Geometry: Properties of Shapes
KS1MA-Y2-D006
Pupils identify and describe properties of 2-D and 3-D shapes including sides, edges, vertices, faces and line symmetry, and compare and sort shapes and everyday objects.
National Curriculum context
In Year 2, the study of shapes moves from recognition and naming (Year 1) to analysis of properties. Pupils handle and name a wide variety of common 2-D and 3-D shapes including quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape — for example, 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. A new concept in Year 2 is line symmetry: pupils identify line symmetry in 2-D shapes presented in a vertical line, connecting geometric symmetry to their experience of reflection and pattern. Pupils identify 2-D shapes on the surface of 3-D shapes — for example, a circle on a cylinder and a triangle on a pyramid — making explicit the connection between 2-D and 3-D geometry. Pupils read and write names for shapes appropriate to their word reading and spelling, and draw lines and shapes using a straight edge.
3
Concepts
2
Clusters
2
Prerequisites
3
With difficulty levels
Lesson Clusters
Identify and describe properties of 2-D and 3-D shapes
introduction CuratedProperties of 2-D shapes (sides, symmetry) and 3-D shapes (faces, edges, vertices) are the foundational analytical skills for this domain. They provide the vocabulary for the connecting concept.
Explore the relationship between 2-D shapes and the faces of 3-D shapes
practice CuratedIdentifying 2-D shapes on the surface of 3-D shapes connects both property clusters and builds deeper spatial understanding. C019 explicitly co-teaches with both C017 and C018.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Properties of 2-D and 3-D Shapes
Mathematics Pattern SeekingPedagogical rationale
Y2 geometry moves from recognition to property-based description. Pupils must describe shapes using mathematical vocabulary (sides, vertices, edges, faces) rather than informal language. The introduction of symmetry adds a new dimension to shape analysis: folding shapes to test for symmetry is a powerful concrete activity. Identifying 2-D shapes on the surfaces of 3-D shapes connects the two domains and deepens understanding of both. Sorting and classifying shapes by properties develops logical reasoning.
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (3)
Properties of 2-D shapes: sides, symmetry
knowledge AI FacilitatedMA-Y2-C017
Year 2 pupils move from recognising 2-D shapes by name (Year 1) to analysing their properties: the number of sides, the number of vertices (corners), and the presence of line symmetry in a vertical line. Pupils handle and name a wider range of 2-D shapes including quadrilaterals and polygons, and identify and compare shapes on the basis of their properties. Mastery means pupils can precisely count and describe sides and vertices, identify whether a shape has vertical line symmetry, and sort shapes by their properties using precise vocabulary.
Teaching guidance
Use physical shape tiles and geoboards so pupils can feel and count sides. Introduce the full range of quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium — pupils should be challenged by these rather than only seeing squares and rectangles. For line symmetry, use mirrors and paper folding: a shape has vertical line symmetry if a vertical fold creates two identical halves. Sort shapes using a two-way table (e.g. has symmetry/does not have symmetry; 4 sides/not 4 sides). Introduce the terms polygon (closed straight-sided shape) and quadrilateral (four-sided polygon).
Common misconceptions
Pupils often confuse vertices and sides, counting vertices as sides or missing corners when counting sides of irregular polygons. Line symmetry in non-vertical lines confuses pupils who have only experienced vertical symmetry; they may claim a shape has no symmetry when it has a diagonal or horizontal line of symmetry (though only vertical symmetry is required at Year 2). Pupils may think regular shapes (equilateral triangles, squares) are the only shapes with symmetry.
Difficulty levels
Counting the number of sides and corners (vertices) of common 2-D shapes by tracing with a finger.
Example task
Trace around this shape. How many sides does it have? How many corners?
Model response: It has 4 sides and 4 corners. It is a rectangle.
Identifying and comparing 2-D shapes by their properties (number of sides, vertices, right angles), including non-standard orientations.
Example task
How are a square and a rectangle similar? How are they different?
Model response: Both have 4 sides and 4 corners with right angles. A square has all sides the same length but a rectangle has 2 long sides and 2 short sides.
Sorting 2-D shapes by properties including line symmetry, and identifying shapes from a description of properties.
