Year 5 maths · Key Stage 2 · Geometry – position and direction

Year 5 reflection and translation: a guide for parents

In Year 5 children learn to reflect and translate shapes. A reflection flips a shape across a mirror line, and a translation slides it to a new position without turning or flipping it. They use grids and coordinates in the first quadrant, describe what has happened using the correct words, and learn that the shape itself stays the same size and shape whatever happens to its position.

Reflection and translation, explained

A reflection gives a mirror image. The original shape is called the object and the reflected shape is the image. Every corner of the image is exactly as far from the mirror line as the matching corner of the object, but on the other side of the line. In Year 5 the curriculum guidance keeps the mirror line parallel to one of the axes, which means it is either vertical or horizontal. A vertical mirror line swaps left and right, and a horizontal one swaps up and down. A corner that sits on the mirror line stays where it is.

Children plot shapes on a coordinate grid in the first quadrant, which means neither number is negative. Coordinates are written with the horizontal number first and the vertical number second, so (4, 7) is 4 across and 7 up. To reflect a corner in a vertical mirror line, they count squares to the line and then the same number again on the other side. The height of the point doesn’t change, so only the first coordinate does. For a horizontal mirror line the first coordinate stays the same and the second one changes.

A translation is a slide. Every point of the shape moves the same distance in the same direction, with no turning and no flipping, so the shape looks identical to the original but sits somewhere else. It is described with a number of squares in each direction, for example “4 squares right and 3 squares up”. On coordinates that means adding 4 to the first coordinate and 3 to the second, so the point (2, 1) moves to (6, 4). The words used matter: children are expected to say “translate”, “reflect”, “mirror line”, “left”, “right”, “up” and “down” correctly.

The third idea is that a shape has not changed. After a reflection or a translation its side lengths, its angles and its area are all the same as before. Only its position changes, and with a reflection its direction, so a flipped shape faces the other way. Children use this when they check their work: if the image has a side that is longer or shorter than the matching side on the object, a corner has been placed in the wrong spot. Tracing paper is a handy way to test it.

Words your child will hear

Reflection: A flip of a shape across a mirror line, giving a mirror image.
Mirror line: The line a shape is reflected in. In Year 5 it is vertical or horizontal.
Translation: A slide: every point moves the same distance in the same direction.
Object and image: The object is the original shape. The image is the shape after it has been reflected or translated.
Coordinates: A pair of numbers that give a position, with the number across first, then the number up.
Axes: The two number lines of a coordinate grid, the horizontal x-axis and the vertical y-axis.
Vertex: A corner of a shape. The plural is vertices.

What the National Curriculum says

In Year 5, pupils should be taught to:

Identify, describe and represent the position of a shape following a reflection, using the appropriate language
Identify, describe and represent the position of a shape following a translation, using the appropriate language
Know that a shape has not changed following a reflection or translation

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Triangle ABC has corners A (1, 2), B (3, 2) and C (1, 5). (a) Reflect it in the vertical mirror line at x = 5. (b) Separately, translate the original triangle 4 squares right and 3 squares up.

(a) Count how far each corner is from the mirror line. A is 4 squares to the left of it, B is 2 squares to the left and C is 4 squares to the left.
Put each corner the same distance on the other side of the line. A goes 4 squares to the right of the line, B goes 2 squares to the right of it and C goes 4 squares to the right of it. Each corner stays at the same height.

Write the coordinates of the image and join them.

A (1, 2) -> A′ (9, 2)
B (3, 2) -> B′ (7, 2)
C (1, 5) -> C′ (9, 5)

Check the image. In the object, B is to the right of A. In the image, B′ is to the left of A′, so the triangle has been flipped, as a reflection should be. The sides A′B′ (2 squares) and A′C′ (3 squares) match AB and AC, so the size and shape haven’t changed.
(b) For the translation, start again from the original triangle. Add 4 to every first coordinate and 3 to every second coordinate. This new image is labelled A″, B″ and C″ so it isn’t confused with the reflection. The shape slides without turning, so it faces the same way as before.
```
A (1, 2) -> A″ (5, 5)
B (3, 2) -> B″ (7, 5)
C (1, 5) -> C″ (5, 8)
```

(a) A′ (9, 2), B′ (7, 2), C′ (9, 5). (b) A″ (5, 5), B″ (7, 5), C″ (5, 8).

Common mistakes and how to help

Sliding the shape across the mirror line instead of flipping it

The image has been copied to the other side but is still facing the same way. That is a translation, not a reflection, and it is easy to do because copying is easier than flipping.

What helps: Check the order of the corners. If the object’s right-angled corner is bottom left, a reflection in a vertical line puts it bottom right. A small mirror or tracing paper turned over is a good test.

Using the same distance for every corner

A child counts the squares between the shape and the line for one corner and then uses that same number for every corner, or counts from the wrong place.

What helps: Count each corner separately from the mirror line. Corners further from the line must end up further on the other side, and a corner on the line doesn’t move.

Swapping the two coordinates

The point (2, 5) gets plotted as 5 across and 2 up. The numbers are easy to mix up when a shape has to be moved several times.

What helps: Use the saying “along the corridor and up the stairs”: across first, then up. Check each point against the axes before joining the dots.

Thinking the shape itself changes

A translated shape may end up looking different because a corner was moved the wrong amount, but children sometimes decide that “sliding” can stretch or turn a shape.

What helps: Remind them that a translation or reflection never changes side lengths, angles or area. Measure matching sides on the object and the image: if they differ, a corner is in the wrong place.

How to help at home

Complete the mirror picture. Draw a vertical or horizontal line on squared paper, draw half a simple shape on one side and ask your child to complete the reflection on the other. Then check with a small mirror stood on the line.
Play coordinate treasure hunt. Draw a grid on paper and hide a treasure at a point such as (6, 3). Give clues as translations: “start at (2, 1), move 4 right and 2 up.” Swap roles so your child writes the clues for you.
Describe moves in board games. On a chess or draughts board, ask your child to describe a piece’s move in squares: “3 squares right and 2 up”. It is translation language in a real setting.
Spot reflections around the home. Look for reflections in a window or a puddle and for mirror patterns in wallpaper. Write words such as MUM, WOW, DAD and BOB in capitals, stand a mirror beside each one and ask which look the same in the mirror and why.

Builds on

Year 4: Coordinates and translations

Leads on to

Year 6: Four-quadrant coordinates, translation, reflection

Everything in Year 5 maths

Updated 20 October 2026.