To develop our children’s ability to master a mathematical concept, we recognise the importance of carefully planned, sequential learning steps that build upon previous learning. Our step by step, progressive planning allows all pupils to access these concepts and ideas and explore the connections between them. It is important to us that our children are encouraged to make explicit links to other areas of mathematics to help support them when learning new concepts or solving problems. Over time and through varied and frequent practice, they are given the opportunity to consolidate a skill before then being challenged to apply it within a context. Images, jottings, models, diagrams and other pictorial representations are used to support our children to 'see' a concept and our children use these to help them reason and solve problems. Across the school, we 'present' maths to our children through pictorial and abstract based sheets.

We adopt the ‘intelligent practice’ approach which ensures our children avoid mechanical repetition; once a concept has been grasped, we expose our children to varied fluency activities which deepen their understanding or challenge them through reasoning based tasks. There is however, time for our children to practise a skill to fully-embedded it. We ensure that our children are given opportunities to engage in rich mathematical discussion and encourage them to feedback with the context in mind, making use of sentence stems through every opportunity. Our children explore, find alternative methods and justify their approaches, not giving one-word responses or seeing maths as just 'giving the answer to the question'.

Nursery:

Our Nursery team use the acclaimed maths programme 'Numberblocks', developed and promoted by the NCETM (National Centre for Excellence in the Teaching of Mathematics).

By focusing on one of the numbers from 0-10 per week, our children are able to develop a strong sense of number. Throughout the week, they will build a picture of 'how we have found ____ this week'. Opportunities are planned in during the start of the day, within family group time and in child-initiated sessions that will encourage discussion and exploration of that number of the week. The staff celebrate the individual and unique ways in which our children find the number of the week and draw their attention to the structure and variety of ways it can be represented. We place great emphasis on variety as we believe this is key when trying to make sense of and establish e.g. the oneness of one. In light of this, we promote the approach that our children need to see these numbers in different ways, compare them to others and make observations about their differences.

'In variation theory, it is assumed that there are critical aspects of a given phenomenon that learners must simultaneously be aware of and focus on in order to experience that phenomenon in a particular way.'

Our children's outdoor experiences are captured, their discussions are built upon and the staff promote the use of different images to establish a strong foundation that can be built upon.

Reception and Y1:

As our children move to Reception and into Y1, our focus turns to concepts such as '5 and a bit' and '10 and a bit' to deepen understanding of numbers 0-20 and look more closely at their structures. 'Numberblocks' continues as a theme for our children and five and tens frames are more formally introduced. One of our key focuses across KS1 is to ensure our children can quickly recall basic number facts and begin to learn skills that will ensure they are 'calculators' rather than counters, building on the foundations set in place from Nursery. The White Rose programme, which is in line with the content needed to be covered from the National Curriculum, is introduced in year 1.

In line with our approach to develop fluency and mental strategies, we introduce MCRAPACODANumbo, a series of mental strategies that our children are taught in order to develop fluency when trying to calculate with all four operations (addition, subtraction, multiplication and division). Partitioning, Counting On and Number Bonds/Number facts are the main focus within Reception and Y1 and this is then built upon as children progress through our school.

Year 2:

As our children move into year 2, we continue to focus on instant recall of basic number facts. The use of tens frames and the knowledge of '5 and 10 and a bit' are further developed with a focus being on refining their ability to calculate across boundaries with confidence. With firm foundations in number established in previous year groups, our children are taught to apply this knowledge when crossing the tens boundaries and in particular when partitioning numbers to support calculations. The White Rose programme of study continues to be followed in line with the National Curriculum with a key emphasis on varied fluency and the application of MCRAPACODANumbo strategies. Reasoning strategies are further developed through the use of open-ended lessons where our children are often asked to prove their thinking or find alternative strategies to solve problems.

By the time our children leave year 2, we look ensure that they are confident at instantly recalling all of the following number facts:

Key Stage 2:

As our children progress through Key Stage 2, we continue to make strong links between different areas of maths to ensure that our children are always applying known knowledge whilst learning new concepts.

Pupils make good progress over time at King Charles because;

• A coherent journey through the curriculum is planned in line with White Rose Maths.

• Teachers carefully consider the most appropriate manipulatives and pictorial representations which expose the structure of the mathematics and plan to address misconceptions in order to develop deep understanding of concepts.

• Children are taught to think mathematically and reason logically - looking for patterns and relationships.

• Precise mathematical language is used consistently when explaining a concept but also when children feedback.

• Adults use skilful questioning to reveal, probe and address misconceptions.

• Mathematical skills are practised, applied and assessed across the curriculum. Gaps in knowledge are then revisited if necessary.

• Consolidation weeks allow for further embedding of skills

• We use recap slides within our planning to revisit previous learning to ensure this knowledge isn't lost.

• A mathematically rich environment supports learning:

• Fluency and flexibility are developed in every lesson (including looking at relationships and making connections)

• Children grasping a concept rapidly will be challenged, deepening their understanding through rich and sophisticated problems and reasoning tasks (such as our RAPA challenges) or the abstract challenges we provide.

• Skilful assessment identifies children who are struggling to grasp concepts, leading to guided groups and consolidation sessions if required.

Impact

The school has a supportive ethos and our approaches support our children in developing their collaborative and independent skills, as well as empathy and the need to recognise the achievement of others. Children can under perform in mathematics because they believe they can't do it or are not naturally good at it. We address these preconceptions by ensuring that all children experience challenge and success in mathematics by developing a growth mindset. Regular and ongoing assessment informs teaching, as well as intervention, to support and enable the success of each child. These factors ensure that we are able to maintain high standards, with progress by the end of Key Stage 2 in line with national averages.