Example task
I am thinking of a shape. It has 3 sides, 3 corners and 1 line of symmetry. Draw it.
Model response: An isosceles triangle. [Draws a triangle with a vertical line of symmetry — two sides the same length]
CPA Stages
concrete
Children handle 2-D shape tiles, tracing around each side with their finger to count sides and touching each corner to count vertices. They use geoboards with elastic bands to make shapes with specific numbers of sides. Mirrors placed along the edge of a shape check for line symmetry.
Transition: Child counts sides and vertices accurately for any 2-D shape by tracing, makes shapes on a geoboard to match given properties, and uses a mirror to check for vertical line symmetry.
pictorial
Children identify properties from drawn shapes, sort shapes using two-way tables (e.g. has symmetry / does not have symmetry × 3 sides / 4 sides / more than 4 sides), and draw lines of symmetry on shapes. They compare shapes by their properties in written descriptions.
Transition: Child sorts drawn shapes by properties (sides, vertices, symmetry) into two-way tables, draws vertical lines of symmetry on shapes that have them, and writes property descriptions.
abstract
Children identify shapes from verbal descriptions of their properties and describe shapes using precise vocabulary (sides, vertices, line of symmetry, polygon, quadrilateral) without visual support.
Transition: Child identifies shapes from property descriptions alone and describes shapes precisely using 'sides', 'vertices', 'line of symmetry', 'quadrilateral' and 'polygon' without needing to see or handle the shape.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (2-D shape tiles (wide variety including irregular shapes), Geoboards and elastic bands). AI delivers instruction; facilitator sets up materials.
Properties of 3-D shapes: faces, edges and vertices
knowledge AI FacilitatedMA-Y2-C018
Year 2 pupils extend their knowledge of 3-D shapes from recognising and naming (Year 1) to identifying and counting their faces, edges and vertices. They work with a wider range of 3-D shapes including cuboids, prisms and cones. Mastery means pupils can accurately count and name the faces, edges and vertices of common 3-D shapes, use this vocabulary precisely, and sort 3-D shapes by their properties.
Teaching guidance
Handle solid 3-D shapes — pupils must feel faces as flat surfaces, trace edges as meeting lines between faces, and identify vertices as sharp corners where edges meet. For a cube: 6 faces, 12 edges, 8 vertices. For a sphere: 0 faces, 0 edges, 0 vertices (or 1 curved surface, depending on how it is categorised — use language appropriate to Year 2). Introduce prisms: a prism has two identical parallel polygon faces (the bases) connected by rectangular lateral faces — a triangular prism has 5 faces, 9 edges, 6 vertices. Connect 2-D and 3-D: identify the 2-D shapes on the surfaces of 3-D shapes (squares on a cube; triangles on a pyramid; circles on a cylinder).
Common misconceptions
Pupils confuse faces and edges, using the terms interchangeably. They often miscount edges (the most numerous feature) of shapes like cubes or cuboids. Some pupils count the same edge or vertex twice. Curved surfaces on shapes like cylinders and spheres are tricky — pupils may not know whether to call the curved surface of a cylinder a 'face'. Pupils often confuse a prism and a pyramid because both come to at least one point.
Difficulty levels
Counting the faces of common 3-D shapes by handling them and touching each face.
Example task
Pick up this cuboid. Touch each face as you count. How many faces does it have?
Model response: 6 faces. I touched the top, the bottom, the front, the back and both sides.
Counting faces, edges and vertices of 3-D shapes including cubes, cuboids and pyramids.
Example task
Count the edges and vertices of this square-based pyramid.
Model response: 8 edges and 5 vertices. 4 edges around the base and 4 going up to the top point.
Describing and comparing 3-D shapes by their faces, edges and vertices, and sorting them by properties.
Example task
Sort these shapes into two groups: those with all rectangular faces and those without. Name the shapes in each group.
Model response: All rectangular faces: cube, cuboid. Not all rectangular: pyramid (has triangular faces), cylinder (has curved surface), triangular prism (has triangular and rectangular faces).
