What’s the difference between 2D and 3D shapes?
The difference between a 2D and 3D shape is depth – a 3D shape is a 2D shape with depth. This makes it ‘stick out’ into the world, rather than being flat. For example, the difference between a square and a cube is a square only has height and width, whereas a cube has height, width, and depth.
Other shapes can be a bit more complicated. Let’s think about circles. We could say that a sphere is a circle that has depth. It can be picked up and moved around.
However, we could also describe a cylinder as a ‘circle with depth’.
Other 2D shapes can be made 3D in multiple ways. For example, we could consider a triangular-based pyramid, a square-based pyramid, and a triangular prism as all different ways of drawing a ‘3D triangle’.
Properties of 2D shapes
We’ve already talked about how 2D shapes have height and width. The other key properties of 2D shapes are ‘sides’ and ‘corners’. We describe the outline of a shape between two corners as a side. Where two sides meet, there is a corner.
The only 2D shape that does not have corners is a circle – it just has one continuous side.
Some 2D shapes have the same number of sides and corners but have different names. Squares and rectangles both have four sides and four corners. This is because a square is a special kind of rectangle – the length of all its sides and the size of all its angles are equal. While a rectangle also has four angles which are all equal and four sides, its sides are not all the same length.
Using maths terms that you might start to see in your child’s work at Key Stage 1, a square is a ‘regular’ shape, and a rectangle is an ‘irregular’ shape. A regular 2D shape is a shape with all sides the same length and all interior angles the same size. An irregular 2D shape has sides of different lengths and/or angles of different sizes. Other irregular four-sided 2D shapes include rhombus, trapeziums, and parallelograms, although these shapes are not common in Key Stage 1.
Other 2D shapes have regular and irregular forms. A regular triangle is an equilateral triangle, while irregular triangles include isosceles and right-angle triangles. For 2D shapes with larger numbers of sides and corners, the same rules apply. For example, the traditional shape you might think of for a hexagon, with all its sides the same length, is a regular hexagon. Any other six-sided shape is an irregular hexagon. This can be applied to any other 2D shape.
Properties of 3D shapes
We have explored how 3D shapes have height and width, just like 2D shapes, but also have depth. 3D shapes also have different properties to 2D shapes. Rather than ‘sides’ and ‘corners’ 3D shapes have ‘faces’, ‘edges’, and ‘vertices’. A face is the (in most cases) flat part of a 3D shape. Shapes like spheres, cones, and cylinders have curved faces. An edge is where two faces meet; it can be thought of as the equivalent of a ‘side’ of a 2D shape. Vertices are the 3D equivalent of a ‘corner’. They are where three or more edges meet and form a point.
Just like how a circle only has one side, and no corners, a sphere only has one face, and no edges or vertices. Cubes and cuboids have the same relationship as squares and rectangles. A cube is a regular cuboid – all its lengths and angles are equal, and all of its faces are squares.
‘Prism’ is also a term that pupils will encounter in Year 1 and Year 2 maths when dealing with 3D shapes. A prism is a 3D shape that has two identical faces, one on either end, and has the same cross section all along it’s length. That is, if you were to cut the shape in two anywhere along its length, the end faces of both parts of the shape would still be the same shape as the original end faces.
KS1 2D and 3D shapes
The national curriculum states that in year 1 pupils learn to “recognise and name common 2-D and 3-D shapes, including:
- 2-D shapes [for example, rectangles (including squares), circles and triangles]
- 3-D shapes [for example, cuboids (including cubes), pyramids and spheres]
Pupils handle common 2-D and 3-D shapes, naming these and relating everyday objects fluently. They recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other.”
In Year 2 the national curriculum states that pupils learn to:
- “identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line.
- Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
- Identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
- Compare and sort common 2-D and 3-D shapes and everyday objects.
Pupils handle and name a wide variety of common 2-D and 3-D shapes including: quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils read and write names for shapes that are appropriate for their word reading and spelling. Pupils draw lines and shapes using a straight edge.”
Below are the 2D and 3D shapes that pupils should know by the end of Key Stage 1.
