At St. Paul's Primary School, Royton, we believe that every child is uniquely created by God with the ability to learn, grow and flourish. Our mathematics curriculum reflects our vision and values by ensuring that all pupils experience success, develop confidence and recognise the importance of mathematics in God's world and in their everyday lives. Rooted in our school values—Together we Grow, Love to Learn, Shine and Make a Difference—we are committed to providing an inclusive, engaging and ambitious curriculum where mathematics is accessible to all learners, regardless of their starting point.
Through adaptive sequenced teaching, pupils develop fluency, reasoning and problem-solving skills within meaningful, real-life contexts that demonstrate the relevance of mathematics beyond the classroom. By making connections between mathematics and everyday experiences, children are equipped with the knowledge, skills and confidence they need for the future. We encourage pupils to Love to Learn by embracing challenge, asking questions and developing resilience as mathematicians.
Collaboration is at the heart of our mathematics curriculum because Together we Grow. Through mathematical talk, partner work and shared investigations, children learn to explain their thinking, value different approaches and work respectfully with others. These experiences foster confidence, perseverance and compassion, enabling every child to Shine as an individual while contributing positively to the learning of others.
As a church school, we recognise that wisdom and understanding are gifts from God. "For the Lord gives wisdom; from his mouth come knowledge and understanding." (Proverbs 2:6). We inspire children to approach mathematics with curiosity, determination and confidence, trusting that effort and perseverance lead to growth. We also celebrate the order and beauty of God's creation, remembering that "But everything should be done in a fitting and orderly way." (1 Corinthians 14:40). Mathematics helps children recognise patterns, think logically and appreciate this order.
By developing confident, resilient and compassionate mathematicians, our curriculum empowers pupils to Make a Difference within our school, local community and the wider world, using their mathematical understanding to solve problems, make informed decisions and fulfil their God-given potential.
Mathematics Curriculum Intent
- To provide every child with a high-quality, ambitious mathematics curriculum that develops secure mathematical knowledge, skills, and understanding.
- To nurture confident mathematicians who approach challenges with resilience, curiosity, and a positive attitude towards learning.
- To ensure all children achieve fluency in number, calculation, and mathematical concepts, providing a strong foundation for future learning and everyday life.
- To develop children's reasoning, problem-solving, and critical thinking skills, enabling them to apply mathematics confidently in a range of real-life contexts.
- To promote a growth mindset, encouraging children to learn from mistakes, persevere through challenge, and celebrate progress.
- To foster human values such as cooperation, respect, honesty, responsibility, and perseverance through collaborative learning, mathematical discussion, and shared problem-solving.
- To provide an inclusive learning environment where every child, regardless of starting point, ability, or background, is supported and challenged to achieve their full potential.
- To adapt teaching, resources, and learning experiences to meet the diverse needs of all learners, ensuring appropriate scaffolding, challenge, and accessibility for children with additional needs.
- To encourage children to communicate their mathematical thinking clearly, using accurate mathematical vocabulary while listening respectfully to the ideas and strategies of others.
- To inspire children to recognise the value and beauty of mathematics in the wider world, equipping them with the confidence, independence, and life skills needed to become successful learners and responsible citizens.
Our curriculum is based around the following knowledge:
Substantive and disciplinary knowledge within mathematics.
Relationship between substantive and disciplinary knowledge
- Substantive knowledge = What pupils know
- Number bonds
- Times tables
- Place value
- Fractions
- Geometric properties
- Mathematical vocabulary
- Disciplinary knowledge = How pupils use and think with that knowledge
- Reason mathematically
- Solve problems
- Make connections
- Justify solutions
- Spot patterns
- Represent ideas in different ways
- Communicate mathematical thinking
Together, substantive and disciplinary knowledge enable pupils not only to become fluent in mathematics but also to think, reason and solve problems with confidence.
The pupils are taught these disciplinary concepts within all domains of mathematics across all year groups: Using and applying, investigating, reasoning, problem solving, analysing and justifying and proving. We use a range of methods to embed our teaching and learning:
Concrete: The unit of work will begin with introducing the skills through the use of real objects or mathematical equipment. This enables the pupils to use a kinaesthetic ‘hands on’ approach. In division in KS1, for example, this could be done by separating apples into red ones and green ones or by sharing 12 biscuits amongst 6 children. In division in KS2, this could be done by using a place value chart and counters to create the number and then moving them on the place value chart to divide by 10, 100 or 1000.
Pictorial: When the children have understood the use of concrete resources, they then move on to representations such as diagrams or pictures. This may include annotating, drawing lines or circling objects. In KS2, this may be where a pupil is asked to draw his or her own charts or diagrams etc.
Abstract: Once the pupil is secure with the use of concrete and pictorial concepts, they should then be able to demonstrate their skills through the use of mathematical symbols, demonstrating their knowledge and understanding of the skill.
Implementation
White Rose is a supporting resource for teaching maths. It supports children in developing the five big ideas of mastery: coherence, connecting new ideas to known concepts; representation and structure, noticing patterns and making connections; mathematical thinking, working on, thinking and reasoning with a taught idea; fluency, quick and efficient recall of facts and procedures; variation, giving examples that display an idea as well as those that don’t for children to notice, and varying practice questions so that repetition is avoided.
Our teachers explicitly model skills to children through their use of teaching and learning time. They model vocabulary to enrich discussions of mathematical concepts and empower children to reason and problem solve. Children need to know how to explain their methods and understanding; through open questioning from adults, children develop their questioning and reasoning skills.
We follow a concrete, pictorial and abstract (CPA) approach, which enables children to visualise the concept by using concrete apparatus first. These manipulatives are used and available across the school so that children can experience these throughout their learning journey.
At St. Paul’s we want the children to describe themselves as Mathematicians by making comments such as:
- I demonstrate quick and efficient recall of facts and procedures.
- I am a Mathematical thinker, who can reason and solve problems.
- I feel confident using Mathematical vocabulary.
- I can make connections between my learning and the world around me.
- I can describe, explain and represent mathematical concepts in a variety of ways.
Impact of the Mathematics Curriculum
Children leave St. Paul’s as mathematical thinkers who can make connections in their learning to the world around them and are ready for the next stage in their education. The impact of our mathematics curriculum is measured through a range of assessment and monitoring strategies, ensuring all pupils make strong progress and are well prepared for secondary education.
- Formative and summative assessments identify progress and inform future teaching.
- High-quality questioning, retrieval practice and pupil discussions address misconceptions and deepen understanding.
- Leaders evaluate the curriculum through book scrutinies, lesson visits, pupil voice and assessment analysis to drive continual improvement.
- Pupils develop secure substantive knowledge alongside disciplinary skills, including reasoning, problem solving and mathematical communication.
- By the end of Year 6, pupils demonstrate fluency, resilience and confidence in applying mathematics across a range of contexts.
- Pupils use precise mathematical vocabulary, justify their reasoning and select efficient strategies independently.
- Children leave our school equipped with the knowledge, skills and confidence to succeed in Key Stage 3 mathematics and beyond.
