Translations on a grid: what children learn
Year 4 pupils describe movements between positions as translations of a given unit to the left or right and up or down.
In this game each card shows a point's start and end coordinates, and children match it to the translation that moves it there. Comparing the x-coordinates gives left or right, and the y-coordinates give up or down.
This topic covers the Year 4 statutory requirement in the National Curriculum in England (Geometry – position and direction): pupils should be taught to “describe movements between positions as translations of a given unit to the left/right and up/down”. Year 4 pupils are usually aged 8–9.
For families following US standards, the closest Common Core standard is 5.G.A.1, which is taught in Grade 5. Formal translations are Grade 8 in Common Core (8.G.A.1).
How to play
Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.
Step by step
- Compare the first numbers. If the x-coordinate gets bigger, the point moved right. If it gets smaller, it moved left.
- Compare the second numbers. If the y-coordinate gets bigger, the point moved up. If it gets smaller, it moved down.
- Find how far. The difference between the numbers is how many squares it moved.
- Say it in order. Give left or right first, then up or down: 4 right, 2 up.
Worked examples
Example 1: (1, 2) to (4, 2)
Working: x: 1 to 4 is 3 more. y does not change.
Answer: 3 right
Example 2: (5, 5) to (5, 1)
Working: x does not change. y: 5 to 1 is 4 less.
Answer: 4 down
Example 3: (2, 1) to (6, 3)
Working: x: 2 to 6 is 4 more. y: 1 to 3 is 2 more.
Answer: 4 right, 2 up
Common mistakes and how to fix them
- Mixing up which number goes with left or right. The first number goes along, so it tells you left or right.
- Giving the end point instead of the movement. A translation is a movement, like '3 right', not a position.
- Getting the direction backwards. Move your finger from the start point to the end point on a grid.
Activities to try at home
- Move a counter on squared paper and describe each move as a translation.
- Give directions on a chessboard: 2 right, 1 up.
- Draw a shape, slide it, and describe the slide.
Ideas for the classroom
- Pupils translate a shape on a grid and record the new coordinates.
- Give start and end coordinates and ask pupils to find the translation without a grid.
- Ask: what translation would bring the point back?
Free printable game and worksheet
The free printable starts with a game sheet, such as a colour-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Does the shape change when it is translated?
No. A translation slides a shape without turning, flipping or resizing it.
Do children need to plot every point?
Not always. Comparing the coordinates is quicker once children understand it.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it, then pick its partner.