ACARA v9 CONTENT DESCRIPTION “describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries”
Builds on Lines, Angles and Symmetry (AC9M4SP01). Year 5 sets shapes in motion with three transformations: translations, reflections and rotations. Performing and describing each one, recognising what changes and what stays the same, and identifying the line and rotational symmetries a shape has builds a clear language for how shapes move and match. Dynamic geometry tools make these movements easy to explore, and the ideas lead into the coordinate geometry of later years.
Translations slide a shape
A translation slides a shape from one place to another without turning or flipping it. Every point of the shape moves the same distance in the same direction, so the shape arrives looking exactly as it started, just in a new position. Sliding a tile three squares right and two squares up is a translation. Because nothing about the shape itself changes, its size, its side lengths, its angles and the way it faces all stay the same. A translation only changes where the shape is, never what it looks like.
Translations slide a shape
Every point moves the same way; nothing turns or flips.
A translation slides the shape to a new place; its size, shape and the way it faces all stay the same.
Reflections flip a shape
A reflection flips a shape over a line, called the mirror line, to produce a mirror image. Each point moves to the opposite side of the line, the same distance away, so the reflected shape is the same size and shape but reversed, like a reflection in a mirror. A shape and its reflection match when the page is folded along the mirror line. Reflecting changes the way the shape faces, turning a left-pointing flag into a right-pointing one, while keeping every length and angle the same.
Reflections flip a shape
Each point moves to the other side of the mirror line.
A reflection flips the shape over the mirror line into a mirror image, the same size but facing the other way.
Rotations turn a shape
A rotation turns a shape about a fixed point, called the centre of rotation, through an angle such as a quarter turn or a half turn. The shape spins around the centre, so it ends up facing a new direction while staying the same size and shape. Turning a shape a quarter turn clockwise about one of its corners is a rotation. Like the other transformations, a rotation keeps the shape itself unchanged; it alters only the direction the shape faces and, unless the centre is inside it, where the shape sits.
Rotations turn a shape
The shape spins about a fixed centre point.
A rotation turns the shape a quarter turn about the centre point, so it faces a new direction but keeps its size and shape.
Lines of symmetry
A shape has line symmetry, also called reflective symmetry, when a line can be drawn so that one half is the mirror image of the other. Folding along that line of symmetry makes the two halves match exactly. A square has four lines of symmetry, a rectangle has two, and an equilateral triangle has three, while many shapes have just one or none at all. Finding the lines of symmetry of a shape means looking for every fold that leaves the two sides matching, which is the same idea as a reflection that maps the shape onto itself.
Lines of symmetry
A line of symmetry folds the shape onto itself.
How many lines of symmetry does this shape have?
Rotational symmetry
A shape has rotational symmetry when it can be turned about its centre by less than a full turn and still look exactly the same. The number of times it matches itself in one complete turn is the order of its rotational symmetry. A square looks the same four times as it turns once around, so it has rotational symmetry of order four; an equilateral triangle has order three, and a rectangle order two. Every shape looks the same after a full turn, so rotational symmetry is only interesting when a shape matches itself before the turn is complete.
Rotational symmetry
Count the matches in one full turn about the centre.
In one full turn, how many times does this shape look the same?
What changes and what stays the same
Across all three transformations, the key question is what changes and what stays the same. Translations, reflections and rotations all keep a shape the same size and shape, with the same side lengths and angles, because the shape is only moved, not redrawn. What can change is where the shape sits and the direction it faces: a translation changes position, a reflection reverses facing, and a rotation turns it. Recognising these constants and changes, and spotting the line and rotational symmetries a shape has, lets a child describe and perform any of these movements with confidence, ready for the coordinate transformations of later years.
Quick self-check
1. A translation moves a shape by...
2. Under a reflection, a shape...
3. A rotation turns a shape about a...
4. Under all three transformations, what stays the same is the shape's...