Geometry: Properties of Shapes

In Key Stage 1, children explore the world of 2-D and 3-D shapes. They begin by naming shapes they see around them, then progress to describing shapes precisely using mathematical properties.

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What This Topic Covers

• Year 1: Recognise and name common 2-D and 3-D shapes
• Year 2: Describe properties (sides, edges, vertices, faces); identify symmetry; find 2-D shapes on surfaces of 3-D shapes; compare and sort shapes

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2-D Shapes (Flat Shapes)

2-D means two-dimensional — shapes that are flat and have only length and width.

Common 2-D Shapes

Shape	Sides	Corners (vertices)	Notes
Circle	0	0	Perfectly round; no straight sides
Triangle	3	3	Any shape with 3 straight sides
Rectangle	4	4	Opposite sides are equal; all angles are right angles
Square	4	4	A special rectangle — all 4 sides equal
Pentagon	5	5
Hexagon	6	6
Octagon	8	8

Important: A square is a special type of rectangle. All squares are rectangles, but not all rectangles are squares.

Properties of 2-D Shapes (Year 2)

Property	Meaning
side	a straight edge of a 2-D shape
vertex (plural: vertices)	a corner where two sides meet
right angle	a square corner (like the corner of a page)

Identifying right angles: Use the corner of a piece of paper as a "right angle tester". A right angle looks like a perfect square corner and is marked with a small square in diagrams.

Shape	Right angles?
Square	Yes — all 4 corners
Rectangle	Yes — all 4 corners
Triangle	Sometimes — only right-angled triangles
Circle	No

Line Symmetry (Year 2)

A shape has line symmetry if it can be folded in half so that both halves match exactly. The fold line is called the line of symmetry (or mirror line).

Shape	Lines of symmetry
Circle	Infinite
Square	4
Rectangle	2
Equilateral triangle	3
Isosceles triangle	1
Scalene triangle	0

In Year 2, children focus specifically on vertical lines of symmetry (a vertical line through the centre of a shape).

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3-D Shapes (Solid Shapes)

3-D means three-dimensional — shapes that have length, width and height. They take up space.

Common 3-D Shapes

Shape	Faces	Edges	Vertices	Example in real life
Cube	6	12	8	dice
Cuboid	6	12	8	cereal box
Sphere	1 curved	0	0	football
Cylinder	3 (2 flat, 1 curved)	2	0	tin of beans
Cone	2 (1 flat, 1 curved)	1	1	ice cream cone
Square pyramid	5	8	5	Egyptian pyramid
Triangular prism	5	9	6	Toblerone box

Properties of 3-D Shapes (Year 2)

Property	Meaning
face	a flat or curved surface of a 3-D shape
edge	a line where two faces meet
vertex (plural: vertices)	a corner where edges meet

Example - Cube:

• 6 square faces (all identical)
• 12 edges (all the same length)
• 8 vertices (corners)

2-D Shapes on Surfaces of 3-D Shapes

Children identify the 2-D shapes they can see on the faces of 3-D shapes:

3-D shape	2-D shape on its face
Cube	square (all 6 faces)
Cuboid	rectangle (all 6 faces)
Cylinder	circle (top and bottom faces)
Square pyramid	square (base) and triangles (4 sides)
Cone	circle (base)
Triangular prism	triangle (2 ends) and rectangles (3 sides)

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Sorting and Comparing Shapes

Children sort shapes using their properties. For example:

Criterion	Shapes that qualify
Has 4 sides	square, rectangle, rhombus
Has all equal sides	square, equilateral triangle
Has a line of symmetry	circle, square, rectangle, equilateral triangle
Has 6 faces	cube, cuboid
Has a curved surface	sphere, cylinder, cone

flowchart TD
  S[Shapes]
  S --> TwoD["2-D shapes<br/>flat"]
  S --> ThreeD["3-D shapes<br/>solid"]
  TwoD --> Circle[Circle]
  TwoD --> Triangle["Triangle<br/>3 sides"]
  TwoD --> Square["Square<br/>4 equal sides"]
  TwoD --> Rectangle["Rectangle<br/>4 sides"]
  ThreeD --> Cube["Cube<br/>6 square faces"]
  ThreeD --> Cuboid["Cuboid<br/>6 rectangle faces"]
  ThreeD --> Sphere["Sphere<br/>curved"]
  ThreeD --> Cylinder["Cylinder<br/>2 circles + curve"]
  ThreeD --> Cone["Cone<br/>1 circle + 1 point"]

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Key Vocabulary

Term	Meaning
2-D	two-dimensional; a flat shape
3-D	three-dimensional; a solid shape
side	a straight edge of a 2-D shape
face	a flat or curved surface of a 3-D shape
edge	a line where two faces of a 3-D shape meet
vertex / vertices	a corner or corners
right angle	a quarter turn; a square corner
line of symmetry	a fold line where both halves match
polygon	a 2-D shape with straight sides
quadrilateral	a 4-sided polygon

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Common Misconceptions

• "Squares and rectangles are different shapes" — A square is a special rectangle. Help children see this by noting all squares have 4 right angles and opposite equal sides — just like rectangles.
• "A triangle must look like an equilateral triangle" — Any shape with exactly 3 straight sides is a triangle, regardless of whether it is pointy, flat or lopsided.
• "3-D shapes always stand up" — A cylinder lying on its side is still a cylinder. Shapes should be recognised in any orientation.
• "All faces are flat" — A sphere has one curved face; a cylinder has one curved face and two flat ones.

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Worked Example for Parents and Teachers

A productive way to teach KS1 shape is to anchor every property in something the child can hold, count and feel. Imagine a Year 2 lesson with the objective: "Children will describe a 3-D shape using faces, edges and vertices."

Step 1 — Hands-on exploration (concrete). Give each pair a tray of solid wooden or plastic shapes — a cube, a cuboid, a sphere, a cone, a cylinder and a square pyramid. Before saying anything technical, ask, "What do you notice? What is the same? What is different?" Children might say "This one rolls", "This one has pointy bits", "These look like dice". Capture their language on the board.

Step 2 — Define vocabulary precisely. Hold up a cube. Run your finger along one edge — "This is where two faces meet, like the seam on the box." Press one face — "This is the flat surface." Touch a corner — "This is a vertex." Repeat with several shapes. Then have children echo your language: "I am pointing to a face. I am pointing to an edge."

Step 3 — Count and record (pictorial). Each pair counts the faces, edges and vertices of every shape. They record results in a table:

Shape    | Faces | Edges | Vertices
Cube     |   6   |  12   |    8
Cuboid   |   6   |  12   |    8
Sphere   |   1   |   0   |    0
Cylinder |   3   |   2   |    0

This is harder than it looks. Children often miscount edges on a cube (the 12 edges include the 4 hidden edges at the back), so model carefully: count all 4 edges around the top, all 4 around the bottom, then 4 connecting them — total 12.

Step 4 — Build and check (abstract). Give children straws and pipe cleaners (or polydron). Ask them to build a cube. They can only succeed if they count correctly: 12 straws, 8 connectors. Failure forces them to revisit their counts — a powerful self-correction.

Verbal prompts:

• "Show me a face. Show me an edge. Show me a vertex."
• "How are a cube and a cuboid the same? How are they different?"
• "Which 2-D shape do you see if you draw round the bottom of this cylinder?"
• "Roll this shape. Which shapes roll? Which slide?"