Year 3 - Geometry - properties of shapes
New Curriculum
- 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 two right angles make a half-turn, three make three quarters of a turn and four 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.
Non-Statutory Guidance
Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.
Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.
Links and Resources
Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.”
– The National Curriculum in England Framework document. September 2013 page 10
Making connections to other topics within this year group
Fractions
When working on geometry: properties of shape and/or fractions, there are opportunities to make connections between them, for example:
In the guidance for fractions it states that the children should continue to recognise fractions in the context of shape. Give children the opportunity to explore these during shape and fractions lessons in order to reinforce and consolidate their learning in both areas. For example, you could ask the children to draw a variety of regular and irregular shapes and explore which ones can be divided into halves, thirds, quarters etc. It is important that the children consider that equal fractions of a shape have the same area rather than parts that look the same which is often how they are presented in textbooks and worksheets. You could ask the children to cut up pieces of their shapes to find out if they are the same. For example, they could draw the rectangle below and its two diagonals:
The resulting parts don’t all look the same, but each is a quarter. Can the children prove this? They could, for example, cut out each triangle and then cut it in half. These pieces are eighths. Two eighths are equal to a quarter therefore the triangles are all quarters.
You might give the children a tangram like this:
Ask them to identify each of the shapes (right angled isosceles triangles, parallelogram and square). They then cut the pieces out and explore the fractions that they can make. For example, the small red triangle is half of the parallelogram, the area of square is half that of the green triangle, the red triangle is a quarter of the green triangle.
You could give the children a selection of 3D shapes and ask them to visualise and sketch what they would become if cut in half. For example a sphere would become a hemisphere, a cube would become a cuboid. They could make triangular prisms out of card or plasticine and explore what these would look like if cut into thirds or quarters. What is the same about them, what is different?
Measurement
When working on geometry: properties of shape and/or measurement, there are opportunities to make connections between them, for example:
One of the requirements in measurement is that the children should be taught to measure the perimeter of simple 2D shapes. You could ask the children to draw regular and irregular triangles, rectangles (including squares), pentagons and hexagons. Once they have, they measure their perimeters. Can they find a quick way of finding the perimeter of regular shapes? Can they make up a formula for this? They may be able to come up with l x n, where l = length and n = number of sides. So, for example a pentagon with sides of 4cm would be 4cm x 5 (20cm).
In the guidance for measurement it encourages the comparison of measurements through simple scaling by integers and link this to multiplication. You could ask the children to draw small shapes and then measure their sides to the nearest centimetre. They could then scale these up so that they are, for example, twice the size or five times bigger. They could then draw their shapes again to the new measurements and compare the two.
Making connections to this topic in adjacent year groups
Year 2
statutory requirements
- identify and describe the properties of 2-D shapes, including the number of sides and 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
Non Statutory Guidance
Pupils handle and name a wider variety of common 2-D and 3-D shapes including: quadrilaterals and cuboids, prisms, cones and polygons, and identify the properties of each shape (e.g. 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.
Year 4
statutory requirements
- 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 two 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
Non Statutory Guidance
Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (e.g. isosceles, equilateral, scalene) and quadrilaterals (e.g. parallelogram, rhombus, trapezium).
Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.
Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the reflected shape.
Cross-curricular and real life connections
Learners will encounter geometry (properties of shapes) in a number of contexts:
Within the art curriculum there are opportunities to connect with geometry: properties of shape, for example, in the requirements the children should be taught to improve their mastery of art and design techniques, including drawing, painting and sculpture with a range of materials (e.g. pencil, charcoal, paint, clay). You could ask the children to make a selection of 3D shapes, such as, spheres, cubes, cuboids and pyramids out of clay and then put them together to make a sculpture of their own design. An activity like this should include a discussion of each shape’s properties, what they can do and where they are seen in real life.
The art curriculum also requires the children to be taught about great artists, architects and designers in history. The Art of Mathematics articles in the Primary Magazine explore the works of many artists. In each article there is a short history of the artist and many mathematical activities to explore through their art work.
Within the design and technology curriculum, the children should be taught the knowledge, understanding and skills needed to design and make things working in a range of relevant contexts. You could give the children opportunities to make packaging for something to be sold. This could involve exploring nets of cubes and cuboids.
