The object is the starting figure before a transformation has been applied.

The image is the resulting figure after a transformation has been applied.

A transformation is a process that may change the size, orientation or position of a shape.

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

A property of a shape is invariant if that property has not changed after the shape is transformed.

Checking understanding of basic transformations

Maths

In this unit, pupils explore the effects of different transformations and whether the transformed shape is congruent or similar to the original shape. This is built on in the future unit where pupils formalise the criteria for determining congruence in triangles and study rotational symmetry

In this unit, pupils translated and reflected simple shapes on the full coordinate grid. In this unit, these processes are formalised and rotation and enlargement are introduced

This unit introduces pupils to shape tranformations: enlargements, rotations, reflections and translations both by hand and with technology.

Transformations

Translation is a transformation in which every point of a shape moves the same distance in the same direction.

Introduction to translation

Displacement is the distance from the starting point when measured in a straight line.

A vector can be used to describe a translation.

Describing a translation

A vertex is the point where two or more line segments meet. The plural is vertices.

Translating objects

The rotation of an object is the turning of an object by a fixed amount and around a fixed point (called the centre of rotation).

Introduction to rotations

Clockwise is the direction that the hands of an analogue clock travel.

Anti-clockwise is the opposite direction to which the hands of an analogue clock travel.

The most common unit of measurement for angle. One whole turn is equal to 360 degrees, written 360°.

Describing a rotation's direction and size

The centre of rotation is the fixed point about which an object is rotated.

Understanding the centre of rotation

A clockwise direction is the direction in which the hands of an analogue clock travel.

An anti-clockwise direction is the opposite direction to which the hands of an analogue clock travel.

The centre of rotation is the fixed point about which an object is rotated. It fixes the location of the image after it is rotated.

Degrees are the most common unit of measurement for angle. One whole turn is equal to 360 degrees, written 360°.

Rotating objects

A reflection of a shape is the mirror image of the shape.  An object is reflected when it is flipped over a fixed line.

The sense of an object is the direction of the orientation of the object.

Introduction to reflections

The line of reflection is the line about which an object is reflected. The object and image are equidistant from the line of reflection.

Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.

Describing a reflection

Reflecting objects

Enlargement is a transformation that causes a change of size.

Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

Introduction to enlargements

The centre of enlargement is the point from which a shape is enlarged.

A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

Transformations

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These lessons will be removed by end of Summer Term 2025.