Foundation Mathematics Study Notes

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 – Discrete mathematics. 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.