Features, sometimes called attributes, are visual characteristics of a shape or object that can be seen.

Shapes and objects have distinguishable characteristics and are named because of their properties.

The properties of two-dimensional (2D) shapes typically include relationships among the number, length and relative position of sides, as well as the number and angle of corners, lines of symmetry, convexity and concavity.

The properties of three-dimensional (3D) objects typically include the shape and relative position of faces, surfaces, edges and vertices (corners).

Classes (i.e. categories) of shapes are defined by their properties, which are relationships among features of similar shapes.

Properties are relationships connecting characteristics of shapes or objects.

Some properties are defining; that is, they describe what a shape must have to belong to a class.

Classification involves establishing criteria to group shapes by their common properties. 

Classification is about working with relationships among properties, where individual shapes are examples of the classes and are hierarchical.

Orientation is the position of a shape on a plane or an object in space, in particular the direction that the features of the shape or object are facing.

The orientation of a shape remains unchanged as it is translated (i.e. shifted) or enlarged, but changes when a shape is reflected or rotated through an angle not equal to 360°.

Transformation is the change in the size, shape or position of a shape or object.

• Isometric transformations

Isometric transformations include translations, rotations and reflections. Note: these do not change the size or proportions of a shape or object.

1. Translation (slide): the movement of a shape to a new position. The length of sides and angles remain unchanged.

2. Rotation (turn): a change to the position of a shape by rotating it about a fixed point through a given angle. The point may be inside or outside the shape.

3. Reflection (flip): a change to the position of a shape by reflecting it along a mirror line. The line may run through the shape or be external to it.

• Non-isometric transformations

Non-isometric transformations include enlargements and reductions (dilations).

A dilation is a change to the size of a shape about a point. The lengths of the sides and/or the angles are changed.

Objects appear differently depending upon the position from which they are viewed.

A shape has symmetry if it maps onto itself by a transformation, particularly through reflection and/or rotation.

• Reflective symmetry 

In reflective symmetry, the locations of the mirror are called lines of symmetry.

• Rotational symmetry

In rotational symmetry, the point is known as the centre of rotation and the angle of rotation is the measure of turn that maps the shape onto itself.

For descriptions and examples on the list below, please go to pages 38-40 on the above link.

• Geometric reasoning

• Point

• Line

• Ray

• Plane

• Two-dimensional shape

• Polygon

• Three-dimensional object

• Polyhedron

• Net

• Congruence

• Similar shapes

• Regular shapes

• Tessellation

• Apex

• Cross-section

• Truncated objects

• Right object

• Oblique object

• Angle

• Adjacent angle

• Complementary angles

• Supplementary angles

• Vertically-opposite angles

• Angles at a point

• Parallel lines

• Transversals

• Corresponding angle

• Alternate angle

• Co-interior angle

The position of an object on a plane or in space can be specified and described relative to a reference point.

The direction (i.e. movement) of an object can be described relative to its starting position and surrounding landmarks.

The orientation of an object can be described in relation to a reference direction.

Usually the reference direction is a compass point or bearing, or axes on a Cartesian plane.

The location of objects on a plane and/or in space can be visually represented; each representation has particular purposes and ways in which they are read and interpreted.

Visual representations include diagrams, plans, grids, maps, directories and networks.

A coordinate system is a system used to locate the position or direction of an object on a plane or in space relative to the distance from an origin.

• Grid reference

An alpha-numeric grid reference defines a region on a map.

An ordered pair reference defines a point, rather than a region, on a map or Cartesian plane.

Cardinal direction

A cardinal direction is a bearing described by north, south, east and west, and is commonly denoted by the direction’s initial.

• The four main points on a compass are:

• north (N) – 0° or 360°

• east (E) – 90°

• south (S) – 180°

• west (W) – 270°.

• Inter-cardinal direction

Inter-cardinal points can also be used:

• north-east (NE) – 45°

• south-east (SE) – 135°

• south-west (SW) – 225°

• north-west (NW) – 315°.

• Other inter-cardinal points include:

• north-north-east (NNE) – 22.5°

• east-north-east (ENE) – 67.5°

• east-south-east (ESE) – 112.5°

• south-south-east (SSE) – 157.5°

• south-south-west (SSW) – 202.5°

• west-south-west (WSW) – 247.5°

• west-north-west (WNW) – 292.5°

• north-north-west (NNW) – 337.5°.

A bearing is the angle between north and another landmark as taken from a fixed point. 

The angle is measured in a clockwise direction.

BOLTSS (i.e. border, orientations, legend, title, scale and source) is standard information to include on a map:

• border – the limits of the area covered by a map

• orientation – an indication of north

• legend – symbols on the map that represent natural or artificial features on the ground; legends are sometimes referred to as ‘keys’ as they ‘unlock’ the meaning of the symbols

• title - the name of the map, identifying the geographic area that it covers

• scale - a ratio indicating distance on a map in relation to distance on the ground

• source - where the information on the map originated.