Mathematics
What does Maths look like at Brill?
At Brill Church of England School, we believe that every child can become a confident and successful mathematician.
Mathematics is essential for understanding and engaging with the world around us. But Maths is about far more than getting the right answer. We want our children to notice, question, explore, make connections, explain their thinking and persevere when something is challenging.
Our approach is based upon the principles of teaching for mastery and is supported by White Rose Maths. In addition, Mastering Number strengthens children’s early number sense and fluency, providing secure foundations upon which future mathematical learning can be built.
Throughout their Brill journey, children develop:
Fluency – knowing, recalling and using mathematics efficiently
Reasoning – explaining, connecting and justifying mathematical thinking
Problem Solving – applying knowledge to increasingly complex and unfamiliar situations
A strong understanding of the fundamentals of mathematics underpins all three.
INTENT
Our Maths curriculum is ambitious for every child.
We believe that secure mathematical foundations matter. Children need a deep understanding of number, alongside increasingly automatic recall of important facts, if they are to confidently access more complex mathematics as they progress through school.
Developing these fundamentals is therefore a particular priority at Brill.
We want children to develop strong number sense, understand the relationships between numbers and operations and become increasingly fluent in recalling and applying key number facts.
Our curriculum aims to ensure that children:
- develop a deep and secure understanding of number;
- become fluent in the fundamentals of mathematics;
- develop conceptual understanding alongside efficient calculation methods;
- recall and apply key number facts with increasing accuracy and automaticity;
- develop secure multiplication and division knowledge;
- reason mathematically using precise mathematical vocabulary;
- identify patterns, relationships and connections;
- explain and justify their thinking;
- solve problems by applying their knowledge in different contexts; and
- develop the resilience to persevere when an answer is not immediately obvious.
Most importantly, we want children to develop a positive mathematical identity.
We want Brill children to believe that mathematics is something they can do. Mistakes are welcomed as part of learning, different strategies are explored and children are encouraged to have a go even when they are unsure.
Our children are encouraged to be bold in exploring ideas, brave when facing challenge and Brill-iant in explaining their mathematical thinking.
IMPLEMENTATION
Teaching for Mastery – White Rose Maths
Maths is taught daily through a mastery approach, supported by White Rose Maths.
Learning is carefully sequenced so that new mathematical knowledge builds upon secure prior understanding. Concepts are broken into manageable steps, allowing children to develop understanding before moving on to increasingly complex applications.
Teachers use questioning, modelling, mathematical discussion and carefully selected representations to uncover children’s thinking and identify misconceptions.
Importantly, learning is regularly revisited.
Children retrieve and apply previously taught knowledge so that important mathematical facts, concepts and procedures are not simply learned for a lesson or unit but remembered and available when children need them.
Building Strong Foundations – Mastering Number
In the early stages of children’s mathematical development, we place particular emphasis on developing strong number sense.
Mastering Number complements our wider Maths curriculum by providing regular opportunities for children to develop fluency and flexibility with number.
Children learn to notice relationships, recognise quantities, compose and decompose numbers and develop increasingly efficient ways of calculating.
Rather than relying upon counting or memorised procedures alone, children develop a deeper understanding of how numbers work and how they relate to one another.
These strong foundations are crucial. When children have secure number sense and can recall key facts automatically, they have greater capacity to tackle the more complex reasoning and problem-solving they encounter later in their mathematical journey.
Securing the Fundamentals
Across Brill, we are placing a particularly strong emphasis on ensuring that children have the fundamental mathematical knowledge they need to succeed.
Teachers use assessment and their knowledge of individual pupils to identify gaps in foundational knowledge and address these before they become barriers to future learning.
Children are given regular opportunities to retrieve, revisit and practise essential knowledge, including:
- number bonds;
- place value;
- addition and subtraction facts;
- multiplication and division facts;
- mental calculation strategies;
- mathematical vocabulary; and
- efficient written and mental methods.
This does not mean mathematics becomes repetitive or simply about memorising facts.
Instead, we want children to develop the right balance of automaticity and understanding – knowing important facts quickly while also understanding the mathematical relationships behind them.
Our aim is simple: secure the foundations so that every child is ready for what comes next.
Multiplication and Times Tables – Years 3 and 4
As children move into Key Stage 2, multiplication and division become an important mathematical priority, with a particular focus in Years 3 and 4.
Secure times-table knowledge unlocks a significant amount of later mathematics. It supports children’s understanding of division, fractions, ratio, area and more complex calculation, while reducing the cognitive load involved in solving increasingly challenging problems.
We therefore provide frequent opportunities for children to learn, practise, retrieve and apply multiplication and related division facts.
In Year 3, children build increasingly secure multiplication knowledge and develop an understanding of the patterns and relationships within and between times tables.
In Year 4, this knowledge is strengthened further, with the aim that children can recall multiplication and corresponding division facts accurately, confidently and with increasing automaticity.
