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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 5 - Geometry - properties of shapes

New Curriculum

  • identify 3-D shapes, including cubes and other cuboids, from 2-D representations
  • know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
  • draw given angles, and measure them in degrees (°)
  • identify:
  • use the properties of rectangles to deduce related facts and find missing lengths and angles
  • distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Non-Statutory Guidance

Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles.

Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools.

Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems.

Links and Resources

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.
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 other topics within this year group

Geometry- position and direction

  • 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.

Making connections to this topic in adjacent year groups

Year 4

  • compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
  • identify acute and obtuse angles and compare and order angles up to two right angles by size
  • identify lines of symmetry in 2-D shapes presented in different orientations
  • complete a simple symmetric figure with respect to a specific line of symmetry

Year 6

  • draw 2-D shapes using given dimensions and angles
  • recognise, describe and build simple 3-D shapes, including making nets
  • compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
  • illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
  • recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

Cross-curricular and real life connections

Work on properties of shape can be integrated with work in several other areas of the curriculum. e.g.

  • When working with 2-D representations e.g. maps, nets, isometric drawings, plans and elevations
  • When using digital technology e.g. Logo, dynamic geometry to create geometric patterns
  • When looking at art and architecture to identify geometric shapes and properties
  • When using digital cameras to capture geometric shapes and objects in the environment and around school

A comprehensive review of the literature on school geometry

This article argues the importance of reasoning when teaching geometry.

Programme of Study statements Activities
A B C D E
identify 3-D shapes, including cubes and other cuboids, from 2-D representations          
know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles          
draw given angles, and measure them in degrees (°)          
identify:
    • angles at a point and one whole turn (total 360°)
    • angles at a point on a straight line and half a turn (total 180°)
  • other multiples of 90°
          
use the properties of rectangles to deduce related facts and find missing lengths and angles          
distinguish between regular and irregular polygons based on reasoning about equal sides and angles          

Activity A: Logo Challenge 1 – Star Square

Use ‘Logo’ to draw the design shown. This requires using knowledge of angle properties of 2D shapes.

Activity B: Cuboids

How many different cuboids can you make with 12, 24, 36… linking cubes?

Challenge the children to draw their formed shapes on isometric paper. In how many different ways can a single cuboid be represented? Does the number of cubes need to be even?

Activity C: Equal angles

Fold along the diagonals of a square piece of paper. Unfold and mark all the angles of the same size. Fold along the lines of symmetry of a square piece of paper. Unfold and mark all angles of the same size.

Repeat for a rectangle. Repeat for other quadrilaterals. Are there the same number of equal angles each time? Why/not?

What if the starting shape was a regular pentagon? Hexagon?

Activity D: Sorting triangles

Cut out a set of a variety of triangles including equilateral, isosceles and scalene and those whose greatest angle is acute, right and obtuse. Ensure there is a set of at least twenty triangles per group. Invite children to find as many ways as possible to sort the triangles.

Summarise by introducing classification by side length: equilateral, isosceles, scalene and classification by greatest angle: acute-angles, right-angles and obtuse-angled. Complete the table, by placing triangles in the space – children could construct their own examples. They must justify any gaps…

  equilateral isosceles scalene
acute-angled      
right-angled      
obtuse-angled      

Activity E: Shape Perimeter

How many shapes can you make with a perimeter of 12cm?

This can be extended to asking about the area of the shapes made and challenging the misconception that a fixed perimeter implies a fixed area.

Useful Resources

  • Squared, plain and dotty papers
  • Logo
  • Dynamic geometry
  • Practical materials for shape

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

Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

These are pictures of 3-D shapes. Which 3-D shapes are pictured here? Put the names in the boxes.

Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

Look at these angles.

Label each angle acute, obtuse or reflex. List the 5 angles in order from smallest to largest.

Draw given angles, and measure them in degrees (°)

Measure A accurately. Use a protractor (angle measurer).


Measure accurately the smallest angle in the above shape. Use a protractor (angle measurer).

This diagram is not drawn accurately. Calculate the size of angle m

Identify:

  • Angles at a point and one whole turn (total 360°)
  • Angles at a point on a straight line and ½ a turn (total 180°)
  • Other multiples of 90°

PQ is a straight line. Not drawn accurately.

Calculate the size of angle x. Do not use a protractor (angle measurer).

This shape is three-quarters of a circle.

How many degrees is angle x?

In the diagram below, if you were standing at X, facing A, what angle would you turn through if you turn and face C?

Use the properties of rectangles to deduce related facts and find missing lengths and angles

 

This diagram is not drawn accurately. Calculate the size of angle m

Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

This resource introduces the properties of 2-dimensional 3 and 4 sided shapes in an engaging way for children. Care needs to be taken when using this resource as it could reinforce the common misconception that there are four types of triangle: equilateral, isosceles, scalene and right angled.

A ‘Masterclass’ on polygons which includes some exciting ideas for teaching in the upper key stage 2 classroom.