Math // Geometry

Edges, vertices, and faces

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

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

Quick check

Can the learner count the faces, edges, and vertices of a 3-D shape like a cube or triangular prism?

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.
  • Count the edges, vertices, and faces of common 3-D shapes
  • Use the terms edge, vertex (vertices), and face correctly
  • Describe a 3-D shape by its properties (e.g. a cube has 6 faces, 12 edges, 8 vertices)

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

2 topics
  • 3-D shapesRequired

    Geometry // Ages 4 to 6

    Describing 3-D properties (edges, vertices, faces) requires knowing the shapes first

  • 3-D shapes (age 5+)Required

    Geometry // Ages 5 to 6

    Formal property description extends informal analysis of shapes

You are here

Edges, vertices, and faces

Ages 6 to 7 // Concept

Leads to

3 topics
  • Sorting 2-D and 3-D shapesRequired

    Geometry // Ages 6 to 7

    Sorting shapes requires knowing their 3-D properties

  • 2-D shapes (age 7+)Required

    Geometry // Ages 7 to 8

    Making/describing 3-D shapes requires knowing their properties (edges, vertices, faces)

  • Nets of 3-D ShapesRequired

    Geometry // Ages 8 to 11

    Predicting which net folds into a shape and checking that its faces, edges and vertices match requires knowing how many faces, edges and vertices common 3-D shapes have

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 to describe common 3-D solids by three distinct properties — faces (flat surfaces, each itself a 2-D shape), edges (the straight line where two faces meet) and vertices (the corner where edges meet) — and to count each reliably for solids such as a cube (6 faces, 12 edges, 8 vertices). The two core challenges are keeping the three properties distinct rather than blurring them under everyday words like 'side' and 'corner', and counting the hidden features on the far side rather than only those visible. A well-supported route for this age is handling real solids (including while looking at a flat picture of the same solid), counting each property by touch in a fixed order with a marking system, and being explicit about how curved solids are described.

Common misconceptions

  • Blurs faces, edges and vertices under everyday words, calling edges 'sides' and vertices 'corners' so the three properties run together when counting.
  • Counts only the faces/edges/vertices that are visible, missing the hidden ones on the far side (gives a cube 3 faces, 9 edges or 4 corners).
  • Counts a curved surface as a 'face' and the curved boundary line as an 'edge' (e.g. says a cylinder has 3 faces).
  • Treats the whole solid as if it were the 2-D shape of a face, not distinguishing the flat face from the 3-D object.

Useful representations

  • Handleable solids (cube, cuboid, pyramid, sphere, cylinder, cone) counted by touch
  • Colour-a-face / trace-an-edge / dot-a-vertex marking system while counting
  • Nets that fold up into the solid, showing each face as a separate 2-D shape
  • A cube-vs-cylinder pair to contrast flat faces with a curved surface

Teaching practices

  • Count by touch in a fixed order — colour or number each face, trace each edge, dot each vertex — so the three properties stay distinct and nothing is double-counted or missed.
  • Hand children the real solid to turn while looking at pictures of it, so hidden faces, edges and vertices are included in the count rather than only the visible ones.
  • Define each term against the object: a face is a flat surface (itself a 2-D shape), an edge is the straight line where two faces meet, a vertex is the corner where edges meet.
  • Be explicit about curved solids: a curved surface is described as a 'curved surface', not a face, and the curved boundary is not an edge — and note that schemes differ, so state the convention being used.
  • Connect faces to 2-D shapes and (later) to nets, where each face appears as a separate flat shape, reinforcing the face count.

Activities to try

  1. 1

    Count a real cube by touch in a fixed order

    Why it works: A face, an edge and a vertex are three different things; counting each property separately in a fixed order, and marking features as you go, keeps them distinct and makes sure nothing hidden is missed or double-counted.

    1. Hold a real cube and turn it in your hands.
    2. Count the faces first: colour or number each flat surface as you touch it, saying 'face' each time, until every face is marked. Record the total.
    3. Then trace each edge with a finger, marking each traced edge (e.g. a gold line or sticker), saying 'edge' each time, until all are traced. Record the total.
    4. Then dot each vertex (corner) with a sticker, saying 'vertex' each time. Record the total.
    5. Recount starting from a different face to check your totals stay the same (6 faces, 12 edges, 8 vertices).
  2. 2

    Predict then count the hidden features

    Why it works: A solid has features on its hidden far side that a flat picture does not show directly; a count based only on what you can see is too small, so you must turn the real object to catch every feature.

    1. Before counting, look at a cube and predict out loud how many edges it has altogether, saying your number first.
    2. Look at a flat picture or drawing of the cube next to the real cube, and point out which edges, faces and corners in the picture are hidden from view.
    3. Now trace and mark every edge on the real cube together, turning it so the far side comes into view and you find the hidden features from the picture.
    4. Compare your prediction with the counted total of 12, and talk about the edges 'round the back' you could not see at first.
    5. Repeat the routine for vertices and faces: each time, predict the visible-only number aloud first, then turn the real solid to reach the full totals (8 vertices, 6 faces).
  3. 3

    Flat face versus curved surface

    Why it works: Under the convention used here, a face is a flat surface and an edge is a straight line where two flat faces meet; the round part of a cylinder or cone is described as a curved surface, not a face, and its curved boundary is not counted as an edge, while a cone has a pointed apex that many schemes call a vertex even though no edges meet there.

    1. Hold a cylinder and run a hand over the round wall and over the flat ends.
    2. Count the flat faces — the two circles on a cylinder — and mark them.
    3. Decide whether the round wall is a face: feel that it is not flat, and name it a 'curved surface' rather than a face.
    4. Check the circle-to-curve boundary: is it a straight line where two flat faces meet? Under the convention we are using, if not, it is not counted as an edge (some schemes call it a curved edge).
    5. Say the full description: a cylinder has two flat (circular) faces and one curved surface.

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/2

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