Ideas and questions about a specific topic can be investigated through collecting data and using it to answer the questions.
Data can vary in different ways (e.g., an object can be different sizes and colours) and it can be organised in different ways and by different characteristics (categorical, numerical).
Data can be represented and communicated in multiple ways including data visualisations.
Patterns can be noticed, described, and analysed in sets of data and by using data visualisations.
Patterns are sequences (repeating or growing) made of numeric or spatial elements governed by a rule.
Patterns exist both in the world and in mathematics. The same pattern structure can be found in many different forms (e.g., numbers, shapes, colours, and rhythm).
A pattern can be described using a rule or you can create a pattern from a rule. To find the rule for a pattern, you need to identify the unit of the pattern (what is repeated or what grows).
In a pattern, the relationship between the ordinal position (e.g., first, second, and third) and the corresponding element is more useful for finding the pattern’s rule than the relationship between successive elements.
Identifying the rule of a pattern brings predictability and allows generalisations to be developed.
Generalisations can be expressed with both words and symbols.
Variables are symbols that take the place of numbers, or ranges of numbers. They have different meanings depending on whether they are being used as representations of quantities that vary or change, representations of specific unknown variables, or placeholders in a generalised expression or formula.