Our approach goes beyond simply learning a sequence of answers. Children explore patterns, make connections, use known facts to derive unknown facts and develop strategies that help multiplication facts become secure and meaningful.
By making multiplication knowledge a strong and consistent focus, we aim to give children the fluency they need to confidently access mathematics throughout Key Stage 2 and beyond.
Concrete, Pictorial, Abstract – CPA
A key feature of our mastery approach is the use of Concrete, Pictorial and Abstract (CPA) representations.
Children encounter mathematical concepts in different ways:
Concrete – using practical equipment and manipulatives to explore mathematical ideas.
Pictorial – representing mathematics through images, diagrams and models.
Abstract – using mathematical symbols, notation and calculations.
These are not simply stages that children ‘grow out of’. Appropriate representations are used throughout the school to help children see mathematics, make connections and explain their thinking.
Manipulatives and representations such as counters, tens frames, number lines, part-whole models, arrays and bar models help children develop conceptual understanding alongside increasingly efficient abstract methods.
Fluency
Fluency is a fundamental part of becoming a successful mathematician.
Children are given regular opportunities to practise and retrieve important number facts, mathematical knowledge and calculation strategies.
We want children to develop accuracy, efficiency and flexibility. This means knowing facts automatically where appropriate, but also being able to select an efficient strategy and adapt their thinking.
As children’s automatic recall develops, less working memory is required for basic calculations, enabling them to concentrate on the more complex mathematical thinking involved in reasoning and problem solving.
Reasoning and Mathematical Talk
Children are taught not simply to give an answer, but to explain how they know.
Mathematical talk is an important feature of lessons. Teachers model precise mathematical vocabulary and children are encouraged to articulate their thinking, compare approaches and listen to the reasoning of others.
Children learn to:
- notice patterns and relationships;
- make and test conjectures;
- compare and classify;
- explain their chosen strategy;
- identify and correct errors;
- prove or justify their thinking; and
- use mathematical vocabulary accurately.
By explaining their mathematics, children deepen their own understanding and learn that successful mathematicians think about the relationships between numbers rather than simply carrying out procedures.
Problem Solving
Problem solving enables children to apply their knowledge in situations where the method or answer may not immediately be obvious.
Children encounter problems in a range of contexts and learn how to identify the mathematics required, select an appropriate strategy and break more complex problems into manageable steps.
We encourage children to embrace productive struggle – to think, explore, try a different approach and persevere rather than expecting every answer to come immediately.
In doing so, children develop independence, resilience and confidence.
Challenge and Support
We are ambitious for every mathematician at Brill.
Children work towards the same important mathematical concepts, with teachers carefully adapting teaching, representations, scaffolds and resources so that all pupils can access and understand the learning.
Where children have gaps in fundamental knowledge, these are identified and addressed quickly through additional teaching, practice and opportunities for retrieval.
Children who grasp concepts rapidly are challenged through greater depth – applying their knowledge in increasingly complex situations, making connections, reasoning and proving – rather than simply racing ahead to new curriculum content.
This allows every child to experience both success and appropriate challenge.
Maths Across Brill Horizons
Mathematics does not exist only within the Maths lesson.
Through our wider Brill Horizons curriculum, children have opportunities to apply mathematical knowledge in meaningful contexts.
They may collect and interpret data in science, explore chronology in history, work with scale and coordinates in geography, measure and calculate in design and technology or investigate pattern and proportion through art.
Children are also encouraged to recognise mathematics in everyday life – including money, time, measurement, travel, sport and the many decisions and problems we encounter beyond school.
These connections help children understand that mathematics is not simply something they do at school; it is a powerful way of understanding and navigating the world.
IMPACT
By the end of their Brill journey, we want our children to see themselves as capable, confident and resilient mathematicians.
We want children to leave Brill able to:
- demonstrate a secure understanding of the fundamentals of number;
- recall and apply key number and multiplication facts with fluency and automaticity;
- demonstrate strong conceptual understanding;
- select appropriate and efficient mathematical methods;
- use mathematical vocabulary accurately;
- explain and justify their reasoning;
- recognise patterns and make connections between mathematical ideas;
- apply their knowledge to unfamiliar problems and real-life situations;
- use representations and resources purposefully to support their thinking;
- identify mistakes, learn from them and adapt their approach; and
- approach mathematical challenge with confidence, curiosity and resilience.
Most importantly, we want children to leave Brill believing:
“I can do maths.”
Successful mathematicians are not simply those who calculate quickly. They are those who notice, think, question, connect, explain and persevere.
By securing strong mathematical foundations from the very beginning and building upon them throughout each child’s journey, we aim to ensure that every Brill child has the knowledge, confidence and curiosity they need for their next stage of education and for life beyond our school.
Be Bold. Be Brave. Be Brill-iant.
