# Maths

At Q.I. Primary School, we believe Mathematics is a discipline that equips children with an essential skill set. It develops children’s ability to reason, apply logical thought, problem solve and think in an abstract way. It also allows children to become financially literate in later life. As being numerate is such an important life skill, we aim to foster a positive and enthusiastic attitude towards mathematics that will stay with them.

We are committed to ensuring that all pupils achieve mastery in the key concepts of mathematics, appropriate for their age group- as set out in the National Curriculum. The National Curriculum sets out year-by-year programmes of study for key stages 1 and 2. This ensures continuity and progression in the teaching of mathematics throughout the primary years.

The aims of the National Curriculum are for pupils to:

• Become fluent in the fundamentals of mathematics through varied and frequent practice with complexity increasing over time.
• Develop conceptual understanding and ability to recall and apply knowledge rapidly and accurately.
• Reason mathematically; follow a line of enquiry, conjecture relationships and generalisations.
• Develop an argument, justification and proof by using mathematical language.
• Problem solve by applying knowledge to a variety of routine and non-routine problems

For our Foundation Year, the EYFS Statutory Framework sets standards for the learning, development and care of children from birth to five years old and supports an integrated approach to early learning. This is supported by the ‘Development Matters’ non statutory guidance.

The EYFS Framework aims for our pupils to:

• develop and improve their skills in counting
• understand and use numbers
• calculate simple addition and subtraction problems
• describe shapes, spaces, and measures

### Overview of Phases

#### Early Years Foundation Stage

Children will have opportunities to practise and improve their skills in counting numbers, calculating simple addition and subtraction problems, and to describe shapes, spaces, and measures. Children will be taught to count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they will be taught to add and subtract two single-digit numbers and count on or back to find the answer. They will be able to solve problems, including doubling, halving and sharing. Children will be taught to use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They will also be taught to recognise, create and describe patterns. Furthermore, they will explore characteristics of everyday objects and shapes and use mathematical language to describe them.

#### Year 1-2

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, they will develop an understanding of how numbers work, so that they are confident in 2-digit numbers and beginning to read and say numbers above 100. A focus on number bonds, first via practical hands-on experiences and subsequently using memorisation techniques, will enable a good grounding in these crucial facts, and ensure that all children leave Y2 knowing the pairs of numbers which make all the numbers up to 10 at least. They will also experience and be taught pairs to 20. Their knowledge of number facts will enable them to add several single-digit numbers, and to add/subtract a single digit number to/from a 2-digit number. Another important conceptual tool is their ability to add/subtract 1 or 10, and to understand which digit changes and why. This understanding will be extended to enable children to add and subtract multiples of ten to and from any 2-digit number.  The most important application of this knowledge will be their ability to add or subtract any pair of 2-digit numbers by counting on or back in tens and ones. Children may extend this to adding by partitioning numbers into tens and ones. Children will be taught to count in 2s, 3s, 5s and 10s, and will have related this skill to repeated addition.  They will meet and begin to learn the associated 2x, 3x, 5x and 10x tables. Engaging in a practical way with the concept of repeated addition and the use of arrays will enable 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.  They 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 will be introduced as numbers and as operators, specifically in relation to halves, quarters and thirds.

#### Year 3-4

In the lower juniors, children will build on the concrete and conceptual understandings they have gained in Year F, 1 and 2 to develop a real mathematical understanding of the four operations, in particular developing arithmetical competence in relation to larger numbers. In addition and subtraction, they will be taught to use place value and number facts to add and subtract numbers mentally and will develop a range of strategies to enable them to discard the ‘counting in ones’ or fingers-based methods of the infants. In particular, they 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 will be taught, learned and consolidated, and written column subtraction will also be introduced.  This key stage is also the period during which all the multiplication and division facts are thoroughly memorised, including all facts up to the 12 x 12 table. Efficient written methods for multiplying or dividing a 2-digit or 3-digit number by a single-digit number will be taught, as well as mental strategies for multiplication or division with large but friendly numbers, e.g. when dividing by 5 or multiplying by 20.  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 one-place decimals, multiplying and dividing whole numbers by 10 and 100.

#### Year 5-6

Children will move on from dealing mainly with whole numbers to performing arithmetic operations with both decimals and fractions.  They 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 two decimal places. Mental strategies for adding and subtracting increasingly large numbers will also be taught. These will draw upon the children’s robust understanding of place value and knowledge of number facts.  Efficient and flexible strategies for mental multiplication and division will be taught and practised, so that children can perform appropriate calculations even when the numbers are large, such as 40,000 x 6 or 40,000 ÷ 8.  In addition, it is in Y5 and Y6 that children will extend their knowledge and confidence in using written algorithms for multiplication and division. Fractions and decimals will also be added, subtracted, divided and multiplied, within the bounds of the children’s understanding of these more complicated numbers, and they will also calculate simple percentages and ratios.  Negative numbers will be added and subtracted.

Breadth of study will include opportunities to:

•  individual,  paired, group and whole class learning and discussions
• problem solving to challenge thinking
•  practical activities and games using a variety of resources
• purposeful practise where time is given to apply their learning
• working with computers as a mathematical tool
• a range of methods to solve problems including C.P.A. (see below) of calculating e.g. practical, mental, pictorial, informal (number lines and jottings) as well as formal methods (e.g. compact column addition)

#### A CPA approach

To develop conceptual understanding in maths, we begin teaching using concrete apparatus so children can understand what they are doing, before moving onto pictorial representation (e.g. drawing the problem) and only moving onto abstract representations when they have conceptual understanding to do so.  This approach is referred to as CPA (Concrete. Pictorial, Abstract)

Task design will present problems in different ways to develop fluency, reasoning and problem solving skills. Question types and task designs will show variation so children can apply learning and make links between different domains of maths.

#### RUCSAC approach to problem solving

A whole school approach to problem solving is used based on RUCSAC.

### The answer itself is not the sole goal

The reasoning behind mathematical processes will be explored.  How answers were obtained will be valued rather than just the answer. Which method was more efficient? Why?  Children will ask themselves:

1. Can I solve it mentally?
2. Can I solve it informally (draw a picture, use a number line, jottings)?
3. Or will I need to use a formal method?

Over time, children will develop a repertoire of strategies to solve problems, allowing them to choose the most efficient one, depending on the problem.