Year 4 maths · Key Stage 2 · Geometry – position and direction

Year 4 coordinates and translations: a guide for parents

In Year 4 children learn a precise way of saying where something is on a grid: coordinates, such as (2, 5). They plot points and join them to draw shapes, and they describe how a shape slides from one place to another, for example 3 squares right and 2 squares up. This work happens in the first quadrant only, so every number is zero or positive.

Coordinates and translations, explained

A coordinate pair gives the position of a point using two numbers. The grid has two number lines called axes. The horizontal axis is the x-axis and the vertical axis is the y-axis. They cross at the origin, which is (0, 0). To read a point such as (2, 5), you start at the origin, go 2 along the x-axis and then 5 up the y-axis. The first number always tells you how far across, and the second how far up. A rhyme that many classrooms use is “along the corridor and up the stairs”.

In Year 4 the grid is only one quarter of the full coordinate plane, the first quadrant, where both numbers are zero or more. Children draw the axes themselves with equal spacing and whole-number labels, and then read, write and use coordinate pairs. The numbers label the lines of the grid, so a point sits where two lines cross, not inside a square. This is different from the grid references on many maps and board games, which label the squares, so it is worth pointing out. Points on an axis have a zero in one place: (0, 3) is on the vertical axis and (4, 0) is on the horizontal axis. Negative numbers, and all four quadrants, come later in primary school.

Once children can plot points, they plot a list of coordinates, join the points in order with straight lines and say what shape they have drawn. Schools often give them three corners of a rectangle or square and ask them to work out the missing fourth corner, which tests whether they understand how the numbers behave. Some schools use coordinate-plotting software on a computer or tablet as well as squared paper.

The second idea in Year 4 is translation, the mathematical word for sliding a shape without turning or flipping it. A translation is described using units to the left or right and up or down, such as “4 right and 1 down”. Every point of the shape moves by exactly the same amount, so the shape stays the same size and faces the same way, only in a new position. Children can describe the movement of a single point as well as a whole shape, and say how its coordinates change: moving 3 right adds 3 to the x-coordinate.

Words your child will hear

Coordinates: A pair of numbers that give a position on a grid, written in brackets such as (3, 4).
x-axis and y-axis: The horizontal number line and the vertical number line of a grid.
Origin: The point (0, 0) where the two axes cross.
Plot: Mark a point on a grid at its coordinates.
Translation: A slide of a shape to a new position, with no turning or flipping.
First quadrant: The part of the grid where both coordinates are zero or positive.
Polygon: A flat shape with straight sides, such as a triangle or a rectangle.

What the National Curriculum says

In Year 4, pupils should be taught to:

Describe positions on a 2-D grid as coordinates in the first quadrant
Describe movements between positions as translations of a given unit to the left/right and up/down
Plot specified points and draw sides to complete a given polygon

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

A worked example

Plot the points (1, 1), (4, 1), (4, 3) and (1, 3), and join them in that order. Name the shape. Then translate it 3 squares right and 2 squares up and write the new coordinates.

Plot (1, 1): start at the origin, go 1 along and 1 up. Plot (4, 1): 4 along and 1 up. Plot (4, 3): 4 along and 3 up. Plot (1, 3): 1 along and 3 up.
Join the points in order and back to the start. The bottom side runs from x = 1 to x = 4, so it is 3 squares long. The side going up runs from y = 1 to y = 3, so it is 2 squares long. Opposite sides match and all four corners are right angles: it is a rectangle, 3 by 2.
Translate each corner 3 right and 2 up. Moving right changes only the first number, so add 3 to each x-coordinate. Moving up changes only the second number, so add 2 to each y-coordinate.
Write the new corners and check that the new shape is still a 3 by 2 rectangle.
```
(1, 1) → (4, 3)
(4, 1) → (7, 3)
(4, 3) → (7, 5)
(1, 3) → (4, 5)
```

The shape is a 3 by 2 rectangle. After the translation its corners are (4, 3), (7, 3), (7, 5) and (4, 5).

Common mistakes and how to help

Writing coordinates the wrong way round

Children plot (2, 5) by going up 2 and across 5, since it seems natural to read numbers in whatever direction feels easiest.

What helps: Always across first, then up: “along the corridor, up the stairs”. Tell your child to put a finger on the origin and walk it along, then up, before marking the point.

Counting the squares instead of the lines

Children treat the grid as a set of boxes and count the square that touches the axis as 1, which puts every point one place too far or too close.

What helps: Year 4 grids put the numbers on the lines, and a point sits where two lines cross. Start counting at 0, on the origin, and say each number as you move along.

Forgetting that the axes start at zero

A child plotting (0, 3) is puzzled that it isn’t inside the grid, or counts the first line as 1.

What helps: Point out that (0, 3) is 0 along and 3 up, so it sits on the vertical axis. Label the origin as (0, 0) clearly on every grid.

Turning or flipping a shape when asked to translate it

The word ‘move’ suggests any kind of movement. Some children also count the point they start from as 1, so the shape ends up one square short.

What helps: Trace the shape on paper, then slide the tracing across the grid without turning it. Count the jumps, not the points you land on, and check that one corner has moved the right distance.

How to help at home

Hide and seek on a grid. Draw a 6 by 6 grid on paper and hide a treasure or a ship on one crossing. Your child guesses coordinates such as (3, 2) until they find it.
Join the dots. Write a list of coordinates that makes a simple picture when joined in order, such as a house or a kite, and let your child plot and draw it. Then ask them to invent one for you.
Give directions on a map. Use a floor plan, a game board or a map with gridlines. Describe how to get from one square to another with moves such as “3 right, 2 up”.
Slide a shape. Cut a shape out of paper and slide it around a grid. Ask your child to say each move and to write down where one corner starts and ends.

Leads on to

Year 5: Reflection and translation

Everything in Year 4 maths

Updated 20 October 2026.