit. Teachers are required to develop a program for their students that meets the requirements of the study design, including areas of study, key knowledge, key skills and outcome statements.
Where possible, the three outcomes outlined in the study design should be integrated and taught as a cohesive and linked set of capabilities:
Outcome 1 details the key knowledge and key skills content area to be taught.
Outcome 2 provides the framework for using investigation, modelling or problem-solving approaches when teaching and assessing the key knowledge and skills prescribed in Outcome 1.
Outcome 3 outlines the approaches to technology which should be used in Outcomes 2 and 3 in the teaching and learning of the mathematics.
There are four areas of study to be covered in VCE Foundation Maths. The order in which the areas of study should be taught is at the discretion of the teacher / school:
- Algebra, number and structure
- Data analysis, probability and statistics
- Discrete mathematics Financial and consumer mathematics
- Space and measurement.
Contextualising the mathematics is encouraged in this study design. Teachers should use contexts that are relatable for students in their life or at work. In Units 1 and 2, contexts should be familiar and include the local community and or environments. In Units 3 and 4 these contexts can be further extended to include federal and global contexts.
It is important to note that the assessment in both Units 1 and 2, and Units 3 and 4 include mathematical investigations of 1–2 weeks’ duration.
These mathematical investigations include the three main components of: formulation, exploration and communication. Students must learn and demonstrate these three steps of an investigative process in class. The School-assessed Coursework draws on the skills and knowledge developed in Outcome 2, and as such it is important that all Outcome 2 is utilised throughout the teaching and learning period.
Teachers should provide opportunities for students to learn the investigative cycle and they should endeavour to include and use different problem-solving models as part of their pedagogical toolkit. Exposure to problem-solving cycles will build investigation skills.
Investigations cover all three outcomes and hence should incorporate the use and application of different technologies and tools as applicable and relevant to the context. Real-life contexts should drive the investigations and engage and motivate the students.
The contexts can be drawn from a range of real-world scenarios and the use of authentic materials is strongly encouraged. Teachers should draw inspiration from the students' own interests, the world of work and the local community when selecting and designing investigations.
School-assessed Coursework (SACs) in Units 3 and 4 are to address content from two or more areas of study through mathematical investigations. There are
three investigation SACs addressing four areas of study. Two areas of study, in particular, underpin the other areas of study. Area of Study 1: Algebra, number and structure underpins the mathematics required in the three other areas of study, while Area of Study 2: Data analysis, probability and statistics, underpins Area of Study 3: Discrete mathematics Financial and consumer mathematics.
One
sample approach to combining and structuring the investigations might be
- Investigation one: Areas of Study 1 and 2
- Investigation two: Areas of Study 2 and 3
- Investigation three: Areas of Study 1 and 4
The duration of each SAC is to be 4–6 hours (several lessons) over a period of 1–2 weeks.
Formal assessment investigations may be presented in any form that adheres to the curriculum requirements, and it is suggested that portfolios, multimedia presentations and reports are all suitable examples.
Teachers should manage the teaching and learning of Units 3 and 4 to allow adequate time to prepare and execute the investigations required for School-assessed Coursework, and to allow adequate exam preparation for the students.
Unit 1 Sample course
| Algebra, number and structure |
|---|
Week 1 | Review numerals, symbols, number facts and operations and strategies for calculations.
Review
place value, truncation and rounding, leading digit
approximation and order of magnitude as a power of 10. |
Week 2
Week 3 | Review application of integers,
fractions and
decimals, their properties and related
operations.
Review estimation,
approximation, accuracy and reasonableness of calculations and results. |
Week 4 | Review
ratios, proportions,
percentages and
rates to solve range of problems. |
|
Data analysis, probability, and statistics |
|---|
Week 5 | Review types of data:
categorical and numerical data.
Review methods for data
collection by
collecting, organising, collating and
representing different types of categorical and numerical data. |
|
Week 6 | Accurately read and interpret diagrams, charts, tables and graphs.
Describe,
compare and analyse data sets and reports of
trends and implications or limitations. |
|
Week 7 | Construct
graphs to
represent data. |
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Week 8 | Summarise statistical
data using common measures of
central tendency (mean, median, mode) and of
spread (range, quartiles). |
|
Week 9 |
Investigation task
Suitable tasks for assessment in this unit may be selected from the following.
Demonstration of achievement of Outcome 1 should be based on the student's performance on a selection of the following assessment tasks: - portfolio
- assignments
- tests
- solutions to sets of worked questions
- summary notes or review notes.
