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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 - properties of shapes

New Curriculum

  • 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 circle, 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.

Non-Statutory Guidance

Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.

Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements.

These relationships might be expressed algebraically for example:

d = 2 × r ; a = 180 – (b + c).

Links and Resources

Connections within Mathematics

When solving practical problems, there are many links to be made between geometry, measures and elements of number and place value. Calculating percentages of angles, e.g. 15% of a circle, of 25% of 360˚ can bring the two mathematical strands together.

Shapes of given properties can be translated, rotated and reflected, and positions described on the full 4-quadrant coordinate grid. Measurement skills can be used to define scale factors between similar shapes, and to calculate areas of parallelograms and triangles.

Making connections to this topic in adjacent year groups

Year 5

  • 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 ½ 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.

Key Stage 3

  • calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
  • draw and measure line segments and angles in geometric figures, including interpreting scale drawings
  • describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
  • derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
  • understand and use the relationship between parallel lines and alternate and corresponding angles
  • use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
  • interpret mathematical relationships both algebraically and geometrically

Cross-curricular and real life connections

Learners will encounter properties of shape in:

The world around them – using their ability to recognise and describe 3-D shapes used in building houses, packaging used by supermarkets and storage boxes used in and around the home.

Design and Technology – using an ability to draw 2-D shapes using given dimensions and angles to make and construct technology projects. Building simple and more complex 3-D shapes using plastic toy construction materials as an example.

Physical Education – e.g. in orienteering, pupils use knowledge of angles to find clues and use an understanding of properties of shapes to solve problems.

ICT- use of programming technology to design sequences, using knowledge of angles, to compare and classify geometric shapes based on their properties. Pupils use knowledge of angles to support program writing and building of 3-D models.

History – Pyramids and obelisks – using plasticine or modelling equipment to build models and gain an understanding of the faces and angles used in building 3-D shapes used throughout history.

Art – the NCETM Primary Magazine provides many useful links for looking at shape within art. Issue 34 provides some useful starting points, using the snail work of Matisse as a stimulus.

Key understandings in mathematics learning – Paper 5: Understanding space and its representation in mathematics

This paper is about children’s informal knowledge of space and spatial relations as well as their formal learning of geometry. It deals with the connection between these two kinds of knowledge.

Going round in circles

This article describes how a pair of PowerPoint presentations can be used to establish mental images that can help pupils to understand, and so recall, the principles that underlie the formulae to calculate the circumference and the area of a circle

You will need to be logged in to the ATM site to view this article – joining as an associate member is simple, quick and free.

Programme of Study statements Activities
A B C D E F G
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            

Activity A - Thinking 3D

A series of activities designed to support the development of transferring a 2D representation of a 3D object into a model of the object itself as well as gaining an understanding of positional language.

3d shape

Activity B - Round a Hexagon

An activity from Nrich supporting the finding of missing angles, including internal and external angles and the use of a protractor.

Hexagon

Activity C - Watching the wheels go round and round

An Nrich activity to support understanding of the term circumference. Links are made to converting units of measure.

Penny Farthing bicycle

Activity D - Quadrilaterals Game

An activity to compare and classify geometric shapes based on their properties in a game that is linked to the card game rummy.

Cards with geometric shapes

Activity E - Property Chart

This activity used property charts to compare and classify geometric shapes based on their properties.

Property chart to classify geometric shapes

Activity F - Cut Nets

An Nrich activity to support the skills of visualisation in building simple 3-D shapes from nets.

Nets to build 3D shapes

Activity G - Dynamic Geometry

An introduction to dynamic geometry with helpful links to websites offering free software to support the exploration of properties of circles and the formation of nets for a comprehensive selection of 3-D shapes.

Useful Resources

Protractors or angle measurers, rulers, dot isometric paper, pair of compasses, set squares, dynamic geometry software, set of folding geometric shapes, pinboards and geoboards, Perspex mirrors, 2-D shape dice, class sets of ‘polydron’ or other 3D shape construction materials.

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

draw 2-D shapes using given dimensions and angles

Children should be able to construct a triangle given two sides and the included angle

Here is a sketch of a triangle. (It is not drawn to scale).

Sketch of a triangle

Draw the full size triangle accurately, below. Use an angle measurer (protractor) and a ruler. One line has been drawn for you.

 

 

 

 

Line

recognise, describe and build simple 3-D shapes, including making nets

Children should be able to identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge of properties to draw 2-D shapes and identify and draw nets of 3-D shapes

They should be able to respond accurately to questions such as;

‘I am thinking of a 3D shape. It has a square base. It has four other faces which are triangles. What is the name of the 3D shape?’

‘Which of these nets are of square based pyramids? How do you know?

Nets of square based pyramids

‘Is this a net for an open cube?’ How do you know?

Net for an open cube

compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

Children should be able to make and draw shapes with increasing accuracy and knowledge of their properties.

They should be able to carry out activities such as;

‘Give me instructions to get me to draw a rhombus using my ruler and a protractor’

‘On the grid below, use a ruler to draw a pentagon that has three right angles’

illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

They should know that:

  • The circumference is the distance round the circle
  • The radius is the distance from the centre to the circumference
  • The diameter is 2 x radius

 

recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

Children should be able to estimate angles, use a protractor to measure and draw them, on their own and in shapes. They should know that the angle sum of a triangle is 180˚, and the sum of angles around a point is 360˚.

They should be able to use this knowledge to respond accurately to questions such as;

‘There are nine equal angles around a point. What is the size of each angle?’

‘There are a number of equal angles around a point. The size of each angle is 24°. How many equal angles are there?’

Children should be able to calculate the size of angle ‘y’ in this diagram without using a protractor.

Calculation of an angle

This resource from Teachers TV (sign-in required to view) features Richard Dunne, Mathematics consultant, who explains that mathematics involves abstraction and symbolism, the ingredients of higher order mental processes, an essential skill that students need to develop.

This series of 24 very short video clips (each lasting a few seconds) challenges children to determine whether a given net can be assembled to make a 3D shape. A good, interactive resources for use in the classroom.