Mathematics

Mathematics at Abbott

At Abbott, we believe that every child can become a confident and successful mathematician. Our mathematics curriculum is carefully designed and sequenced so that pupils build secure knowledge, develop fluency and learn to apply their understanding to a wide range of problems. We teach mathematics through small, carefully structured steps, ensuring that children have the knowledge and understanding they need before moving on to new learning. Through regular practice, retrieval and opportunities to apply their knowledge, we want our children to know more, remember more and use mathematics with increasing confidence and independence. Our curriculum develops three connected types of mathematical knowledge: declarative, procedural and conditional knowledge.

Knowing That, Knowing How and Knowing When

Declarative knowledge – “I know that…”

Declarative knowledge is the mathematical knowledge that children need to remember. This includes facts, concepts, rules, vocabulary, formulae and important relationships between mathematical ideas. For example, children learn number bonds, multiplication facts, properties of shapes and the relationships between fractions, decimals and percentages. We want children to develop a secure bank of mathematical knowledge that they can recall accurately and use as a foundation for future learning.

Procedural knowledge – “I know how…”

Procedural knowledge is knowing how to carry out a mathematical method or process. Children learn efficient mental and written methods and develop the ability to carry out calculations accurately. This might include knowing how to use a formal written method for addition, multiplication or division, or knowing how to calculate with fractions. Through carefully sequenced teaching and purposeful practice, children develop increasing fluency, accuracy and efficiency.

Conditional knowledge – “I know when…”

Conditional knowledge is knowing when and why to use particular mathematical knowledge or methods. This is where children bring their knowledge together to reason and solve problems. They learn to recognise what a problem is asking, select an appropriate strategy, explain their thinking and justify their answer. For example, a child may know how to use several different methods, but a confident mathematician also understands which method is most appropriate and why. This combination of knowing that, knowing how and knowing when helps our pupils to become flexible and independent mathematicians who can apply their knowledge to unfamiliar situations.

Our Mathematics Curriculum

Mathematics is essential for everyday life and helps children to make sense of the world around them. It develops logical thinking, problem-solving, creativity and the ability to recognise patterns and relationships.

At Abbott, we want pupils to develop a genuine understanding of mathematics rather than simply learn procedures. We want children to be able to:

• recall important mathematical facts accurately;
• understand the concepts behind the methods they use;
• develop fluency through purposeful practice;
• reason and explain their mathematical thinking;
• make connections between different areas of mathematics;
• solve familiar and unfamiliar problems;
• choose appropriate and efficient strategies;
• use precise mathematical vocabulary;
• persevere when a problem is challenging.

We believe that children should understand why a method works as well as how to carry it out. Rather than children simply learning one method to answer five questions, we want them to develop the understanding and flexibility to consider different ways of approaching one problem.

Power Maths

In Key Stage 1 and Key Stage 2, we use Power Maths as the core programme to support the teaching and sequencing of our mathematics curriculum. Power Maths is a mastery-based programme which provides a coherent structure for developing mathematical knowledge and understanding. It supports our teachers in breaking learning down into manageable steps while providing opportunities for pupils to develop fluency, reasoning and problem-solving.

We chose Power Maths because it:

• supports a carefully sequenced progression of mathematical knowledge;
• develops pupils' conceptual understanding as well as their procedural fluency;
• provides regular opportunities for reasoning and problem-solving;
• uses a Concrete–Pictorial–Abstract approach to help children develop understanding;
• provides opportunities for children to explain and discuss their mathematical thinking;
• supports the development of mathematical vocabulary;
• encourages children to develop confidence and resilience when learning mathematics;
• provides appropriate challenge and opportunities to apply learning in different contexts.

Power Maths is used alongside teacher expertise and assessment. Teachers adapt and supplement the programme where necessary to respond to pupils' needs, address misconceptions and ensure that all pupils have the opportunity to make progress.

Mathematics in the Early Years

In the Early Years, we recognise that strong mathematical foundations are essential for future success. Our mathematics curriculum is guided by the EYFS Statutory Framework and Development Matters. Children experience mathematics throughout the day through a combination of purposeful play, exploration, practical experiences and structured teaching.

Children develop their understanding of:

• number and quantity;
• counting and cardinality;
• subitising;
• comparing quantities;
• number patterns;
• shape and space;
• measures;
• mathematical language and reasoning.

We provide opportunities for children to play, explore, actively learn and develop their mathematical thinking through focused, continuous and enhanced provision. Children also take part in structured mathematical activities, including adult-led sessions and independent activities. Indoor and outdoor learning, guided activities and purposeful play all contribute to the development of children's mathematical knowledge and confidence. In Nursery, we use Master the Curriculum to support our mathematics teaching and promote strong early number sense. In Reception, Power Maths supports the development of secure foundations in number and mathematical understanding.