In real life, shape and pattern are everywhere. You could ask the children to explore shape in their environment. What 3D shapes can they see in the classroom? What 2D shapes can they see in patterns? You could follow the ideas on Islamic patterns in The Art of Mathematics in issue 13 of the Primary Magazine. You could show the children the works of famous artists such as Mondrian and Kandinsky and ask the children to explore the shapes that they can see, the angles, parallel and perpendicular lines and so on. The Art of Mathematics in the Primary Magazine provides a useful resource for this.
| Programme of study statements | Activities | |||
| A | B | C | D | |
| draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them | ||||
| recognise that angles are a property of shape or a description of a turn | ||||
| identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four 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 | ||||
Activity set A
You could ask the children to make a repeating pattern by drawing squares or equilateral triangles in different orientations.
Ask the children to look at pictures in magazines and books and identify and draw the 2D shapes that they can see.
You could give the children card and a polyhedron, for example a cube or a cuboid. Ask the children to make their shape using the card. It is interesting to observe the children as they do this. Some children may draw around each face, cut them out and stick the pieces together. Others might draw around several faces side by side so beginning to make a net. These methods produce useful discussion. For example, if they have drawn this for a cube:
You could discuss what they could have done to make a closed cube (add another square to one of the four exterior squares).
You could give each child a piece of plasticine and ask them to make a sphere. Discuss how they do this. Once they have a sphere talk about its properties: one curved surface, no edges, no vertices. It might be worth pointing out that an edge occurs when two faces meet and a vertex occurs when three or more edges meet. Discuss what a sphere can do and where one can be seen in real life. Next, ask the children to turn their sphere into a cube. What do they need to do? Flatten the curved surface to make flat faces. Recap the properties of a cube, including the shape of the faces and the lines of symmetry in each one. Where would they see one in real life? Follow this process for a cuboid and then a square based pyramid. When they have the pyramid, ask them to visualise what it would look like opened up and draw what they see. Most children will draw this:
You could ask them to cut their drawing out and put it together to make a pyramid. As this is made from a sketch it might not fit exactly. Discuss what the children would need to do to make it more accurate. Agree that the square base must be square and the triangles must be the same size. You could ask them to draw an accurate net and then make the shape. You could repeat this for a cube.
Activity set B
The children need to recognise that angles can be found where the sides of a 2D shape meet. You could ask the children to draw an irregular shape on a piece of paper. Once they have done this ask them to identify the angles according to whether they are acute, right, obtuse or greater than a straight line.
You could ask them to identify angles in paintings, such as, Kandinsky’s Composition VII which can be found in The Art of Mathematics in issue 9 of the Primary Magazine.
You might like to try the activity from Nrich ‘More Transformation on a Pegboard’ which asks the children to make triangles with different angles.
The children also need to recognise that angles are a description of a turn (dynamic angles). When the children are familiar with what a right angle looks like, you could ask them to stand and make a turn of the same size. Repeat this for half a turn and point out that this is equivalent to two quarter turns or a straight line. Repeat again for three and four quarter (whole) turns.
‘How Safe are You?’ from Nrich asks the children to explore the angles of turn needed to open a safe.
Activity set C
Children need to identify whether angles are greater than or less than a right angle and name these as acute of obtuse. You could ask the children to draw different acute and obtuse angles and give their drawings to a friend to label with the correct vocabulary. They could also draw stick men with joints such as elbows, knees and ankles positioned to show acute, right and obtuse angles.
You could follow the suggestions for the painting ‘Ballet’ by Laura Knight in The Art of Mathematics in issue 56 of the Primary Magazine.
You might like to explore ‘Right Angle Challenge’ from Nrich which asks the children to explore right angles using sticks.
Activity set D
As well as angles the artist Kandinsky’s Composition VII is a great painting to explore perpendicular and parallel lines.
Another good painting for this is Mondrian’s Komposition which can be found in The Art of Mathematics in issue 11 of the Primary Magazine.
After exploring these paintings and asking the children to identify all the perpendicular and parallel lines that they can, you could ask them to make their own versions of the paintings. Great for a classroom display!
