Overarching Key Ideas for all Mathematical Concepts
The overarching key ideas for all mathematical concepts are: estimation, benchmarks, visualisation, equality and equivalence, language and strategies. These six key ideas have a broad application and are fundamental to enabling students to connect concepts across all areas of mathematics. Consequently, they need to be considered by educators when developing each unit of work. The overarching key ideas are outlined in more detail below.
Estimation
Estimation is an approximation or judgement of a value, quantity or measure.
An estimation is an educated approximation about a value that is as close to the exact value as is needed. All estimation is dependent on the estimator having benchmark numbers, facts or measures from which to work. Estimations may involve calculation, such as approximating the answer to 47 × 19 by rounding both numbers up to create 50 × 20. Estimation is also important in measurement.
Benchmarks
Benchmarks are trusted quantities or numbers used as reference points to estimate, calculate or compare.
Visualisation
Visualisation is the making, storing, retrieval and manipulation of imagined objects and events.
These images can be true-to-life pictures of real-life objects or events, shapes, symbols, words and ideas associated with those objects or events.
Visualisation is important to a broad range of subject areas as it allows students to predict the result of actions in their head, without the need to necessarily carry out those actions.
Equality and equivalence
Equality and equivalence involve describing the relationship between two or more quantities as being ‘the same as’ in size, quantity, value, or in some other way.
Equality is important to arithmetic and algebra.
Equivalence is used in a similar way.
Language
Language is specific vocabulary, graphics and symbols used to communicate mathematically with others.
It is used productively to create representations of ideas and receptively to interpret the ideas of others.
Language is an important tool for students to express mathematical concepts. Specialised mathematical language, such as ‘factor’, ‘triangle’ and ‘average’, embodies concepts that, in turn, can become ideas for students to use in their thinking.
Symbols and diagrams, such as tables and graphs, provide means to represent, communicate and work with ideas in efficient and sophisticated ways.
Strategies
Strategies are methods to solve mathematical problems.
They can be used: as general methods to solve problems (such as trial and improve or guess, check and refine); to solve a simpler, related problem; to make a table; or to look for a pattern. Strategies can also be specific to a type of problem.
