Mathematics scale

• Space and shape relates to spatial and geometric phenomena and relationships, drawing on the discipline of geometry. It requires looking for similarities and differences when analysing the components of shapes, recognising shapes in different representations and different dimensions as well as understanding the properties of objects and their relative positions.

• Change and relationships involves mathematical manifestations of change as well as functional relationships and dependency among variables. It relates most closely to algebra. Mathematical relationships often take the shape of equations or inequalities, but relationships of a more general nature (e.g., equivalence, divisibility, inclusion) are relevant as well. Relationships are given a variety of different representations, including symbolic, algebraic, graphical, tabular and geometrical representations. Since different representations may serve different purposes and have different properties, translation between representations often is of key importance in dealing with situations and tasks.

• Quantity involves numeric phenomena as well as quantitative relationships and patterns. It relates to the understanding of relative size, the recognition of numerical patterns, and the use of numbers to represent quantities and quantifiable attributes of real-world objects (counts and measures). Furthermore, quantity deals with the processing and understanding of numbers that are represented in various ways. An important aspect of dealing with quantity is also quantitative reasoning, which involves number sense, representing numbers, understanding the meaning of operations, mental arithmetic and estimating. The most common curricular branch of mathematics with which it is associated is arithmetic.

• Uncertainty involves probabilistic and statistical phenomena and relationships that become increasingly relevant in the information society. These phenomena are the subject of mathematical study in statistics and probability.