The key idea of transformation at level 4 is that some properties of objects do not change under different transformations.
An object’s size, internal angles, position, and orientation may change under some transformations. For example, a square that has been enlarged by a scale factor greater than one will have longer sides, and a larger area than the original object, and a non-symmetric object that has been rotated around a point distant to itself will have changed both its position and its orientation as a result of the rotation.
The table below indicates which particular properties of objects may change under each transformation.
| Properties | Transformation | |||
| Rotation | Reflection | Translation | Enlargement | |
| Size (length of sides, area and volume) | √ | |||
| Orientation | √ | √ | √ | |
| Position | √ | √ | √ | √ |
| Size of internal angles | ||||
Note that although some transformations have the ability to change particular properties, they may not always do so. For example, an object’s position will not change if it is rotated around its centre point, but it will change if it is rotated around a point outside of itself. A shape will only change orientation under enlargement if the scale factor is negative.
This key idea develops from the key idea of transformation at level 3 that specific items are needed to describe different transformations.
This key idea is extended in the key idea of transformation at level 5 that changes to an object under different transformations can be calculated.