Mathematics in Key Stage 1

In Years 1 and 2, pupils develop secure foundations in number, counting and place value. They develop fluency with addition and subtraction and begin to develop their understanding of multiplication and division.

Pupils learn to:

• understand and use place value;
• recall and apply important number facts;
• develop efficient mental and written calculation methods;
• recognise patterns and relationships;
• solve mathematical problems;
• explain and justify their thinking;
• recognise, describe, compare and classify shapes;
• measure and compare quantities;
• develop their understanding of money and time;
• use mathematical vocabulary accurately.

By the end of Year 2, pupils should have secure knowledge of number bonds within 20 and a strong understanding of place value. Regular practice and retrieval help pupils to develop fluency, while opportunities to reason and solve problems enable them to apply their mathematical knowledge.

Mathematics in Lower Key Stage 2 – Years 3 and 4

In Years 3 and 4, pupils build on their existing knowledge and develop increasing fluency and accuracy with the four operations. They work with increasingly large numbers and develop efficient mental and written methods of calculation. They deepen their understanding of fractions and begin to make important connections between fractions, decimals and other areas of mathematics.

Pupils develop their understanding of:

• place value and larger numbers;
• multiplication and division;
• fractions and decimals;
• money and measures;
• properties of shapes and angles;
• statistics;
• mathematical reasoning;
• problem-solving.

Children are encouraged to explain their thinking, identify relationships and apply their knowledge to a range of mathematical situations. By the end of Year 4, pupils are expected to know their multiplication tables up to and including the 12 times table. Regular practice helps pupils to develop the fluency and confidence needed to apply these facts across mathematics.

Mathematics in Upper Key Stage 2 – Years 5 and 6

In Years 5 and 6, pupils deepen and extend their mathematical understanding and make increasingly sophisticated connections between different areas of mathematics.

They develop their knowledge of:

• larger numbers and place value;
• the four operations;
• fractions, decimals and percentages;
• ratio and proportion;
• geometry and measures;
• statistics;
• properties of numbers;
• algebraic thinking;
• reasoning and problem-solving.

Pupils are increasingly encouraged to select appropriate and efficient methods for themselves. They solve increasingly complex problems, explain their reasoning and justify their conclusions. By the end of Year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and work confidently with fractions, decimals and percentages. We also place a strong emphasis on mathematical vocabulary, ensuring that pupils can communicate their ideas clearly and accurately.

Fluency, Reasoning and Problem-Solving

The three aims of the National Curriculum underpin our approach to mathematics.

Fluency

Pupils develop secure knowledge of mathematical facts and efficient methods through regular, purposeful practice. This allows them to recall and apply important knowledge accurately and efficiently.

Reasoning

Pupils learn to explain their mathematical thinking, identify patterns and relationships, make connections, make conjectures and justify their answers using appropriate mathematical language.

Problem-solving

Pupils apply their mathematical knowledge to a wide range of problems, including unfamiliar situations. They learn to break problems down, select appropriate strategies and persevere when a solution is not immediately obvious. These three areas are interdependent. Secure knowledge supports fluency; fluency supports reasoning; and all three enable pupils to become successful problem solvers.

Supporting Every Child to Succeed

At Abbott, we have high expectations for all pupils. We recognise that children learn mathematics at different rates and that some concepts may require additional explanation, practice or support. Teachers continually check pupils' understanding through questioning, discussion, observation and the work that pupils produce. This enables teachers to identify misconceptions and adapt teaching so that pupils can secure important knowledge before moving on. Where additional support is needed, pupils receive further opportunities to practise and consolidate their learning. Where pupils are ready to deepen their understanding, they are challenged to reason, make connections and apply their knowledge in increasingly sophisticated ways. Our aim is for every pupil to develop secure mathematical knowledge and the confidence to use it successfully.

Developing Confident Mathematicians

We want children to leave Abbott with more than a collection of mathematical procedures. We want them to have secure knowledge, strong reasoning and problem-solving skills, and the confidence to tackle unfamiliar mathematical challenges. We encourage children to learn from mistakes, persevere when mathematics is challenging and explain their thinking. Ultimately, we want our pupils to understand that mathematics is not about simply finding an answer. It is about thinking, making connections, choosing strategies, explaining ideas and solving problems. Through our carefully sequenced curriculum, supported by Power Maths and delivered through high-quality teaching, we aim to ensure that children know more, remember more and can do more with mathematics as they progress through Abbott and beyond.

Our Curriculum Information

Our mathematics long-term plans, progression maps and year-group curriculum information provide further detail about how mathematical knowledge and skills are carefully sequenced and developed throughout the school. They show how pupils revisit important knowledge, build on previous learning and develop increasingly sophisticated mathematical understanding from the Early Years through to the end of Key Stage 2.