# Mathematics

## Our approach to Mathematics

At Woodford, we are using the Abacus scheme of work across all year groups. The Abacus 'philosophy' is built around four pillars: place value, number facts (number pairs and bonds, multiplication and division facts), models and images and maths functions (such as doubling and halving).

Key Stage 1

Children in Years 1 and 2 will be given a really solid foundation in the basic building blocks of mental and written arithmetic. Through being taught place value, children will develop an understanding of how numbers work, so that they are confident with 2-digit numbers and beginning to read and say numbers above 100. They are encouraged to develop a range of mental skills and strategies and use these when solving calculations. They learn about shape and space through practical activities and where possible these are linked to other topic areas they are learning about. They are encouraged to use mathematical language what talking about how they solved a problem.

• Addition and Subtraction: A focus on number bonds, first via practical hands-on experiences and subsequently using memorisation techniques, enables a good grounding in these crucial facts, and ensures that all children leave Year 2 knowing the pairs of numbers which make all the numbers up to 10 at least. Children will also have experienced and been taught pairs to 20. Children’s knowledge of number facts enables them to add several 1-digit numbers, and to add/subtract a 1-digit number to/from a 2-digit number.  Another important conceptual tool is the ability to add/subtract 1 or 10, and to understand which digit changes and why. This understanding is extended to enable children to add and subtract multiples of 10 to and from any 2-digit number. The most important application of this knowledge is the ability to add or subtract any pair of 2-digit numbers by counting on or back in 10s and 1s. Children may extend this to adding by partitioning numbers into 10s and 1s.
• Multiplication and Division: Children will be taught to count in 2s, 3s, 5s and 10s, and will relate this skill to repeated addition. Children will meet and begin to learn the associated ×2, ×3, ×5 and ×10 tables. Engaging in a practical way with the concept of repeated addition and the use of arrays enables children to develop a preliminary understanding of multiplication, and asking them to consider how many groups of a given number make a total will introduce them to the idea of division. Children will also be taught to double and halve numbers, and will thus experience scaling up or down as a further aspect of multiplication and division.
• Fractions: Fractions will be introduced as numbers and as operators, specifically in relation to halves, quarters and thirds.

Lower Key Stage 2

In Lower Key Stage 2, children build on the concrete and conceptual understandings they have gained in Key Stage 1 to develop a real mathematical understanding of the four operations, in particular developing arithmetical competence in relation to larger numbers.

• Addition and subtraction: Children are taught to use place value and number facts to add and subtract numbers mentally and they will develop a range of strategies to enable them to discard the ‘counting in 1s’ or fingers-based methods of Key Stage 1. In particular, children will learn to add and subtract multiples and near multiples of 10, 100 and 1000, and will become fluent in complementary addition as an accurate means of achieving fast and accurate answers to 3-digit subtractions. Standard written methods for adding larger numbers are taught, learned and consolidated, and written column subtraction is also introduced.
• Multiplication and division: This key stage is also the period during which all the multiplication and division facts are thoroughly memorised, including all facts up to 12 × 12. Efficient written methods for multiplying or dividing a 2-digit or 3-digit number by a 1-digit number are taught, as are mental strategies for multiplication or division with large but ‘friendly’ numbers, e.g. when dividing by 5 or multiplying by 20.
• Fractions and decimals: Children will develop their understanding of fractions, learning to reduce a fraction to its simplest form, as well as finding non-unit fractions of amounts and quantities. The concept of a decimal number is introduced and children consolidate a firm understanding of 1-place decimals, multiplying and dividing whole numbers by 10 and 100.

Upper Key Stage 2

Children move on from dealing mainly with whole numbers to performing arithmetic operations with both decimals and fractions.

• Addition and subtraction: Children will consolidate their use of written procedures in adding and subtracting whole numbers with up to 6 digits and also decimal numbers with up to 2 decimal places. Mental strategies for adding and subtracting increasingly large numbers will also be taught. These will draw upon children’s robust understanding of place value and knowledge of number facts. Negative numbers will be added and subtracted.
• Multiplication and division: Efficient and flexible strategies for mental multiplication and division are taught and practised, so that children can perform appropriate calculations even when the numbers are large, such as 40 000 × 6 or 40 000 ÷ 8. In addition, it is in Years 5 and 6 that children extend their knowledge and confidence in using written algorithms for multiplication and division.
• Fractions, decimals, percentages and ratio: Fractions and decimals are also added, subtracted, divided and multiplied, within the bounds of children’s understanding of these more complicated numbers. Children will also calculate simple percentages and ratios.

### Targets

All children have Maths targets. In Key Stage 1 these targets are based on their NumberNauts charts which all children start in Year 1. By Year 2, all children are working towards their 2x, 5x and 10x tables, and can earn a Times Tables Champion hat when they know them off by heart.

In Key Stage 2 the children move onto learning the rest of their multiplication tables, practicing them in their classrooms on the ‘Challenge Chair’. Initially the children learn to count in the multiples of the table they are learning, they then move onto learning the tables facts in order. To achieve their target the children need to be able to recall the multiplication facts in a random order, and also know the division facts that are linked to them. For example, knowing 4 x 8 = 32 means they can solve a problem like this: 32 ÷ ? = 4.

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