Year 3 maths · Key Stage 2 · Geometry – properties of shapes
Year 3 right angles, parallel lines and 2-D and 3-D shapes
In Year 3 geometry children look more closely at shapes and begin to study angles. They draw 2-D shapes and make 3-D shapes from modelling materials, learn that an angle is a measure of turn, spot right angles, and decide whether other angles are bigger or smaller than a right angle. They also learn what horizontal, vertical, perpendicular and parallel lines are.
Right angles and parallel lines, explained
Children draw 2-D shapes carefully with a ruler, on squared paper and on plain paper, and describe them by their sides, corners (vertices) and angles. They make 3-D shapes with modelling materials, for example straws or sticks joined with clay, or building blocks, and count their faces, edges and vertices as they go. They also learn to recognise 3-D shapes however they are turned: a cuboid on its side is still a cuboid, and a triangular prism resting on one of its rectangular faces is the same shape as one standing on its triangular end.
An angle can be a property of a shape, where two sides meet at a corner, or a description of a turn. Thinking of angle as an amount of turn is the key idea this year. A full turn is a complete circle back to where you started, a half turn is a straight line and a quarter turn is a right angle. Degrees are measured later in primary school, so for now children compare angles by turn and by eye.
A right angle is a quarter of a turn, like the corner of a sheet of paper or a book. It’s usually marked with a small square. Children learn that 2 right angles make a half turn, 3 make three-quarters of a turn and 4 make a full turn. They use a right-angle checker, which can be a corner of paper or card, to decide whether other angles are greater than or less than a right angle. The curriculum guidance suggests describing these angles as acute (smaller than a right angle) and obtuse (bigger than a right angle but smaller than a straight line), so many schools introduce the words now. Identifying acute and obtuse angles becomes a requirement in Year 4.
Children also learn the language of lines. Horizontal lines are level, like the horizon, and vertical lines go straight up and down. Two lines that meet at a right angle are perpendicular. Lines that stay the same distance apart and never meet, however far they are extended, are parallel. They look for these in rectangles, on the grid and in the classroom. Alongside this they practise drawing and measuring straight lines accurately in centimetres and millimetres, because a good drawing depends on careful measuring.
Words your child will hear
- Right angle
- A quarter turn, like the corner of a piece of paper. Often marked with a small square.
- Vertex
- A corner where sides or edges meet. The plural is vertices.
- Horizontal
- A line that is level, going from side to side like the horizon.
- Vertical
- A line that goes straight up and down.
- Perpendicular
- Two lines that meet at a right angle.
- Parallel
- Two lines that stay the same distance apart and never meet.
- Face and edge
- On a 3-D shape, a face is a flat surface and an edge is where two faces meet.
What the National Curriculum says
In Year 3, pupils should be taught to:
- Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
- Recognise angles as a property of shape or a description of a turn
- Identify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle
- Identify horizontal and vertical lines and pairs of perpendicular and parallel lines
Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.
Try it: turning through right angles
The minute hand of a clock points straight up at 12 and turns clockwise to point at the 9. How many right angles has it turned through? Then decide whether the angle between the hands at 2 o’clock is greater or less than a right angle.
- A full turn is 4 right angles, or 4 quarter turns. Turning from 12 to 3 is one quarter turn, which is 1 right angle.
- Turning on from 3 to 6 makes a half turn, which is 2 right angles in total. A straight line is a half turn.
- Turning on from 6 to 9 makes three-quarters of a full turn, which is 3 right angles in total.
- Now think about the hands at 3 o’clock: the minute hand points at 12 and the hour hand at 3, a quarter turn apart, so the angle is exactly a right angle.
- At 2 o’clock the hour hand is on the 2, which is nearer the 12, so the hands are closer together than at 3 o’clock. That is a smaller angle. At 4 o’clock they are further apart, which is a bigger angle.
The hand turned through 3 right angles, which is three-quarters of a full turn. At 2 o’clock the angle is less than a right angle, and at 4 o’clock it is greater than a right angle.
Common mistakes and how to help
Thinking an angle with longer arms is a bigger angle
Children notice the lines they can see. An angle drawn with long arms looks larger than the same angle drawn with short ones.
What helps: Compare angles by how far one arm turns from the other, not by how long they are. Lay a paper corner over both and see that they match.
Only recognising right angles when they are upright
Most right angles in books sit with one side horizontal and one vertical, so a tilted corner doesn’t look “right”.
What helps: Turn the page, or turn a right-angle checker, to test corners in all positions. A right angle is a right angle however the shape is rotated.
Mixing up parallel, perpendicular, horizontal and vertical
The words sound similar and look similar on paper. Some children think parallel lines must be horizontal or the same length.
What helps: Use the railway track picture for parallel lines (always the same distance apart) and the corner of a table for perpendicular lines. Parallel lines can be at any slope, and they don’t need to be the same length.
Not recognising a 3-D shape that has been turned
Children often see shapes in one position only, so a cube balanced on a corner or a prism on its end looks like a different shape.
What helps: Handle real objects and turn them over. Count the faces, edges and vertices from different positions to show that they don’t change.
How to help at home
- Go on a right-angle hunt. Fold a sheet of paper twice to make a right-angle checker. Walk round the house testing corners of doors, books and windows. Which are right angles, and which are bigger or smaller?
- Build 3-D shapes. Join lolly sticks or straws with small balls of modelling clay to build a cube or a pyramid. Count the faces, edges and vertices, then try to build one with a different number.
- Play a turning game. Stand in a clear space and call out “quarter turn clockwise”, “half turn” or “three-quarter turn anticlockwise”. Your child works out which way they will face, then you swap roles.
- Spot parallel and perpendicular lines. Look for pairs of lines in a room: the edges of a bookcase, the bars of a stair gate, the lines on a tiled floor. Ask which pairs are parallel and which meet at a right angle.
- Draw shapes with a ruler. Set a challenge such as “draw a rectangle 6 cm by 3 cm”, then check that every corner is a right angle using the paper checker. Accurate drawing is a real skill.
Related topics
Builds on
- Year 2: Properties of 2-D and 3-D shapes
Leads on to
- Year 4: Shapes, angles and symmetry
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