Westmorland Primary School 

             Mathematics Calculation Policy

Introduction

At Westmorland, we are dedicated to developing our children into confident mathematicians, where they are able to solve problems, reason about mathematical concepts and fluently apply mathematical skills in a variety of contexts, including real-life experiences across the curriculum and in the wider world. In order to achieve this, we are committed to developing all children by giving MORE.

Our curriculum is based around Memorable Learning, Oracy, Reading and Experiences.

At the centre of the mastery approach to the teaching of mathematics is the belief that all children have the potential to succeed. They should have access to the same curriculum content and, rather than being extended with new learning, they should deepen their conceptual understanding by tackling challenging and varied problems.

Similarly with calculation strategies, children must not simply rote learn procedures but demonstrate  their understanding of these procedures through the use of concrete materials and pictorial representations.

This policy outlines the different calculation strategies that should be taught and used in line with the requirements of the 2014 Primary National Curriculum to ensure that all children:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

INTENT:

At Westmorland, our Maths curriculum is designed to offer every child MORE. We are committed to providing Memorable learning opportunities, which are accessible to all, through a concrete, pictorial and abstract approach. All children are encouraged to discuss and share mathematical thinking using rich vocabulary and explore real-life problems both independently and in collaboration with their peers.

The principle of the concrete-pictorial-abstract (CPA) approach is that, for children to have a true understanding of a mathematical concept, they need to master all three phases

To support the CPA approach, Westmorland Primary School have 5 core representations in which the teaching of the four operations can be supported with. These are a combination of concrete and pictorial representations to support the children before they are able to work in the abstract.

These core representations are:

• Tens Frame
• Base 10 / Dienes
• Part, Part, Whole
• Bar Model
• Number Line

This is a system of learning that uses physical and visual aids to build a child’s understanding of abstract topics. Pupils are introduced to a new mathematical concept through the use of concrete resources.

When they are comfortable solving problems with physical aids, they are given problems with pictures – usually pictorial representations of the concrete objects they were using. Then they are asked to solve problems where they only have the abstract i.e. numbers or other symbols.

Reinforcement is achieved by going back and forth between these representations. For example, if a child has moved on from the concrete to the pictorial, it does not mean that the concrete cannot be used alongside the pictorial. Or if a child is working in the abstract, ‘proving’ something or ‘working out’ could involve use of the concrete or pictorial.

IMPLEMENTATION:

From Year 1 to Year 6, we adhere to our Progression of skills document which outlines the progression of strategies and methods to be taught. EYFS have a separate skills document and have daily Maths lessons and Maths continuous provision. We have created our long and medium-term plans in line with Maths No Problem small steps, but if needed and in agreement with the Maths Lead, have altered the order to suit and benefit the needs of our children so that connections between units of learning are easier to recognise.

Lessons are planned and sequenced so that new knowledge and skills build on what has been taught before. Teachers follow the school’s Progression of skills document and refer to the Calculation Policy when teaching formal methods, understanding that sometimes children find their own efficient methods along the way. Teachers also have access to White rose Maths hub materials. Teachers understand that the small steps are not lessons, but are learning intentions that must be achieved before moving on to the next, and how to progress children who achieve this by using problems of greater complexity (i.e. where the approach is not immediately obvious), demonstrating creativity and imagination and independently exploring and investigating mathematical contexts and structures, communicating their results clearly and systematically. Year 3 onwards also have access to their own personal account of ‘Times Tables Rockstar’ where they can compete against other pupils and classes in school. 

By using a variety of planning resources, and having our progression of skills and calculation policy at the heart of our Maths, we believe that we provide a bespoke teaching and learning experience that is designed to interest, inform and inspire our children. - Using prior knowledge as a starting point for all future planning and teaching, we plan lessons which are required for all pupils to make good progress.

Children, in Year 6, who require extra support in Maths are identified and assigned a tutor from Third space learning where following initial and ongoing assessments, lessons are chosen specifically to plug each pupil's individual gaps

IMPACT:

The impact of our mathematics curriculum is that children understand the relevance and importance of what they are learning in relation to real world concepts. Children know that Maths is a vital life skill that they will rely on in many areas of their daily life. Children have a positive view of Maths due to learning in an environment where Maths is promoted as being an exciting and enjoyable subject in which they can investigate and ask questions; they know that it is reasonable to make mistakes because this can strengthen their learning through the journey to finding an answer. Children are confident to ‘have a go’ and choose the equipment they need to help them to learn along with the strategies they think are best suited to each problem. Our children have a good understanding of their strengths and targets for development in Maths and what they need to do to improve. 

A mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations. Children demonstrate quick recall of facts and procedures. This includes the recollection of the times tables. The flexibility and fluidity to move between different contexts and representations of mathematics. The ability to recognise relationships and make connections in mathematics. Children show confidence in believing that they will achieve. -Children show a high level of pride in the presentation and understanding of the work.

We achieved 81% expected or greater depth in 2021-2022.