YEAR 11-12
VCE Foundation Mathematics
Subject Area
Maths
VCE Units
1-4
About the Course
Foundation Mathematics Units 1 and 2 focus on providing students with the mathematical knowledge, skills, understanding and dispositions to solve problems in real contexts for a range of workplace, personal, further learning, and community settings relevant to contemporary society. They are also designed as preparation for Foundation Mathematics Units 3 and 4 and contain assumed knowledge and skills for these units.
In Unit 1 students consolidate mathematical foundations, further develop their knowledge and capability to plan and conduct activities independently and collaboratively, communicate their mathematical ideas, and acquire mathematical knowledge skills to make informed decisions in their lives. The areas of study for Foundation Mathematics Unit 1 are ‘Algebra, number and structure’, ‘Data analysis, probability and statistics’, ‘Discrete mathematics’, and ‘Space and measurement’. The content should be developed using contexts present in students’ other studies, work and personal or other familiar situations.
In undertaking these units, students are expected to be able to apply techniques, routines and processes involving integer, rational and real arithmetic, sets, lists and tables, contemporary data displays, diagrams, plans, geometric objects and constructions, algorithms, measures, equations and graphs, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, statistical and financial functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.
UNIT 1
Area of Study 1 : Algebra, number and structure
In this area of study students cover estimation, and the use and application of different forms of number and related calculations in practical, everyday and routine work contexts.
This area of study includes:
application of integers, fractions and decimals, their properties and related operations
use of ratios, proportions, percentages and rates to solve problems
estimation, approximation and reasonableness of calculations and results.
Area of Study 2: Data analysis, probability and statistics
In this area of study students cover collection, presentation and analysis of gathered and provided data from community, work, recreation and media contexts, including consideration of suitable forms of representation.
This area of study includes:
collection and representation of data in diagrammatic, tabular and graphical forms and the features, conventions and terminology used in these processes
construction of charts, tables and graphs to represent data
interpretation of data to summarise and communicate findings and possible conclusions.
Area of Study 3: Financial and consumer mathematics
In this area of study students cover the use and interpretation of different forms of numbers and calculations, and their application in relation to the understanding and management of personal, local and national financial matters.
This area of study includes:
personal financial services and information such as borrowing, bills and banking
income calculations including rates of pay and payslips
personal taxation and superannuation
taxation as a community and contribution to government
fees and interest
cost structures and related information associated with financial transactions.
Area of Study 4: Space and measurement
In this area of study students cover time, and the use and application of the metric system and related measurements in a variety of domestic, societal, industrial and commercial contexts.
This area of study includes:
standard metric units and measures, including common derived metric measures
reading and interpretation of scales on digital and analogue instruments
estimation and approximation strategies
time and duration including time and date specifications, conventions, schedules and timetables.
UNIT 2
Area of Study 1 : Algebra, number and structure
In this area of study students cover estimation and the use and application of the representation of generalisations and patterns in number, including formulas and other symbolic expressions, in everyday and routine work contexts.
This area of study includes:
construction, use and interpretation of formulas and symbolic expressions to describe relationships between variables and to model and represent generalisations and patterns
manipulation of symbolic expressions and solution of equations
estimation, approximation and reasonableness of calculations and results..
Area of Study 2: Data analysis, probability and statistics
In this area of study students cover the analysis of gathered and provided data from community, work, recreation and media contexts, including consideration of suitable forms of data summaries.
This area of study includes:
creation of a range of charts, tables and graphs to represent and compare data
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
interpretation, summary and comparison of related data sets to report findings and draw possible conclusions.
Area of Study 3: Financial and consumer mathematics
In this area of study students cover the use and interpretation of different forms of numbers and calculations and their application in relation to the understanding and management of personal, local and national financial matters.
This area of study includes:
products and services such as comparison of health products, informed spending choices, decision making according to criteria
managing money: earning and spending, life-stage financial planning, servicing of current and future commitments such as HECS-HELP debt, child-care support and other benefits
local, community and national financial and economic data and trends over time (national/community/ local) such as CPI, interest rates, wages and house prices.
Area of Study 4: Space and measurement
In this area of study students cover shape and location concepts, and their use and application in a variety of domestic, societal, industrial and commercial contexts.
This area of study includes:
description, representation and properties of simple and composite shapes and objects
two-dimensional plans, models and diagrams of objects
location, maps, directories and digital maps including birds-eye and street views
routes and itineraries, including location and direction, speeds, distances and estimated travel times, for example daily work route and diversions, and itinerary for travel.
UNIT 3
Area of Study 1 : Algebra, number and structure
In this area of study students cover estimation, the use and application of different forms of numbers and calculations, algorithmic and computational thinking, and the representation of formal mathematical expressions and processes including formulas and other algebraic expressions to solve practical problems in community, business and industry contexts.
This area of study includes:
mathematical conventions notations for number and number operations
rational numbers and irrational numbers related to measurement, ratios and proportions in a practical context
direct and indirect variation
symbolic expressions, equations and formulas
graphical and algebraic analysis of relations including transposition of formulas and finding a break-even point using simultaneous equations
estimation and approximation including interval estimates, rounding, significant figures, leading-digit approximations, floor and ceiling values and percentage error.