The national curriculum will be what Key Stage 1 SATs questions on 2D and 3D shapes will be based on, so it’s important that Year 1 and Year 2 pupils can do everything covered by the curriculum.*Any of the 2D shapes they have learned can be made into a prism e.g. hexagonal prism, octagonal prism.
2D and 3D shapes are important topics to learn in Year 1 and Year 2 because they come up in many other areas of maths that Key Stage 1 pupils learn. For example, when learning fractions, 2D shapes are often used as visual aids where knowing the properties of the shapes is important. 2D and 3D shapes are used when learning about perimeter and area, where it is important to know about regular and irregular shapes. When pupils learn about transformations, such as translating, rotating, and reflecting shapes, being able to draw regular and irregular shapes is essential. Therefore, it is important that students grasp this topic well in Key Stage 1.
Drawing 2D shapes
When drawing 2D shapes a ruler is essential to keep lines straight and to measure the lengths of sides. Grid paper is also very helpful as the squares can be used to measure lengths more easily than a ruler, and to make sure that shapes with right-angles can be drawn easily.
When drawing shapes, it may also be helpful to refer to a table like the one above listing the number of sides and corners of different 2D shapes. This can be used to aid with drawing shapes and for checking that each shape has been drawn correctly. For example, we can use the table to see that a triangle has three sides and three corners. After drawing a triangle, we can count the number of sides and corners in our drawing to check it is correct.
Pupils should be able to draw circles, squares, rectangles, and triangles relatively easily, although may need to work on keeping lines straight and the right length. Drawing a neat circle in Key Stage 1 can be difficult (pupils won’t have learned how to use a compass yet!). To make this easier, they can try plotting four points (top, bottom, right, left) on squared paper and use them as a guide to draw a relatively neat circle by joining the dots with curved lines.
Drawing shapes with more than four sides may be harder for Key Stage 1 pupils. For these shapes, you can try the ‘look, cover, draw, check’ method. Show them an example of a shape, for example a pentagon. Discuss how many sides and corners it has. Then cover up the picture and have them try and recreate it. Check how well they did and repeat until they are happy with the shape.
Drawing 3D shapes
Drawing 3D shapes is a lot trickier than 2D shapes. It also relies on being able to draw 2D shapes. Again, a ruler and grid paper are very useful for drawing 3D shapes.
For many 3D shapes, the same technique can be used to draw them. This works for cubes, cuboids, cylinders, and any kind of prism. Below shows each step to draw these shapes, using a cuboid as an example.
When drawing a cube, be careful to make sure that the lines that connect the two 2D shapes together are the same length as each of the sides of the square you drew in step 1.
For tricker shapes, such as cones and pyramids, a different technique can be used.
These techniques should cover most 3D shapes that pupils will be expected to draw at Key Stage 1.
2D and 3D shapes worksheets
Here are some Key Stage 1 maths online worksheets on the topic of 2D and 3D shapes.
- Look around the room. How many 2D and 3D shapes can you see? Draw some of them!
- What are the properties of a 2D shape?
- Fill in the table.
- A 2D shape has 4 sides and 4 corners. The top and bottom side are the same length as each other. The left and right side are the same length as each other. The top and bottom sides are not the same length as the left and right sides. What shape is it?
- A 2D shape has 1 side and no corners. What shape is it?
- A 2D shape has 8 sides and 8 corners. What shape is it?
- Look at the picture. How many of each shape can you see?
There are ______ triangles
There are ______ circles
There are ______ squares
There are ______ rectangles
- Complete the table of 3D shapes.
9. Match the 2D shape to the 3D prism.
- What are the properties of a 3D shape?
- A 3D shape has 6 faces, 12 edges, and 8 vertices. Which two shapes could it be?
- A 3D shape has 2 faces, 1 edge, and 1 vertices. What shape is it?
- A 3D shape has 3 faces, 3 edges, and no vertices. What shape is it?
- A 3D shape has 5 faces, 8 edges, and 5 vertices. What shape is it?
- Which 2D shape makes up the 6 faces of a cube?
- A 2D shape has 5 sides and 5 corners, but they are not all equal in size. Is the shape regular or irregular? What shape is it?
- Draw a cone.
- How many faces, edges, and vertices does a triangular-based pyramid have?
- Draw a hexagonal prism.
- Draw an octagonal prism.
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