The key idea of shape at level 3 is that shapes can be defined by their geometric properties.

At level 3 students are becoming aware that there are rules for defining groups of shapes. For example “all shapes with three straight sides are triangles” or “all shapes with four sides are quadrilaterals”. Commonly shared rules for defining groups of shapes are important for communicating ideas about shape. These rules may initially be incomplete or inaccurate, such as “shapes with four sides are squares”. Rules for defining shapes can be understood both in terms of the attribute and in terms of the shape, for example, “all shapes with three straight sides are triangles” and “all triangles have three straight sides”. Quadrilaterals provide a particularly interesting collection of rules. For example, all squares are also rectangles, but not all rectangles are squares. The diagram below illustrates the relationships between the main types of quadrilaterals.

Features of shapes that can be used to define groups include number of sides, symmetry, parallel and perpendicular sides, right angles and, angles that are smaller or larger than right angles. Partitioning shapes and combining shapes together help in understanding their geometric properties, symmetry in particular.

This key idea develops from the key idea of shape at level 2 where students are able to sort shapes by their attributes, but may not yet have formalised rules to define groups of shapes.

This key idea is extended in the key idea of shape at level 4 by making links between 2- and 3-dimensional shapes.