CPA Stages
concrete
Children handle solid 3-D shapes, touching each face, tracing each edge with a finger, and touching each vertex. They count faces, edges and vertices systematically, marking each one with a sticker or dot to avoid counting twice. They use a recording table to organise their findings.
Transition: Child counts faces, edges and vertices of any common 3-D shape by systematic marking, recording correctly in a table without double-counting.
pictorial
Children identify faces, edges and vertices from 3-D shape diagrams and photographs. They compare 3-D shapes by their properties and sort them into groups using property-based criteria (e.g. 'shapes with all flat faces' vs 'shapes with curved surfaces').
Transition: Child identifies faces, edges and vertices from diagrams of 3-D shapes without handling them, and sorts shapes into groups by property-based criteria.
abstract
Children describe and compare 3-D shapes using faces, edges and vertices without seeing the shape, and identify shapes from verbal property descriptions.
Transition: Child identifies any common 3-D shape from a description of its faces, edges and vertices, and compares shapes using precise property vocabulary.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Solid 3-D shapes (cube, cuboid, pyramid, prism, cone, cylinder), Stickers for marking counted features). AI delivers instruction; facilitator sets up materials.
2-D shapes on the surface of 3-D shapes
knowledge AI FacilitatedMA-Y2-C019
Identifying the 2-D shapes that form the faces of a 3-D shape (e.g. a circle on a cylinder, a triangle on a pyramid, a square on a cube) connects the two-dimensional and three-dimensional worlds of geometry. This concept also develops mathematical reasoning about how 3-D shapes are constructed from 2-D faces. Mastery means pupils can correctly identify all 2-D face shapes on common 3-D shapes and explain the relationship.
Teaching guidance
Use physical 3-D shapes and have pupils press each face onto paper to trace the 2-D face shape — this makes the connection concrete and memorable. Sorting activities: group 3-D shapes by which 2-D shapes appear on their faces. Connect to the earlier concept of 'nets' (though not formally required until Year 4): unfold a cardboard box to see the 2-D rectangle faces. The curriculum includes this objective with the example of 'a circle on a cylinder and a triangle on a pyramid', so ensure both examples are covered explicitly.
Common misconceptions
Pupils may not distinguish between the face of a 3-D shape and the whole shape itself. They may identify a square on the face of a cube but not recognise all six faces as squares. The curved surface of a cylinder is confusing: the circular faces at top and bottom are clearly circles, but the curved lateral surface does not map to a simple 2-D shape in the same way.
Difficulty levels
Pressing a face of a 3-D shape onto paper and identifying the 2-D shape it makes.
Example task
Press the face of this cube onto the paper and trace around it. What shape did you draw?
Model response: I drew a square. The face of a cube is a square.
Naming all the 2-D face shapes on common 3-D shapes without tracing.
Example task
What 2-D shapes can you see on a cylinder?
Model response: Two circles (top and bottom) and a curved surface (which unrolls into a rectangle).
Identifying all face shapes on 3-D shapes and explaining how the 2-D shapes combine to form the 3-D shape.
Example task
A triangular prism has faces that are different 2-D shapes. Name them and say how many of each.
Model response: 2 triangles (the ends) and 3 rectangles (the sides). 5 faces in total.
CPA Stages
concrete
Children press each face of a 3-D shape onto paper and trace around it to discover the 2-D shapes that make up its surface. They sort the tracings by shape name and count how many of each type a 3-D shape has.
Transition: Child traces all faces of common 3-D shapes, names the 2-D shapes found, and counts how many of each type, stating the relationship clearly.
pictorial
Children identify the 2-D face shapes on drawn 3-D shapes without tracing. They label diagrams of 3-D shapes with the names of their faces and match 3-D shapes to their 2-D face components.
Transition: Child identifies and names all 2-D face shapes on 3-D shape diagrams without physical tracing, and matches 3-D shapes to their component 2-D faces.
abstract
Children identify the 2-D faces of 3-D shapes from verbal descriptions and explain how 2-D shapes combine to create 3-D shapes.
Transition: Child lists the 2-D faces of any common 3-D shape without visual support and explains how they combine, using precise shape names.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Solid 3-D shapes, Paper and crayons for tracing). AI delivers instruction; facilitator sets up materials.