Constructing in 2D and 3D
Constructing in 2D and 3D
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Constructing in 2D and 3D
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Learning goal
I can recognise 2D and 3D shapes, use nets, plans and elevations, and calculate surface area and volume for common 3D shapes.
The prompt gives a broad course-style structure rather than a single narrow lesson goal, so this objective keeps the whole sequence together in one student-friendly statement.
What words come to mind when you hear 3D shapes?
Use this to surface prior knowledge such as cube, prism, net, face, edge, vertex, area or volume. Invite a few students to explain one word they added.
2D and 3D shape names
2D shapes are flat shapes.
Examples: triangle, square, rectangle, pentagon, hexagon, circle.
3D shapes are solid shapes.
Examples: cube, cuboid, cylinder, prism, pyramid, sphere.
Emphasise that 2D shapes have length and width, while 3D shapes have length, width and height.
Faces, edges and vertices
When we describe a 3D shape, we look at its parts:
Face - a flat or curved surface
Edge - where two faces meet
Vertex - a corner where edges meet
These words help us compare different solids.
For KS3, it is fine to note that some solids such as cylinders have curved surfaces, even though 'edge' and 'vertex' are mainly used for polyhedra.
What is a prism?
A prism has:
the same cross-section all the way through
two matching, parallel end faces
side faces joining the ends
Examples include cuboids, cubes and triangular prisms.
Link the idea of a prism to a shape being 'stretched' in one direction.
Recognising prisms
A shape is a prism if its cross-section stays the same from one end to the other.
A cuboid is a rectangular prism.
A cube is a special cuboid, so it is also a prism.
A triangular prism is a prism.
A pyramid is not a prism because it narrows to a point.
Students often confuse prisms and pyramids. Stress the constant cross-section test.
What is a net?
A net is a 2D pattern that folds to make a 3D shape.
each face must be the correct shape
faces must be joined in the right places
the net must fold without overlaps
You may mime folding or sketch tabs separately, but tabs are not part of the mathematical net itself.
Drawing an accurate cuboid net
To draw a cuboid net accurately:
Measure the length, width and height.
Draw the six rectangular faces to scale.
Check that opposite faces are equal.
Place the faces so they fold together correctly.
A cuboid always has 3 pairs of equal faces.
Highlight that accuracy matters: students should use a ruler and correct measurements, not freehand sketches.
Sketching and checking nets
When you sketch a net, ask:
Are all the needed faces included?
Are the face sizes correct?
Do the faces meet along matching edges?
Will the shape fold without gaps or overlaps?
A net can look different and still make the same 3D shape.
Useful misconception: students may think there is only one correct net for a cube or cuboid. Mention that several different nets can work.
Which shape is not a prism?
Cube
Cuboid
Pyramid
Triangular prism
Checks the constant cross-section idea from the prism slides. Pyramid is the key misconception because it narrows to a point.
Complete the summary
A prism has the same cross-section all the way through. A net is a 2D pattern that folds to make a 3D shape. A cuboid has 3 pairs of equal faces, and the faces must fold without overlaps.
All blanks come directly from the first subtopic: prisms, nets and accurate cuboid nets.
How do you check if a net will work?
Expected ideas: there can be more than one correct net for the same 3D shape, but all needed faces must be included, sizes must be correct, matching edges must meet, and the net must fold without gaps or overlaps.
Plans and elevations
These drawings show a 3D shape from different views:
Plan - view from above
Front elevation - view from the front
Side elevation - view from the side
They help us represent solids on flat paper.
Keep the wording consistent: plan from above, front elevation from the front, side elevation from the side.
Reading views of a shape
Each view shows only two dimensions:
a plan shows length and width
a front elevation shows width and height
a side elevation shows length and height
Together, the views describe the full 3D shape.
This is the key link between 2D drawings and 3D objects.
Area of 2D shapes
We need area before we can find surface area.
rectangle: length × width
triangle: 1/2 × base × height
circle: πr²
Area is measured in square units such as cm².
Only include formulas that support later surface area work in this lesson.
