Math // Geometry

2-D faces on 3-D shapes

Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid)

Ages
6 to 7
Type
Concept
Builds on
3 topics
Leads to
0 topics
Standards
1 code

Quick check

Can the learner look at a 3-D shape and name the 2-D shapes on its faces — for example, saying a cylinder has circles on the ends and a rectangle wrapped round the side?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Point out a circular face on a cylinder or cone
  • Identify triangular faces on a pyramid
  • Recognise that the faces of 3-D shapes are 2-D shapes

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics
  • 3-D shapesRequired

    Geometry // Ages 4 to 6

    Must recognise 3-D shapes to examine their surfaces

  • 2-D shapesRequired

    Geometry // Ages 4 to 6

    Must recognise 2-D shapes to identify them on 3-D surfaces

  • Flat vs Solid ShapesRequired

    Geometry // Ages 5 to 6

    Must understand the distinction between 2-D and 3-D to recognise 2-D shapes on 3-D surfaces

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2-D faces on 3-D shapes

Ages 6 to 7 // Concept

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Geometry

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Children aged 6–7 learn that the flat faces of a 3-D solid are themselves 2-D shapes — a circle on a cylinder, triangles on a pyramid. A solid with only flat faces, such as a cube or pyramid, is built FROM those flat faces; some solids, such as a cylinder, also have a curved surface, which is not a flat face. The core teaching moves are taking solids apart (unfolding or popping up a solid so faces lie flat), tracing or paint-stamping a face to print its 2-D shape, and handling solids to feel which surfaces are flat faces and which are curved. A face keeps its 2-D shape whether drawn on paper or sitting on the solid; the whole tin is a cylinder, but each flat end is a circle.

Common misconceptions

  • Names a face by the whole solid's name — calls the flat round end of a cylinder 'a cylinder' rather than 'a circle'.
  • Cannot separate face from solid because the solid itself is mis-named — a cube called 'a square' has no distinct square faces to find (Mohamed & Kandeel 2023).
  • Sees the solid as one undifferentiated whole and does not decompose it into faces (van Hiele visual level).

Useful representations

  • Pop-up / unfoldable solids whose faces flatten into 2-D shapes
  • Paint-stamp or trace-around prints of each face
  • A cube shown as six squares; a pyramid as triangles plus a square base; a cylinder as two circles plus a curved surface
  • Face-count charts (faces, edges, vertices)

Teaching practices

  • Unfold or 'pop up' a solid from flat paper so children see the faces are 2-D shapes and can touch and count them (Mohamed & Kandeel 2023).
  • Trace round, or dip-and-stamp, a face to print its 2-D shape — the print of a tin's end is a circle.
  • Name the face by its 2-D shape (circle, triangle, square) distinct from the solid's name (cylinder, pyramid, cube).
  • Contrast flat faces (rest flat on the table) with curved surfaces (roll), so a cylinder's curved side is not mistaken for a flat face.
  • Link explicitly: a cube is made of six squares; a cylinder has two circular faces — every 3-D shape is made up of 2-D shapes.

Activities to try

  1. 1

    Take a solid apart into its flat faces

    Why it works: A solid's flat faces are 2-D shapes; a solid with only flat faces (such as a cube or pyramid) is built from them, while a cylinder also has a curved surface. A face keeps its 2-D shape whether it is drawn on paper or sitting on the solid.

    1. Handle a real solid (a tin/cylinder, a cube, a square-based pyramid) and run a finger over its surfaces.
    2. Unfold or 'pop up' a solid made from flat paper/card so its faces lie flat, then touch and count the separated faces.
    3. Name each flattened face by its 2-D shape (circle, triangle, square) and rebuild the solid face by face. If a paper cylinder is unrolled, its curved side flattens into a rectangle, but on the cylinder that part is the curved surface, not a flat face.
    4. State the link aloud: 'a cube is made of six squares', 'a cylinder has two circular faces and a curved surface'.
  2. 2

    Print the face: trace and paint-stamp

    Why it works: The print of a solid's flat face is a plain 2-D shape (a tin's end prints a circle), making concrete that the face is itself a 2-D shape.

    1. Dip the flat end of a tin in paint (or ink pad) and stamp it on paper; name the shape that appears.
    2. Trace round a flat face of a cube or the square base of a pyramid and name the printed 2-D shape.
    3. Set the printed 2-D shape beside the solid and say which face of the solid it came from.
  3. 3

    Flat faces versus curved surfaces

    Why it works: A flat face rests flat and has a 2-D shape; a curved surface rolls and is not a flat face — so a cylinder's curved side should not be counted as a flat face.

    1. Try to rest each surface of a cylinder flat on the table: the two ends sit flat, the curved side rolls.
    2. Sort surfaces into 'flat faces' (rest flat) and 'curved surfaces' (roll).
    3. Count and name the flat faces on a cube, a square-based pyramid, and the cylinder; note the cylinder's side is curved, not a flat face.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y2/GPS/3

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