Space and Shape encompasses a wide range of phenomena that are encountered everywhere in our visual and physical world: patterns, properties of objects, positions and orientations, representations of objects, decoding and encoding of visual information, navigation and dynamic interaction with real shapes as well as with representations. Geometry serves as an essential foundation for space and shape, but the category extends beyond traditional geometry in content, meaning and method, drawing on elements of other mathematical areas such as spatial visualisation, measurement and algebra.
Change & Relationships involves understanding fundamental types of change and recognising when they occur in order to use suitable mathematical models to describe and predict change. Mathematically this means modelling the change and the relationships with appropriate functions and equations, as well as creating, interpreting, and translating among symbolic and graphical representations of relationships.
Quantity may be the most pervasive and essential mathematical aspect of engaging with, and functioning in, our world. Engaging with the quantification of the world involves understanding measurements, counts, magnitudes, units, indicators, relative size, and numerical trends and patterns. Aspects of quantitative reasoning – such as number sense, multiple representations of numbers, elegance in computation, mental calculation, estimation and assessment of reasonableness of results – are the essence of mathematical literacy relative to quantity.
Uncertainty is a phenomenon at the heart of the mathematical analysis of many problem situations, and the theory of probability and statistics as well as techniques of data representation and description have been established to deal with it. The uncertainty and data content category includes recognising the place of variation in processes, having a sense of the quantification of that variation, acknowledging uncertainty and error in measurement, and knowing about chance.
Personal questions include those focusing on activities of one’s self, one’s family or one’s peer group e.g. food preparation, shopping, games, personal health, personal transportation, sports, travel, personal scheduling and personal finance.
Occupational questions are centred on the world of work e.g. measuring, costing and ordering materials for building, payroll/accounting, quality control, scheduling/inventory, design/architecture and job-related decision making.
Societal questions focus on one’s community (whether local, national or global) e.g. voting systems, public transport, government, public policies, demographics, advertising, national statistics and economics. Although individuals are involved in all of these things in a personal way, in the societal context category the focus of problems is on the community perspective.
Scientific questions relate to the application of mathematics to the natural world and issues and topics related to science and technology e.g. weather or climate, ecology, medicine, space science, genetics, measurement and the world of mathematics itself.
Formulating situations mathematically means being able to recognise and identify opportunities to use mathematics and then provide mathematical structure to a problem presented in some contextualised form.
Employing mathematical concepts, facts, procedures and reasoning means being able to apply mathematical concepts, facts, procedures, and reasoning to solve mathematically-formulated problems to obtain mathematical conclusions.
Interpreting, applying and evaluating mathematical outcomes means the ability to reflect upon mathematical solutions, results, or conclusions and interpret them in the context of real-life problems.