Math // Geometry

3-D shapes (age 5+)

Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes

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

Quick check

Can the learner describe what makes two shapes different — for example, explaining that a triangle has 3 corners and 3 sides while a square has 4 of each?

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 sides and corners of a shape
  • Compare a triangle and a rectangle by number of sides
  • Describe a cube as having 'square faces' and 'corners'

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

    Analysing 3-D shapes requires recognising and naming them

  • 2-D shapesRequired

    Geometry // Ages 4 to 6

    Analysing and comparing shapes requires being able to name them first

You are here

3-D shapes (age 5+)

Ages 5 to 6 // Concept

Leads to

5 topics
  • Building & Drawing ShapesRequired

    Geometry // Ages 5 to 6

    Modelling shapes by building/drawing requires knowing their attributes (sides, vertices)

  • 2-D shapes (age 6+)Required

    Geometry // Ages 6 to 7

    Formal property description extends informal analysis of sides and vertices

  • Defining attributes of shapesRequired

    Geometry // Ages 6 to 7

    Identifying defining attributes builds on informal analysis and comparison of shapes

  • Edges, vertices, and facesRequired

    Geometry // Ages 6 to 7

    Formal property description extends informal analysis of shapes

  • Combining Simple ShapesHelpful

    Geometry // Ages 5 to 6

    Composing shapes benefits from understanding shape attributes to know how pieces fit together

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

Help 5-6 year olds move from naming shapes by their overall look to describing them by countable parts: sides and corners for flat (2-D) shapes; flat faces, edges and corners for solids (3-D). The central work is attending to component attributes rather than the holistic silhouette, comparing two shapes on a single countable property, and grasping that each flat face of a solid is itself a 2-D shape. Best taught with real, handleable shapes children touch and count, with varied examples so attention shifts from appearance to structure. Corner/face counting is clearest with flat-faced solids such as cubes and cuboids; curved solids (sphere, cylinder, cone) are described by their curved surfaces. On-screen rotatable models may add value by exposing hidden back features and peeling faces, but complement rather than replace physical handling.

Common misconceptions

  • Judges a shape by its overall look or size rather than counting its sides/corners (the bigger-drawn shape 'has more').
  • Counts only the sides/corners/faces that are visible in a picture or facing them, missing the hidden ones.
  • Uses everyday words loosely — 'corner' and 'side' blur the difference between a solid's face, edge and vertex.
  • Treats a 3-D solid as if it were the 2-D shape of one of its faces (calls a cube 'a square').

Useful representations

  • Handleable wooden/plastic 2-D shape tiles and 3-D solids (cube, cuboid, sphere, cylinder, cone)
  • Geoboards / pin-boards for making and counting the sides of a 2-D shape
  • Feely-bag: describe a solid by touch alone (forces attention to faces/edges/corners, not colour)
  • A 'peel-off' image of a solid whose faces lift away as separate 2-D shapes

Teaching practices

  • Give children physical 2-D tiles and 3-D solids to hold; count sides, corners and faces by touching and MARKING each one (sticker/pen) so none is double-counted or missed.
  • Compare pairs of shapes on ONE countable property at a time ('which has more sides?'), deliberately varying size and orientation so children learn the property is independent of how big or which way up the shape is drawn.
  • Model precise-but-informal language ('this face is a square', 'this shape has 3 straight sides and 3 corners') and have children echo it while pointing.
  • Draw out the distinction between a flat 2-D shape and the flat FACE of a 3-D solid — each face of a solid is itself a 2-D shape; use the 'can you pick it up? is it flat or solid?' test.
  • Use atypical, 'wonky' exemplars (long thin triangles, tilted rectangles) and non-examples to break reliance on a single prototypical picture.

Activities to try

  1. 1

    Count by touching and marking every part

    Why it works: A shape's number of sides/corners/flat faces is found by systematically counting all of them, including the ones round the back, not by guessing from the front view.

    1. Hold a physical 2-D tile to count its sides and corners, or a flat-faced solid such as a cube or cuboid to count its corners and flat faces (curved solids like a sphere, cylinder or cone have curved surfaces rather than a full set of flat faces and corners, so describe those separately).
    2. Count each side, corner or flat face by touching it and placing a sticker or pen mark on each one as it is counted, so none is double-counted or missed.
    3. For a flat-faced solid (cube, cuboid), turn it over and count again from a different starting face to check the total stays the same.
  2. 2

    Compare two shapes on one countable property

    Why it works: Which shape has more sides is decided by counting, not by which is drawn bigger: the count is independent of size and orientation.

    1. Look at a triangle drawn large and a rectangle drawn small, placed side by side.
    2. Decide which has more sides, and count each side by touching and marking it.
    3. Say which has more sides and how you know, using the count rather than the size.
  3. 3

    Each face is a 2-D shape; flat vs solid

    Why it works: A flat-faced solid such as a cube has flat faces that are 2-D shapes, but the solid is not the same as one of those faces: a cube is not 'a square'. Curved solids such as a sphere have curved surfaces instead of, or as well as, flat faces.

    1. Point to one face of a cube and name its 2-D shape ('this face is a square').
    2. Check whether all the faces are the same 2-D shape.
    3. Compare a single thin tile with the whole cube: the tile is almost flat and shows one 2-D shape, while the cube has depth and six flat faces. Note that a real tile or card has a little thickness but stands for an ideal flat shape, so talk about the shape it represents rather than whether you can pick it up.
    4. Match everyday objects to solids and, where they have them, their flat faces (ball = sphere, no flat faces; box = cuboid, rectangle faces; can = cylinder, two circle faces and a curved surface).

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
K.G.4

Math // Geometry

More in Geometry

All 69 topics