Planning
Accreditation period Units 1-4 from 2023
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.
Foundation Mathematics Sample Planner: Units 1 and 2
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. |
| Week 8 | Summarise statistical data using common measures of central tendency (mean, median, mode) and of spread (range, quartiles). |
| Week 9 | Investigation task
Demonstration of achievement of Outcome 2 should be based on the student's performance on a selection of the following assessment tasks:
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 | |
| 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 |
| Week 13 | Investigation task |
| Space and measurement | |
| Week 14 | Review of metric system including the metric units. |
| 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 |
| Discrete mathematics Financial and consumer mathematics | |
| Week 9 | Compare products and services: Financial basics modules Essi money game Money smart |
| 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 |
| Space and measurement | |
| Week 14 | Two-dimensional plans, models and diagrams of objects. |
| Week 15 | Review maps, directories and digital maps. |
| Week 16 | Investigate routes, itineraries and timetables. |
| Week 17 | Investigation task |
Foundation Mathematics Sample Planner: Units 3 and 4
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 Uses simultaneous equations and develop graphical and algebraic solutions. |
| Data analysis, probability, and statistics | |
| Weeks 7–8 | Topic: Statistical cycle Read and interpret charts, tables and graphs. Use long-term data and relative frequencies in practical situations to make informed interpretations and decisions about the likelihood of events or outcomes. |
| 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. |
| Investigation task | |
| 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. |
| Discrete mathematics Financial and consumer mathematics | |
| Weeks 14–15 | Topic: Business maths Topic: Tax and super |
| 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. |
| Week 18 | Examine the mathematics involved with insurance, communication (phone) plans, rent, and other personal financial payments. |
| Investigation task | |
| 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? |
| Space and measurement | |
| Weeks 21–22 | Topic: Mensuration Convert between metric and non-metric measures. |
| Weeks 23–24 | Topic: Geometry Undertake transformations of shapes, investigate symmetry and similarity. Solve problems with triangles and other polygons. |
| Week 25 | Topic: Maps, plans and diagrams Create and modify diagrams, plans, maps or designs using drawing equipment |
| Investigation | |
| 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
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.
Employability skills
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.
| 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 |
| Short written responses | Communication, problem solving |
| Problem-solving tasks | Communication, problem solving, team work, use of information and communications technology |
| 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.
| 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.
External website resource list
General teaching websites
The BBC in the UK has a wide range of maths and numeracy resources that are suitable for use in Foundation mathematics. Some resources have been referenced in the sample weekly planners earlier, but more are available here:
Maths Eyes supports learners to change their view of mathematics as being simply something everyone just does in school. With maths eyes people see the mathematics they do every day so that mathematics becomes real and meaningful to them.
Maths300 is a library of maths lessons that is owned and maintained by the Australian Association of Mathematics Teachers (AAMT). The lessons are available to teachers in Australia and internationally through a subscription.
Clickview (incorporating the former VEA videos) has a range of materials and videos available, many based around maths in the real world. They include: ALGEBRA: A Piece of Cake!,Algebraic Notation – Maths as a Foreign Language, and more.
New Zealand maths resource contains resources and activities.
The NRICH Project is a University of Cambridge resource
Developing investigations
The reSolve: Maths by Inquiry is a collaboration of the Australian Academy of Science and the Australian Association of Mathematics Teachers.
A Team competition for secondary school students aims to promote mathematical modelling to solve problems of real-world importance.
The ‘Maths Inside’ project has been developing resources to help teachers bring maths to life for high school students. It is a collaboration between UTS, CSIRO and the AAMT.
Census: What is a statistical question? is a teacher resource from the US Census.
Census at school is a New Zealand initiative that supports the teaching of statistics.
NRICH Project is a University of Cambridge resource.
Stanford Youcubed is an initiative from Stanford University Education.
Computational thinking
VCAA Computational and algorithmic thinking in Mathematics
Financial and consumer
Data analysis probability and statistics
Space and measurement
2023 Implementation videos
VCE Foundation Mathematics (2023) implementation videos
Online video presentations which provide teachers with information about the new VCE Foundation Mathematics Study Design for implementation in 2023.