Mathematical development depends on becoming confident and competent in learning and using key skills. This area of learning includes counting, sorting, matching, seeking patterns, making connections, recognising relationships and working with numbers, shapes, space and measures. Mathematical understanding should be developed through stories, songs, games and imaginative play, so that children enjoy using and experimenting with numbers, including numbers larger than 10.

To give all children the best opportunities for effective mathematical development, we will give particular attention to:

• many different activities, some of which will focus on mathematical development and some of which will draw out the mathematical learning in other activities, including observing numbers and patterns in the environment and daily routines
• practical activities underpinned by children's developing communication skills
• activities that are imaginative and enjoyable
• help for those children who use a means of communication other than spoken English in developing and understanding specific mathematical language
• opportunities to observe, assess and plan the next stage in children's learning
• relevant training to improve practitioners' knowledge, skills and understanding

Numbers as labels and for counting

Numbers can be used as 'labels'. For example, houses and other buildings have numbers to help people find them in a street, cars and other road vehicles have registration numbers, and buses have numbers that indicate their routes. Children may see numbers being used when a television channel is selected, the video recorder is programmed or food heated in the microwave. At an early stage, children notice where numbers are used, begin to recognise their form and learn some number names.

Counting involves saying the number names in order, matching the numbers to objects counted, knowing that you say one number for each object you count, and knowing that when you count, the last number you say gives the number of objects in the group. Children will later see that counting involves knowing that the number in a group is the same even if the objects are counted in a different order.

Problem solving

The act of problem solving at this stage is all about using numbers in practical contexts, being able to talk about numbers in everyday life and beginning to make logical deductions about these numbers. It involves comparing numbers of objects (leading to subtraction), combining numbers of objects (addition), sharing objects equally between some children or grouping objects in, say, twos or threes (division) and adding groups of the same number of objects (multiplication). The 'objects' referred to here may be actual objects such as bricks or pencils, but could also be 'events' such as a number of jumps or sounds.

Shape, space and measures

The words 'shape' and 'object' in this section apply to two-dimensional or three-dimensional objects or shapes. Experiencing the properties of shapes is much more important than the naming of shapes (triangles, cubes, etc), although some mathematical names may be introduced.