Area of Study 2: Data analysis, probability and statistics
In this area of study students cover collection, presentation and analysis of gathered and provided data from community, work, recreation and media contexts, including consideration of suitable forms of representation and summaries. This area of study incorporates the ability to critically reflect on statistical data and results, and to be able to communicate and report on the outcomes and any implications.
This area of study includes:
development and specification of data collection requirements and methods, including consideration of audience and purpose of data collection, errors and misrepresentations in statistics
collection and modelling of data, including the construction of tables or spreadsheets and graphs to represent data and correct representations
contemporary representations of data and graphs derived from technology including reviewing appropriateness of graphical representations, including pictograms, bubble, Mekko, radar, sunburst, heat map and stacked area charts
long-term data and relative frequencies in practical situation such as in relation to epidemics, climate, environment, sport and marketing
interpolation and extrapolation of data, predictions, limitations, inferences and conclusions comparing and interpreting data sets and graphs, including using measures of central tendency and spread (percentiles and standard deviation) and cumulative frequency.
Area of Study 3: Financial and consumer mathematics
In this area of study students cover the use and application of different forms of numbers and calculations, relationships and formulae, and their application in relation to the analysis of, and critical reflection on, personal, local, national and global financial, consumer and global matters.
This area of study includes:
money management including investments and loans, credit and debit, comparing mortgages versus rental costs and debt consolidation
taxation systems at the personal and business level
income and expenditure calculations such as GST, invoicing and BAS
comparison of financial products and services such as insurance
informal consideration of financial risk at the national and global level (short, medium and long term)
analysis and interpretation of financial information and data sets, trends and economic indicators and their impact (at the personal, community, national or global level) such as gender pay gap, career trends and interruption, currency fluctuations and inflation, stock market movements and recessions.
Area of Study 4: Space and measurement
In this area of study students cover the use and application of the metric system and related measurement in a variety of domestic, societal, industrial and commercial contexts, including consideration of accuracy, precision and error.
This area of study includes:
spatial and geometric constructions including transformations, similarity, symmetry and projections
calculations of enlargement and reduction using scaling techniques for two-dimensional and three-dimensional plans, diagrams and models
measurements and related quantities including derived quantities, metric and relevant non-metric measures
conventions, properties and measurement of perimeter, area, surface area and volume of compound shapes and objects
calibration and error in measurement, including tolerance, accuracy and precision.
UNIT 4
Area of Study 1 : Algebra, number and structure
In this area of study students cover estimation, the use and application of different forms of numbers and calculations, algorithmic and computational thinking, and the representation of formal mathematical expressions and processes including formulas and other algebraic expressions to solve practical problems in community, business and industry contexts.
This area of study includes:
mathematical conventions notations for number and number operations
rational numbers and irrational numbers related to measurement, ratios and proportions in a practical context
direct and indirect variation
symbolic expressions, equations and formulas
graphical and algebraic analysis of relations including transposition of formulas and finding a break-even point using simultaneous equations
estimation and approximation including interval estimates, rounding, significant figures, leading-digit approximations, floor and ceiling values and percentage error.
Area of Study 2: Data analysis, probability and statistics
In this area of study students cover collection, presentation and analysis of gathered and provided data from community, work, recreation and media contexts, including consideration of suitable forms of representation and summaries. This area of study incorporates the ability to critically reflect on statistical data and results, and to be able to communicate and report on the outcomes and any implications.
This area of study includes:
development and specification of data collection requirements and methods, including consideration of audience and purpose of data collection, errors and misrepresentations in statistics
collection and modelling of data, including the construction of tables or spreadsheets and graphs to represent data and correct representations
contemporary representations of data and graphs derived from technology including reviewing appropriateness of graphical representations, including pictograms, bubble, Mekko, radar, sunburst, heat map and stacked area charts
long-term data and relative frequencies in practical situation such as in relation to epidemics, climate, environment, sport and marketing
interpolation and extrapolation of data, predictions, limitations, inferences and conclusions comparing and interpreting data sets and graphs, including using measures of central tendency and spread (percentiles and standard deviation) and cumulative frequency.
Area of Study 3: Financial and consumer mathematics
In this area of study students cover the use and application of different forms of numbers and calculations, relationships and formulae, and their application in relation to the analysis of, and critical reflection on, personal, local, national and global financial, consumer and global matters.
This area of study includes:
money management including investments and loans, credit and debit, comparing mortgages versus rental costs and debt consolidation
taxation systems at the personal and business level
income and expenditure calculations such as GST, invoicing and BAS
comparison of financial products and services such as insurance
informal consideration of financial risk at the national and global level (short, medium and long term)
analysis and interpretation of financial information and data sets, trends and economic indicators and their impact (at the personal, community, national or global level) such as gender pay gap, career trends and interruption, currency fluctuations and inflation, stock market movements and recessions.
Area of Study 4: Space and measurement
In this area of study students cover the use and application of the metric system and related measurement in a variety of domestic, societal, industrial and commercial contexts, including consideration of accuracy, precision and error.
This area of study includes:
spatial and geometric constructions including transformations, similarity, symmetry and projections
calculations of enlargement and reduction using scaling techniques for two-dimensional and three-dimensional plans, diagrams and models
measurements and related quantities including derived quantities, metric and relevant non-metric measures
conventions, properties and measurement of perimeter, area, surface area and volume of compound shapes and objects
calibration and error in measurement, including tolerance, accuracy and precision.