Demonstration of achievement of Outcome 2 should be based on the student's performance on a selection of the following assessment tasks: - portfolio
- modelling tasks
- problem-solving tasks
- mathematical investigations.
Demonstration of achievement of Outcome 3 should be based on the student’s performance on aspects of tasks completed in demonstrating achievement of Outcomes 1 and 2 that incorporate opportunity for computational thinking and the effective and appropriate use of technology. |
|
Discrete mathematics Financial and consumer mathematics |
|---|
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Week 10 |
Read, calculate and interpret financial services such as
banking and
utility bills. |
|
Week 11 | Investigate
financial services cost structures, fees and interest.
Calculate various types of income. Describe and interpret factors that influence income.
Fairwork Pay and wages
Primezone financial plan for a market garden |
|
Week 12 | Calculate tax, GST and superannuation.
Income tax rates
Moneysmart
Money matters lesson plan
Be Moneysmart |
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Week 13 |
Investigation task |
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Space and measurement |
|---|
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Week 14 | Review of
metric system including the
metric units. |
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Week 15 | Conversion of metric
units, including
length,
area, volume, capacity,
time, mass,
temperature and other common derived units. |
|
Week 16 |
Estimate and measure different
quantities using
appropriate measurement tools. |
|
Week 17 | Using standard formulas for calculating length,
area,
surface area,
volume and
capacity. |
|
Week 18 |
Investigation task |
Unit 2 Sample course
| Algebra, number and structure |
|---|
Week 1 | Review of symbols,
numerals,
number facts,
operations and strategies for calculations. |
Week 2 | Review the concepts of constants, pro-numeral and
formula.
Manipulate symbolic
expressions and solutions of
equations. |
Week 3–4 | Develop simple
formulas. Check for accuracy and reasonableness of
calculations and results. |
|
Data analysis, probability, and statistics |
|---|
Week 5 | Create a range of charts,
tables and graphs to
represent and compare
data including when to use which type of data given, and the type of data, i.e. Categorical and Numerical.
Read and interpret
charts,
tables and
graphs. |
|
Week 6 | Use measures of
central tendency and simple measures of spread (such as range and interquartile range) to
summarise and interpret data and
compare sets of related data. |
|
Week 7 | Interpret, summarise and compare related
data sets to report findings and
draw possible conclusions. |
|
Week 8 |
Investigation task |
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Discrete mathematics Financial and consumer mathematics |
|---|
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Week 9 | Compare products and services:
Financial basics modules
Essi money game
Money smart
|
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Week 10 | Managing money:
Financial basics modules
Essi money game
Be Money smart
Money smart bite size activities |
|
Week 11 | Review
local, community and national financial and
economic data and trends over time. |
|
Week 12–13 |
Investigation task |
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Space and measurement |
|---|
|
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Week 14 | Two-dimensional plans, models and diagrams of objects. |
|
Week 15 | Review
maps, directories and digital
maps. |
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Week 16 | Investigate
routes,
itineraries and timetables. |
|
Week 17 |
Investigation task |
Unit 3 and 4 Sample course
| Algebra, number and structure |
|---|
Weeks 1–2 |
Topic: Number and structure
Review of conventions of formal
mathematical terminology and notations.
Review of
operations, number facts and
computation strategies. |
Weeks 3–4 | Investigate
percentages,
ratios, proportions and
percentage error.
Develop skills around
estimations and approximations.
Apply rounding, significant figures, leading-digit
approximations, floor and ceiling values. |
Weeks 5–6 |
Topic: Algebra
Manipulation and transposition of formulas to find unknown values.
Algebraic formulas
Algebraic expressions
Algebraic formulas Uses simultaneous equations and develop graphical and algebraic solutions.
Simultaneous linear equations and
Mathematical Modelling: Pricing for Profit |
|
Data analysis, probability, and statistics |
|---|
Weeks 7–8 |
Topic: Statistical cycle
Undertake
data collection, organise, collate, and graph data.
Data Investigation and Interpretation 9
Census at School
Handling data Read and interpret charts, tables and graphs.
Data and Statistics
Australian Bureau of Statistics
Promoting a Spirit of Inquiry
Statistics: Student Profiling
Statistics and probability Use long-term data and relative frequencies in practical situations to make informed interpretations and decisions about the likelihood of events or outcomes.
Probability: Forensic Investigations
Probability: Flooding Likelihood
Statistics and Probability: Dairy Herd Data
Probability: Using Weather
Relative Frequency of Events |
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Weeks 9–10 | Calculate common measures of
central tendency and spread, and standard deviation using technology.
