Year 4 maths · Key Stage 2 · Geometry – properties of shapes
Year 4 shapes, angles and symmetry: a parent’s guide
In Year 4 children move from naming shapes to describing and sorting them by their properties: the number of equal sides, parallel sides and types of angle. They compare angles as acute, right or obtuse, put them in order of size, find lines of symmetry in shapes turned in different directions, and complete a symmetrical picture on a grid.
Shapes, angles and symmetry, explained
Classifying a shape means deciding which group it belongs to and being able to say why. Children sort triangles by their sides. An equilateral triangle has three equal sides, an isosceles triangle has two equal sides and a scalene triangle has no equal sides. They sort quadrilaterals, which are all four-sided shapes, using words such as parallel (staying the same distance apart, like railway lines), equal sides and right angles. A rectangle has four right angles and opposite sides equal, a square has four equal sides and four right angles, a rhombus has four equal sides and two pairs of parallel sides and looks like a square that has been pushed over, a parallelogram has two pairs of parallel sides, with opposite sides equal, and a trapezium has one pair of parallel sides. Children also decide whether a polygon is regular, with all sides and all angles equal, or irregular.
An angle is a measure of turn. Children compare angles with a right angle, which is the corner of a piece of paper or a square. An angle smaller than a right angle is acute, and one bigger than a right angle but smaller than a straight line is obtuse. Two right angles make a straight line, and Year 4 work stops there: children order angles up to two right angles by size, often by eye, or by using a paper corner or a pair of strips joined with a split pin. Measuring angles in degrees with a protractor is taught in Year 5, so the aim now is a secure sense of how big an angle is.
A line of symmetry is a fold line that splits a shape into two halves that match exactly, like a mirror. Children find lines of symmetry by folding, tracing and using a mirror, then predict them without help. A rectangle has two lines of symmetry, a square has four, an equilateral triangle has three and an isosceles triangle that isn’t equilateral has one. The lines are not always vertical, so children practise on shapes in different orientations, including diagonal mirror lines.
Finally, children complete a symmetrical figure: given half a pattern on squared paper and a mirror line, they draw the other half. The trick is to treat each corner separately, counting its distance from the mirror line and putting its partner the same distance on the other side, then joining the corners up.
Words your child will hear
- Quadrilateral
- Any flat shape with four straight sides.
- Parallel
- Lines that stay the same distance apart and never meet.
- Acute angle
- An angle smaller than a right angle.
- Obtuse angle
- An angle bigger than a right angle but smaller than a straight line.
- Line of symmetry
- A line that splits a shape into two matching halves, one the mirror image of the other.
- Regular polygon
- A flat shape with all sides equal and all angles equal.
- Isosceles / scalene
- A triangle with two equal sides, or with no equal sides.
What the National Curriculum says
In Year 4, pupils should be taught to:
- Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
- Identify acute and obtuse angles and compare and order angles up to 2 right angles by size
- Identify lines of symmetry in 2-D shapes presented in different orientations
- Complete a simple symmetric figure with respect to a specific line of symmetry
Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.
A worked example
A quadrilateral has four sides of equal length, two pairs of parallel sides and no right angles. What is it called, and how many lines of symmetry does it have?
- Start with the properties. Four equal sides rules out a rectangle that isn’t a square, because its sides come in two different lengths. That leaves a square or a rhombus.
- A square has four right angles. This shape has none, so it cannot be a square. Its angles come in two matching pairs, one pair acute and one pair obtuse.
- A four-sided shape with all sides equal and no right angles is a rhombus. It is a special parallelogram, because it has two pairs of parallel sides.
- Now find the lines of symmetry. Folding along either diagonal, corner to corner, makes the two halves match. A fold across the middle, parallel to the sides, does not.
It is a rhombus, with 2 lines of symmetry (its diagonals). It is irregular, because its angles are not all equal.
Common mistakes and how to help
Thinking a shape changes name when it is turned
A square tipped onto a corner looks like a ‘diamond’, and a triangle pointing downwards looks unfamiliar. Children often meet each shape in just one position.
What helps: Show shapes in many orientations and ask which properties stay the same. Cut a square from paper and turn it in your hands: the sides and corners never change.
Judging an angle by the length of its arms
An angle drawn with long lines looks bigger than the same angle drawn with short ones.
What helps: Compare with a paper corner and say that angle size is how far one line turns from the other. Draw the same angle with long and short arms and test them.
Believing every diagonal of a rectangle is a line of symmetry
Squares and rhombuses have diagonal lines of symmetry, so children assume rectangles do too.
What helps: Cut out a rectangle and fold it along a diagonal. The corners don’t line up. Unless the rectangle is a square, only the two folds through the middle of opposite sides work.
Saying that a square is not a rectangle
Children are taught the two names separately and treat them as different types of shape.
What helps: Use the properties: a rectangle has four right angles and opposite sides equal. A square has all of this and more, so it is a special rectangle. Many schools teach this explicitly.
How to help at home
- Shape hunt. Look for triangles, parallelograms, trapezia and rectangles in windows, signs, furniture and food packaging. Ask your child why a shape belongs, not just what it is called.
- Angle spotting with a paper corner. Fold a piece of paper to make a right angle. Use it to test corners around the house and decide whether each angle is acute, right or obtuse.
- Fold and mirror. With child-safe scissors, cut simple shapes from folded paper, such as a heart or a snowflake, then open them up and find the fold lines. A small mirror stood on a drawing shows whether a line is a true line of symmetry.
- Finish the picture. Draw half of a butterfly or a house on squared paper with a mirror line down the middle. Your child draws the other half, counting squares from the line to each corner.
Related topics
Builds on
- Year 3: Right angles and parallel lines
Leads on to
- Year 5: Angles in degrees and polygons
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