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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 4 - Geometry - position and direction

New Curriculum

  • describe positions on a 2-D grid as coordinates in the first quadrant
  • describe movements between positions as translations of a given unit to the left/right and up/down
  • plot specified points and draw sides to complete a given polygon.

Non-Statutory Guidance

Pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of coordinates, for example (2, 5), including using coordinate-plotting ICT tools.

Links and Resources

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.
Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

– National Curriculum in England Framework Document, September 2013, p10)

Connections within Mathematics

Making connections to this topic in adjacent year groups

[NB This topic does not appear in Year 3, so we are including Year 2 statutory requirements here]

Year 2

Pupils should be taught to:

  • order and arrange combinations of mathematical objects in patterns and sequences
  • use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti- clockwise).

Non-statutory guidance:

Pupils should work with patterns of shapes, including those in different orientations.

Pupils use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (e.g. pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles).

Year 5

Statutory requirements:

  • 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.

Non-statutory guidance:

Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes.

Cross-curricular and real life connections

Learners will encounter coordinates in:

  • Geography, when learning about map referencing and directions.

Learners will encounter translation in:

  • DT, when designing rooms, planning buildings and construction projects
  • Art, when looking at patterns and architecture

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

Programme of Study statements Activity
A B C
Describe positions on a 2-D grid as coordinates in the first quadrant
Describe movements between positions as translations of a given unit to the left/right and up/down    
Plot specified points and draw sides to complete a given polygon    

Activity A - Coordinate Challenge

  • NRICH Activity
    Position letters according to clues on a grid. Also supports symmetry.

    Letters

Activity B – A Cartesian Puzzle

  • NRICH Activity
    Plot coordinates given and identify missing coordinates to create particular shapes.

    Cartesian puzzle

Activity C - Translation or Destination 1

Resources – large grids or chess boards numbered on two axes, counters, two dice, Counter with T (translation) on one side and D (destination) on the other.

Children work in pairs using a large grid or chess board and counters.

They roll the dice to get starting coordinates and place one counter on the board at the starting coordinates. Roll the dice again. Toss the coin.

If T then use dice to give the translation up/down and left/ right. Children establish which directions are possible given the size of the board. Place a second counter at the new position.

If D then use the second roll of the dice as the new coordinates and children describe the translation taking place between the two sets of coordinates using the language up/down left/right.

Grid

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

describe positions on a 2-D grid as coordinates in the first quadrant

Shaded square

 

describe movements between positions as translations of a given unit to the left/right and up/down
I can describe where a shape will be after translation

This triangle is translated two squares to the left and one square down.

Give the coordinates of its vertices in the new position.

 Triangle

 

plot specified points and draw sides to complete a given polygon

Plotting points

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