Draw inferences and
conclusions from the data. |
|
Week 11 | Investigate financial and
economic data and report on trends and outcomes.
Develop skills to explain limitations and implications of statistical studies. Identify and interpret
errors and misrepresentations in data sets. |
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Investigation task |
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Weeks 12–13 | This could be held earlier or later depending on coverage of relevant concepts, skills and processes with respect to content and context for the application task.
Sample application task –
Cleanest air in the world or
Medicine dosages. |
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Discrete mathematics Financial and consumer mathematics |
|---|
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Weeks 14–15 |
Topic: Business maths
Investigate income and expenditure of businesses including
invoicing,
BAS, superannuation and
leave entitlements.
Topic: Tax and super
Examine
taxation and superannuation. |
|
Weeks 16–17 |
Topic: Financial products and services
Investigate interest repayments including
simple interest and
compound interest in relation to the different types of loans. |
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Week 18 | Examine the mathematics involved with insurance,
communication (phone) plans, rent, and other
personal financial payments. |
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Investigation task |
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Weeks 19–20 | This could be held earlier or later depending on coverage of relevant concepts, skills and processes with respect to content and context for the application task.
Sample application task –
Can small changes make big differences? |
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Space and measurement |
|---|
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Weeks 21–22 |
Topic: Mensuration
Determine area, surface area of shapes, and volume, capacity and density of objects.
Area, Volume and Surface Area
Cones, Pyramids and Spheres
Mathematical Modelling: Packaging Designer
Renovate, Calculate! Convert between metric and non-metric measures.
Choose and convert units of measurement for area and volume
Measuring: Imperial and metric
Investigate
errors in measurement. |
|
Weeks 23–24 |
Topic: Geometry
Investigate the properties of shapes and objects.
Properties of 2D shapes and 3D objects
Shapes: 2D shapes
Geometry
Geometry and measure Undertake transformations of shapes, investigate symmetry and
similarity. Solve problems with triangles and other polygons.
Pythagoras' Theorem
From triangles to computer graphics |
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Week 25 |
Topic: Maps, plans and diagrams
Create and modify diagrams, plans,
maps or designs using drawing equipment |
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Investigation |
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Weeks 26–27 | This could be held earlier or later depending on coverage of relevant concepts, skills and processes with respect to content and context for the application task.
Sample application task –
Dehydration effects on people in summer |
Aboriginal and Torres Strait Islander Perspectives in the VCE
On-demand video recordings, presented with the Victorian Aboriginal Education Association Inc. (VAEAI) and the Department of Education (DE) Koorie Outcomes Division, for VCE teachers and leaders as part of the Aboriginal and Torres Strait Islander Perspectives in the VCE webinar program held in 2023.
Units 1 and 2
Foundation Mathematics Units 1 and 2 provide 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.
Each employability skill contains a number of facets that have a broad coverage of all employment contexts and designed to describe all employees. The table below links those facets that may be understood and applied in a school or non-employment related setting, to the types of assessment commonly undertaken within the VCE study.
Students undertaking the following types of assessment, in addition to demonstrating their understanding and mastery of the study, typically demonstrate the following key competencies and employability skills.
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 in the VCE study.
| Assessment task | Employability skills selected facets |
|---|
Assignments | Use of information and communications technology |
Tests | Self management, use of information and communications technology |
Summary or review notes | Self management |
Mathematical investigations | Communication, team work, self management, planning and organisation, use of information and communications technology, initiative and enterprise |
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Short written responses | Communication, problem solving |
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Problem-solving tasks | Communication, problem solving, team work, use of information and communications technology |
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Modelling tasks | Problem solving, planning and organisation, use of information and communications technology |
Units 3 and 4
Students undertaking the following types of assessment, in addition to demonstrating their understanding and mastery of the content of the study, typically demonstrate the following key competencies and employability skills.
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 in the VCE study.
| Assessment task | Employability skills selected facets |
|---|
Modelling or problem-solving task | Planning and organising, solving problems, using mathematical ideas and techniques (written) communication, use of information and communications technology, self management |
Application task | Planning and organising, solving problems, using mathematical ideas and techniques (written) communication, use of information and communications technology, self management |
*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.
2023 Implementation videos
VCE Foundation Mathematics (2023-2027) implementation videos
Online video presentations which provide teachers with information about the new VCE Foundation Mathematics Study Design for implementation in 2023.