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
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
- 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
- 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
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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
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.
- 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).
- 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.
- 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
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.
- Look at a triangle drawn large and a rectangle drawn small, placed side by side.
- Decide which has more sides, and count each side by touching and marking it.
- Say which has more sides and how you know, using the count rather than the size.
- 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.
- Point to one face of a cube and name its 2-D shape ('this face is a square').
- Check whether all the faces are the same 2-D shape.
- 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.
- 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
- Common Core State Standards for Mathematics
- K.G.4
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