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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 2 - Geometry - properties of shapes

New Curriculum

  • identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
  • identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
  • identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
  • compare and sort common 2-D and 3-D shapes and everyday objects.

Non-Statutory Guidance

Pupils handle and name a wider variety of common 2-D and 3-D shapes including: quadrilaterals and cuboids, prisms, cones and polygons, and identify the properties of each shape (e.g. number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces.

Pupils read and write names for shapes that are appropriate for their word reading and spelling.

Pupils draw lines and shapes using a straight edge.

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.

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

Making connections to other topics within this year group

Geometry (position and direction)

Within other areas of the mathematics curriculum for Year 2, there will be opportunities to link work on Geometry (properties of shape) with:

  • 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).

Making connections to this topic in adjacent year groups

Year 1

recognise and name common 2-­D and 3-­D shapes, including:

  • recognise and name common 2-D and 3-D shapes, including:
  • 2-­D shapes (e.g. rectangles (including squares), circles and triangles)
  • 3-­D shapes (e.g. cuboids (including cubes), pyramids and spheres)

Non Statutory Guidance

Pupils handle common 2-D and 3-D shapes, naming these and related everyday objects fluently. They recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other.

Year 3

  • draw 2-­D shapes and make 3-­D shapes using modelling materials; recognise 3-­D shapes in different orientations and describe them
  • recognise angles as a property of shape or a description of a turn
  • identify right angles, recognise that two right angles make a half-­turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
  • identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Non-Statutory guidance

Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.

Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.

Cross-curricular and real life connections

Children need to be encouraged to use the language associated with shape in order to describe the physical world and their environment. Understanding how things fit together (or when and why they do not) is important for making connections.

For example, building anything involves a lot of critical consideration about shape in three dimensions, as well as angles. Reading maps and simple plans also involves an understanding of the relationship between 2-D and 3-D shape.

  • Haylock, D. (2008). Understanding Mathematics for Young Children, Chapter 8, Understanding Shape and Space. Available: 978-1-4129-4726-8

    Haylock and Cockburn give an accessible and thorough introduction and subject knowledge guidance on Shape and Space in this very readable book.

  • The Development of Spatial and Geometric Thinking: the Importance of Instruction.

    Article by Jenni Way for Nrich highlighting three levels of thinking and their application to 2-dimensional shape

  • Taking shape magazine article | Published in TES Newspaper on 11 May, 2008 | By: Marjorie Gorman

  • Mason.J. (2010). Thinking Mathematically, Chapter 7 page 105, Developing an Internal Monitor. Available: 978-0-273-72891-7.

    In this chapter Mason explores thinking. What do we do, how do we do it, how can we support it, use, develop it? I suggest that by considering how we think mathematically and applying these principles to our own subject knowledge and mathematical experiences, we can begin to unravel the complexities of what we ask children to do every day. In this chapter Mason et al have moved from advice on ‘how to think’, towards ‘reflecting’ and the power of using those experiences as ‘critical moments of an investigation’.

  • What’s Inside/outside/under the Box?

    Back, J and Pumfrey L.. (c. 2005). What's Inside/outside/under the black box.

    Extract: “Shape and space offers wonderful opportunities for enriching children's experiences in mathematics in practical ways, as well as making links with other areas of the curriculum, such as art, religious education and history. If it is simply reduced to making tables about the properties of different kinds of triangles and quadrilaterals then we are missing plenty of mathematical treats”.

    In this useful article Back and Pumfrey discuss ways to extend and enrich this important area of mathematics.

Programme of Study statements Activities
A B C D E
Identify and describe the properties of 2-­D shapes, including the number of sides  and  symmetry in a vertical line          
Identify and describe the properties of 3-­D shapes, including the number of edges, vertices and faces          
Identify 2­D shapes on the surface of 3-D shapes, for example a circle on a cylinder and a triangle on a pyramid          
Compare and sort common 2-­D and 3-­D shapes and everyday objects          

Activity A: Skeleton Shapes

Children think about how much modelling clay and straws they would need to create outlines of 3D shapes.

How many balls of modelling clay and how many straws does it take to make the cube?

