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# National Curriculum - Geometry : Key Stage 2 : Mathematics Content Knowledge

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Key Stage 2
National Curriculum - Geometry
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# 1. How confident are you that you understand the meaning of

## Example

A Translation is a transformation in which every point of an object moves the same distance in the same direction.

If a translation is on a coordinate grid, the moves parallel to the x-axis and parallel to the y-axis must be specified.

## What this might look like in the classroom

Activity

In the hall invite three children to join hands to make, for example, a triangular shape. Challenge them to translate the shape by moving in a coordinated way so that the shape remains the same size and is not rotated. Ask the other children to consider how well they have managed this.

Question

Using the Interactive Teaching Program Area (from the former National Strategies), draw some translations of this starting shape − make one of them a horizontal translation, one a vertical translation and one a diagonal translation.

The pink shape is a translation of 6 squares to the right; the yellow shape is a translation of 7 squares up; the white shape is a translation of 7 squares right and 6 squares up.

## Taking this mathematics further

A translation can be described in terms of a vector. For example, the translation 4 squares right and 1 square up could be described by the vector

(41)

while the translation 1 square left and 3 squares down would be

(- 1- 3)

Note that the top number represents the horizontal movement. The vector can be drawn by joining any pair of corresponding vertices on the shape and its translation, with an arrow indicating the direction from the original shape (object) to its translation (image), as shown below:

Some tessellations can be made simply by translating an original shape − that is there are no rotations or reflections needed. Rectangles and hexagons tessellate like this:

Investigate other shapes that will tessellate with a simple translation.

## Making connections

Link this to work on coordinates. Give the children a set of coordinates that will draw a simple shape. Then get them to, for example, add 8 to the first coordinate in every pair, and 6 to the second coordinate. What happens to the shape?

Translation is one of the four basic transformations, the others being reflection, rotation and enlargement. Translations, reflections and rotations result in congruent shapes; i.e. they have the same shape and size, but the position varies. Enlargement of a shape results in similar shapes; mathematically similar shapes have the same shape, but a different size.

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