Translations
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- What Is a Translation?
Understand translation as sliding a shape - Translate Using Vectors
Move shapes using column vectors - Describe Translations
Describe the translation that maps one shape to another - Challenge — Translation Problems
Complex translation problems with multiple steps
Common Mistakes
- Confusing the direction of the vector — thinking the top number moves up/down and the bottom number moves left/right
In a column vector, the TOP number is the horizontal movement (positive = right, negative = left) and the BOTTOM number is the vertical movement (positive = up, negative = down). Think of it as reading order: across first, then up. - Moving only one vertex and guessing the rest of the shape instead of translating every point
Every single point of the shape must move by exactly the same amount. Pick each corner, apply the vector, plot the new point, then join them up. The shape stays the same size and the same way round.
Tips for Parents
- Use squared paper and draw a simple shape like an L. Then practise sliding it around using vectors: "Move it 3 right and 2 up" = vector (3, 2).
- Explain that a translation is just a slide — the shape does not flip, turn, or change size. It is the simplest transformation.
- Relate it to real life: "If you move your chair 2 tiles to the right and 1 tile forward, that is a translation." The chair does not rotate or change shape.
- Practise describing translations: show two identical shapes on a grid and ask your child to write the vector that maps one onto the other.
Key Words
- Translation — Sliding a shape to a new position without rotating, flipping, or resizing it.
- Column vector — A pair of numbers written vertically that describes horizontal and vertical movement — e.g. (3, -2) means 3 right and 2 down.
- Image — The new position of a shape after a transformation has been applied.
- Object — The original shape before a transformation is applied.
- Map — To move a shape from one position to another using a transformation — "the vector maps shape A onto shape B."
Where This Fits
Before this topic: Children should be confident plotting and reading coordinates in all four quadrants and understand basic properties of 2D shapes.
After this topic: Translations combine with reflections, rotations, and enlargements to form the full set of transformations studied through to GCSE.
How MathCraft Teaches This
In MathCraft, Translations is taught through the Coordinates & Statistics adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Translations with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
Try MathCraft Free No credit card required