Translation (using vectors)
GCSE Mathematics – Numeracy and GCSE Mathematics
GCSE Mathematics
Understanding and using properties of position, movement and transformation
 Transformations, including: Translation; description of translation using column vectors
Possible learning objectives
 Carry out transformations
 Describe transformations
Possible learning outcomes
 Translate a shape horizontally or vertically using a worded description
 Translate a shape horizontally and vertically using a worded description
 Describe a translation using words
 Understand notation for column vectors
 Translate a shape using a column vector
 Describe a translation using a column vector
Pedagogical notes
 Students may well have previously experienced transforming shapes by reflecting,
rotating or translating. However, in the case of translation they will have used
words to describe the movement.
 A column vector can itself be represented on grid. It has size and direction, and is
drawn as
Prerequisites
 Use the language of transformations: object, image, map
 Understand horizontal and vertical movement
Mathematical language
Transformation
Translate, translation
(Column) vector
Horizontal
Vertical
Object
Image
Map
Notation
(𝑎𝑏) notation for column vectors. a is the distance right and b
is the distance up. Negative values therefore move in the
opposite direction.
This can be used to check the translation: in the case of a translation of (52), joining
each pair of corresponding vertices on the object and image should result in an
identical diagram of the vector (5 units across and 2 up), with the arrow in the
direction of movement. For example:
Image
Object
Reasoning opportunities and probing questions
 Show me an example of a vector which would move a shape left and
up / right and up / down only, …
 Always / Sometimes / Never: A vector of the form (𝑎𝑏) moves the
shape right and up
2
 What is the same and what is different: (−3
), (−2
), (−2
) and (−2
)?
−3
−3
3
Possible activities
Hwb: Question 38: Transformations
Hwb: Question 59: Which way now?
Hwb: Question 62: Lost in translation
Kangaroo Maths: Moving House
NRICH: Vector Racer
 WJEC: New content guidance includes worked examination questions and
annotated candidates’ responses.
Potential misconceptions
 Some students may think that there is a horizontal bar within the
vector, as in a fraction
 Some students may think that the numbers in the vector indicate the
space between the object and the image, rather than the distance
that is to be moved
 Some students may think that the top number indicates the
up/down movement and vice versa
 Some students may confuse the left/right movement (thinking that a
negative value of a moves the shape to the right) or the up/down
movement