Numeracy 6: Shape and Space

Overview

This Element reviews key concepts and effective teaching strategies in relation to Shape and Space. Based on the National Numeracy Strategy, it highlights the properties of shape and positional vocabulary. Emphasis is placed on the development of mathematical language and the use and application of skills at each level.

This Professional Development Element will help you to:

become more familiar with the standards and levels in the shape and space section of the core curricula

review approaches to teaching the properties of shape and space

explore some practical approaches to teaching positional language

recognise the skills required to solve problems involving shape and space

be aware of the importance of language as part of the development process.

Shape and Space (MSS2)

Learners need to be given opportunities to develop an understanding of geometric properties and relationships. They can then apply this knowledge to everyday situations and problems. Many learners will have an understanding of shapes and this should be used as a foundation for developing a learning programme

Much of MSS2 addresses the properties of 2D and 3D shapes. These skills can be introduced and reinforced by using everyday objects and comparing them to mathematical shapes.

The following activities will help you to become familiar with the skills required for shape and space and to be able to track progression through the levels.

Use the progression and Shape and Space curriculum section pages to identify how the learner's skills, knowledge and understanding of the properties of shape and space is developed over the levels and identify a sample activity you could use. Use the table provided to record your results.

Language of Shape and Space

The development of mathematical language used with shape and space is fundamental and is identified at all levels in the curriculum as part of the underpinning knowledge and understanding. For some learners the terminology used can be complex to grasp. Difficulties can be experienced differentiating between terms such as side/face or vertices/corner. Confusion can arise over the classification of shapes, eg identifying a polygon. There are many practical activities that you can use to help learners extend their use and understanding of vocabulary. Some examples are given here.

Complete the following table of definitions for shape

Language of Shape and Space (cont'd)

Write clear instructions that would enable someone following them to draw the given image. Once you have completed the activity try doing it without using positional vocabulary.

Positional vocabulary can be developed by using street maps and giving directions to a local landmark. This also links in with the speaking and listening Element from the literacy and ESOL curricula.

Language of Shape and Space (cont'd)

Joe Francis is working at a large DIY store and needs to be familiar with the means of exiting the building safely in event of an emergency. There are a variety of routes that he could take, depending on where he is in the building at the time of the emergency. As a part of his job he might also be required to give directions to members of the public. Joe is working towards Entry 3 for MSS.

Using the curriculum, identify the skills and knowledge he already should have.

Consider the approaches and strategies you could use to enable him to develop the necessary skills required for his work. Feedback your ideas to your colleagues.

Visualisation

The visualisation of shapes is an important aspect of conceptual development of shape and space. Many adults will have previously found it difficult to develop the abstract aspects of mathematics. Visualising 2D or 3D shapes in a different orientation is particularly complex, ie a square that has been translated and rotated. Learners will need plenty of practice in developing and reinforcing these processes.

The purpose of this activity is to demonstrate how you might use a visualisation activity as a starter activity.

How could you use the visualisation activity as a starter for a mixed ability group.

You can do this activity in the classroom by printing off a Tanagram then asking learners to: cut out the seven shapes, name all the shapes, name all the shapes they can find by rearranging the elements.

It could be used at a variety of levels including MSS2/E2.1, MSS2/E2.2, MSS2/E3.1, Questioning about the various properties would also bring in positional vocabulary. Could be used at L1 and L2 to investigate properties when tessellated or in different orientations.

Problem solving

Problem solving is a skill, which should be developed across the entire curriculum and cannot be taught in isolation. At the higher skills levels, learners are expected to be able to solve problems which could include applying techniques such as symmetry or tessellation. The following activities illustrate how you could use simple tasks to develop problem solving skills.

Tanagrams are ancient Chinese puzzles consisting of only seven pieces, which can be arranged to produce a variety of shapes. As well as developing problem solving skills, Tanagram activities develop spatial-visualisation skills.

There are many other exercises you could do with Tanagrams. If you need ideas, take a look on the Internet. What skills would learners be developing with Tanagrams?

Problem solving (cont'd)

Complete the pattern which is symmetrical around the x and y axes. At what level is this problem?

Discussion topic: Is a square a rectangle?

MSS2/E1.1: Draw common shapes using Paint

MSS2/E2.1: Experiment with shapes using Paint

MSS2/E2.3: Look at web site such as www.streetmap.co.uk

MSS2/L1.1 - Use 'draw' in Word to create tessellations

MSS2/L1.2: Use 'draw' in Word to draw 2D shapes

MSS2/L2.1: Draw 3D shapes in Word

Using ILT for developing shape and space

Technology can be used in a variety of ways enabling a learner to experiment with shape and space. The 'Drawing toolbar' available on Word or PowerPoint provides a number of tools enabling the learner to draw and explore a variety of 2D and 3D shapes. These can also be manipulated into a variety of representations. 'Paint' can be used by learners to experiment as well as importing shapes or images from clip art or the internet.

The internet is a valuable source of information about shape and space. There are numerous sites which provide information about shapes, tessellation and symmetry, as well as providing useful resources that you could adapt for use with your learners.

Look in the curriculum, where have examples of using ILT been outlined?

Summary

Sorting and recognition of properties of 2D and 3D shapes is developed through all the levels.

Positional vocabulary is developed at Entry 1 and Entry 2.

The vocabulary used throughout shape and space is part of the underpinning knowledge and understanding.

The visualisation of shapes is an important aspect of the conceptual development of shape and space.

Problem solving using the properties of shapes is developed throughout the curriculum.