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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 6 - Geometry - position and direction

New Curriculum

  • describe positions on the full coordinate grid (all four quadrants)
  • draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Non-Statutory Guidance

Pupils draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers.

Pupils draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes. These might be expressed algebraically for example, translating vertex (a, b) to (a - 2, b + 3); (a, b) and (a + d, b + d) being opposite vertices of a square of side d.

Links and Resources

Connections within Mathematics

Pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

Making connections to this topic in adjacent year groups

Year 5

  • identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

Key Stage 3

  • recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
  • interpret mathematical relationships both algebraically and graphically
  • identify properties of, and describe the results of translations, rotations and reflections applied to given figures
  • identify and construct congruent triangles, and construct similar shapes by enlargement, including on coordinate grids

Cross-curricular and real life connections

In geography, learners will encounter coordinates through map work.

In Design & Technology, learners may be required to use their knowledge of translation, in particular, scaling up and down.

Coordinates and translation may also be used when designing rooms, planning buildings and floor layouts, or when scaling drawings or patterns in Art & Design.

This short article looks at the importance of representing position, space and movement mathematically

Programme of Study statements Activities 
A B
describe positions on the full coordinate grid (all four quadrants)    
draw and translate simple shapes on the coordinate plane, and reflect them in the axes    

Activity A – Transformation Tease

An investigation into positioning and transforming through reflection and rotation. using all four quadrants

Calculation of an angle

Activity B – Battleships

The traditional game of battleships can provide a useful reminder for children when using coordinates. Challenge the children to create their own version of the game, perhaps with a different theme, using all four quadrants.

Useful Resources

Squared paper

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

describe positions on the full coordinate grid (all four quadrants)

Children should be able to answer questions such as;

The two shaded squares below are the same size.

Positions on a coordinate grid

A is the point (17,8). B is the point (7,-2).

What are the co-ordinates of the point C?

draw and translate simple shapes on the coordinate plane, and reflect them in the axes

Children should be able to draw a shape with corners at given vertices, and describe the properties of the shape. Can they create the same shape where all of the coordinates will be positive? Negative?

They should be able to sketch the reflection of a simple shape in two mirror lines at right angles and find the coordinates of selected points.

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