The national curriculum makes it clear that children at key stage 1 should develop their knowledge and understanding of shape and space through practical activity, exploration and discussion. With the introduction of the National Numeracy Strategy, schools recognised that the three-part lesson would provide opportunities for pupils to describe and explain their work. Providing practical resources for whole-class hands-on experience need not be expensive.
I have been working with some KS1 teachers on developing shape and space activities in their infant classes. The building blocks, construction toys and sets of plastic shapes found in most nurseries and reception classes are useful for an informal exploration of 2-D and 3-D shapes but children in Year 1 are ready for more formal work. There is a wide range of materials available but most have a distinct disadvantage - the shapes are entirely regular. Fortunately a good deal of work on shape and space, particularly with Year 1, can be done using materials costing next to nothing. Card off-cuts and pieces of coloured paper can be used to pose questions and help children name and describe many mathematical shapes. In a quickly gathered collection we found all kinds of shapes and sizes of triangles, pentagons and hexagons that could be displayed in different orientations.
We added other shapes and used the collection to play a range of shape games. Pupils took a shape from a hat and described it, counted the number of sides and gave it a name if they could. We talked about the different ways of naming shapes - a triangle but a pentagon and a hexagon. We linked the work to literacy activities and asked the children to use different-shaped paper for their writing. The aim was to try to make the names more than labels.
I then introduced the class to a giant pack of Mathematical Activity Tiles - usually thought more appropriate for junior and secondary pupils. The tiles (available from the Association of Teachers of Mathematics, tel: 01332 346599) are made of card and look like decorated beer mats. Pupils loved the attractive patterns and colours and enjoyed trying out different ideas. The teachers liked the selection of shapes and the large quantities, particularly of the smaller shapes, with sufficent for whole-class lessons.
The activities provided opportunities for pupils to solve problems and acquire a rich mathematical vocabulary. One lessn was on triangles. There were two types of triangles in the chosen pack - equilateral and isosceles. The pupils called them the yellow and orange ones. The challenge was to find out what other shapes they could make using these triangles. One group using the yellow triangles found they could make a hexagon, change it into a larger triangle and then into an even larger hexagon. They thought it was wonderful. "What if you had more yellow triangles?" asked the teacher.
After thinking for a minute, pupils suggested: "It would go on and on making triangles and hexagons, triangles and hexagons - through the wall and into the playground. We could cover the world."
Those using the orange triangles found they could not make hexagons, but they did make star shapes and larger and larger triangles. The teacher asked about the number of smaller triangles in the larger. "How many triangles in the next-size triangle? How do you know?" During another lesson the challenge was to find out which shapes fitted together without leaving spaces. Pupils working with 10-sided shapes had to use the floor to spread out the shapes. They discovered to their delight that they had some star-shaped spaces. Those using the pentagons got quite frustrated as they kept moving the shapes around to close a gap only to find another gap opened up elsewhere.
Some Year 2 pupils asked whether they could make some of the shapes into pyramids. Following instructions, they dipped the edges of the tiles briefly in the glue and held them together while they counted to 20. Most pupils made triangular or square-based pyramids. Some even used pentagons as a base. There was an interesting discussion about different kinds of pyramids. One girl was intrigued by the pentagons and made a great impression on her classmates by building up a dodecahedron. She was so thrilled by her success that she overcame her shyness and described to the rest of the class how she had made this very special shape with the name they all learned very quickly.
Discussion, both during and at the end of all the sessions, was meaningful and important to the pupils, who wanted to share with others the interesting things they had learned. Striving to relate their experiences helped them to extend their vocabulary and clarify their own thoughts - so important for geometric reasoning and the development of proof in later key stages.
Marjorie Gorman is a former primary and advisory teacher and is now a consultant and author of 'Success in Mental Arithmetic' (Ginn)