Surface area of cubes and cuboids
Surface area is the total area of all the outer faces.
Cube: 6 equal square faces
Surface area of a cube = 6 × side²
Cuboid: add the areas of all 6 rectangular faces
A cuboid can also be grouped as 2lw + 2lh + 2wh
Show the connection to nets: surface area is the total area of the net.
Surface area of a triangular prism
A triangular prism has:
2 triangular faces
3 rectangular faces
To find the surface area, add:
area of both triangles + area of all 3 rectangles
Students do not need a single memorised formula here; the structure of the faces is more important.
Surface area of a cylinder
A cylinder has:
2 circular ends
1 curved surface
Surface area = 2πr² + 2πrh
The curved surface comes from a rectangle in the net, with width 2πr and height h.
This is a strong moment to connect nets to formulas: the curved surface unwraps into a rectangle.
Which view shows width and height?
Plan
Front elevation
Side elevation
Net
Plan shows length and width; side elevation shows length and height. Net is included as a plausible but wrong term from the previous block.
Complete the surface area facts
A plan is the view from above. Surface area is the total area of the outside of a shape. For a cube, surface area is 6 × side². For a cylinder, the curved surface comes from a rectangle in the net.
This ties together plans and elevations with the surface area block, echoing the exact lesson wording.
Volume of cubes and cuboids
Volume is the space inside a 3D shape.
Cube: side × side × side
Cuboid: length × width × height
Volume is measured in cubic units such as cm³
Contrast square units and cubic units clearly. Students often mix area and volume units.
Volume of prisms
For any prism:
volume = area of cross-section × length
This works because the same cross-section repeats all the way through the shape.
It includes cuboids and triangular prisms.
This is the main generalisation of the lesson: cuboid volume is a special case of prism volume.
Volume of a cylinder
A cylinder is also a prism because it has the same circular cross-section all the way through.
So:
volume = area of circle × height
volume = πr²h
Students may not immediately think of a cylinder as a prism-like shape. Link back to constant cross-section.
Other volumes at a glance
Some important volume formulas are:
cone: 1/3 πr²h
pyramid: 1/3 × base area × height
sphere: 4/3 πr³
These shapes do not have a constant cross-section, so they are not prisms.
Treat this as an overview only, as the prompt requests. The key contrast is with prisms and cylinders.
Connecting surface area and volume
Surface area and volume measure different things.
Surface area measures the outside of a shape.
Volume measures the inside of a shape.
Surface area uses square units.
Volume uses cubic units.
A shape can have a larger surface area without having a larger volume.
This slide resolves a common confusion by directly comparing the two ideas.
What is the volume of any prism?
base + height
area × length
2πr + 2h
side × 6
Tests the main generalisation in Part 3: volume of prism = area of cross-section × length.
Complete the volume and units summary
Volume measures the space inside a 3D shape. A cuboid has volume length × width × height. A cylinder has volume πr²h. Volume is measured in cubic units.
Reinforces the difference between formulas for volume and surface area, and between cubic and square units.
How are surface area and volume different?
Expected ideas: surface area is the outside, volume is the inside; surface area uses square units and volume uses cubic units; students may mention that a shape can have larger surface area without larger volume.
What is one thing you learned well today?
Reflection prompt with no right answer. Encourage students to name one clear idea, method or formula they feel they now understand better.
Which part of this lesson felt hardest?
Reflection prompt with no right answer. Useful for identifying whether nets, views, surface area or volume need more practice.
Glossary
2D shape - a flat shape with length and width
3D shape - a solid shape with length, width and height
face - a flat or curved surface of a 3D shape
edge - where two faces meet
vertex - a corner where edges meet
prism - a 3D shape with the same cross-section all the way through
net - a 2D pattern that folds to make a 3D shape
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Glossary
plan - a view of a 3D shape from above
front elevation - a view of a 3D shape from the front
side elevation - a view of a 3D shape from the side
surface area - the total area of the outside faces or surfaces
volume - the amount of space inside a 3D shape
cross-section - the shape made by slicing through an object
cylinder - a 3D shape with two equal circular ends and one curved surface
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