Here are some piles of modelling clay balls and straws:

Look at the shapes below and decide which piles are needed to make a skeleton of each shape.

 

Activity B: Shadow Play

Stage: 1

Why do this problem?

This problem requires learners to visualise 3D shapes, and therefore consolidates knowledge of their properties. Pupils are also reminded that there is not necessarily one right answer in mathematics!

Activity C: Data Shapes

This problem uses simple shapes on cards in three colours for sorting data in different ways. Some excellent extension ideas for moving the children on in their understanding of shape.

If you would like to make your own cards like these they can be downloaded from NRICH using the link above.

Activity D: Dismantling Boxes

– Haylock and Cockburn, Page 200

Haylock, D. (2008). Understanding Mathematics for Young Children Available: 978-1-4129-4726-8

Objective: To help children identify the plane shape forming the constituent parts of a solid shape

Materials: Ask the children to bring in 2 each of any interestingly shaped boxes from home, ideally from the family shop. If necessary supplement these with your own examples: cylinder, pyramids, tetrahedral, cubes, cuboids, prisms.

Activity: The children should go round the edges of one of one of the boxes with a thick, preferably black, marker. Then they dismantle the box, cut out, and identify the shapes that have been marked out. Discard any flaps. The complete box in the pair, and the cut out shapes from the other are then put in a display to show the various flat surfaces used to make the solid shape.

Activity E: Stolen Shape

Haylock and Cockburn, Page 197

Haylock, D. (2008). Understanding Mathematics for Young Children Available: 978-1-4129-4726-8

Objective: To develop young children’s ability to sort shapes according to attributes

Materials: to differentiate consider breadth of knowledge and use a variety of

  • Plastic shapes – 2 D (colour, size, shape) Expand selection to include more names and variations on family group (Polygons, Triangles)
  • Plastic shapes – 3D (colour, size, shape) Expand selection to include more names and variations on family groups (Tetrahedra, Prisms)
  • Real life objects – 3D

Activity: First, two or three children discuss the shapes and work together to sort them into different categories. Perhaps the children can annotate their categories with signs, symbols. Given the opportunity to present their findings children may design their own display, labelling, table of results? Supporting their discussion by providing the language prompts, ensuring the children understand the language needed to discuss properties. Do the children know how to think, share their thoughts with others, and listen to the ideas of others? How can you support their findings and ideas, though annotation, scaffolding where necessary (EAL/ SEN)?

Then the children take turn to close their eyes while the shapes are jumbled back up. The teacher, adult or child in the group then ‘steals’ a shape. The children open their eyes and have to work out, through discussion, which shape has been stolen. Once decided they must describe it to the teacher, adult or child “the large red circle”. Once mastered the number of shapes ‘stolen’ could be increased.

What ways do the children record their solutions, annotate their findings?

How does the correct use of language support their conversation, and their generalising (talk) about shape?

Useful Resources

Lolly sticks, string, elastic, drinking straws and modelling clay (or even marshmallows if this does not contravene any of your school’s policies - Healthy Schools, H&S etc), boxes of shapes, paper for folding and cutting, a range of interestingly shaped containers.

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

identify and describe the properties of 2-D shapes, including the number of sides and symmetry in a vertical line

Venn diagram

identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

Grid

identify 2-D shapes on the surface of 3-D shapes, for example a circle on a cylinder and a triangle on a pyramid

Cube

compare and sort common 2-D and 3-D shapes and everyday objects.

Children can sort two sets of 2D and 3D shapes in 2 or more different ways using different criteria each time. For example, they might choose ‘dimensions’ or ‘right angled’

  • Shape and Space (Video)

    The video ‘Shape and Space’ looks at games and activities which help children develop their understanding of shape and space.

  • Real-life Application of Mathematics (video) Oxford School Improvement, Oxford University

    Andrew Jeffrey discusses how to strengthen the use and application of maths in school.

    3 min 54 seconds

  • National STEM Centre

    An entire unedited Year 2 Shape lesson; but the starter of this lesson is a good example of children problem-solving using 2-D and 3-D shape; the teacher uses keywords and describes a shape which children have to name or draw.