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Mathematics
Mathematics at William Shrewsbury Primary School
At William Shrewsbury, we feel Mathematics is a key life skill. It involves confidence and competence with numbers and measures. We aim to give pupils an understanding of the number system and an ability to solve problems in a variety of contexts. Mathematics also demands a practical understanding of the ways in which information is gathered by counting and measuring, and is presented in graphs, diagrams, charts and tables.
As a school, we aim to develop positive learners who take pleasure in their Mathematics. Our learning consists of much more than the knowledge of a set of useful skills. It is a source of enjoyment, offering pupils intellectual stimulation and a sense of achievement.
Mathematics makes a considerable contribution to the whole curriculum as work in many areas and topics involve mathematical activities.
The school policy is matched to the requirements of The National Curriculum (2014) and aims to develop fluency, reasoning and problem solving.
You will find videos for the calculation areas of Addition, Subtraction, Multiplication and Division in the information below. There are also videos on other areas of Mathematics which you may find of use, as well as links to a range of different websites and resources.
How Mathematics is taught at William Shrewsbury Primary School
The teaching of Mathematics at our school is built upon a Teaching for Mastery approach, which is expertly supported by the structured, progressive materials of the CanDo Mathematics scheme. This synergy ensures that all pupils move through the curriculum together, with a strong emphasis on achieving deep and secure understanding rather than accelerating through content.
What is ‘Teaching for Mastery'?
When taught to master Mathematics, children develop their conceptual and procedural fluency without having to resort to rote learning. As a result, they are able to solve non-routine problems in unfamiliar contexts without relying on memorised procedures. Not only do they understand how to solve problems, but they can use their conceptual understanding to explain why their solution works. The 'Teaching for Mastery' approach firmly believes that all pupils can achieve success in Maths. We believe that all of the children at our school 'CanDo' Maths! To support our curriculum and mastery approach, we work alongside the NCETM's Maths Hubs as well, as our trust schools, in order to ensure that all members of staff have the most up to date subject knowledge.
What is 'CanDo' Maths?
The CanDo Maths scheme is a comprehensive, progressive teaching resource to support schools in achieving maths improvement goals, particularly within a 'Teaching for Mastery' framework. The scheme is designed to deepen and secure mathematical understanding for pupils from Reception to Year 6 by providing a clear, fully planned curriculum that builds confidence and fluency. The structure of a Maths lesson using the CanDo Maths scheme follows a defined pathway, typically breaking down learning into small, carefully sequenced steps. This ensures that pupils master the foundational concepts before moving on, employing a range of approaches including the Concrete-Pictorial-Abstract (CPA) model. The lessons are structured to include time for guided practice, allowing teachers to address misconceptions immediately, and independent practice where pupils apply their knowledge, often through carefully varied fluency questions and structured problem-solving tasks, ultimately aiming for long-term retention and the ability to reason mathematically.
Concrete, Pictorial and Abstract approach to learning
At William Shrewsbury, we use concrete apparatus (things pupils can touch, hold and manipulate) and pictorial representations (things they can see) to help children to visualise and internalise mathematical concepts. This allows them to access and understand the mathematical structure of the concepts they are learning about. Through the consistent use of these apparatus and representations, our pupils gain confidence as independent learners to use resources and solve problems until they are able to record using abstract written methods.
Problem Solving
At William Shrewsbury, children have the opportunity to apply their mathematical knowledge to problem solving tasks on a regular basis. At the end of each CanDo Maths unit, pupils work with others to apply their learning to a range of problems from both the CanDo website or from NRICH. Mathematical problem-solving lessons are vital in primary schools because they are the engine for developing metacognition and a rich network of mathematical knowledge, which the Education Endowment Foundation (EEF) strongly recommends. According to the EEF, explicitly teaching pupils strategies for solving problems—such as modelling a 'think aloud' approach—helps children gain insight into their own thinking, learn from errors, and effectively monitor their progress towards a goal. This is crucial for developing independence and self-regulation as pupils move from needing teacher-led guidance to confidently tackling genuine problem-solving tasks where the method is not immediately obvious. Moreover, these lessons challenge pupils to select and apply the most efficient strategies, reinforcing the connections between different mathematical concepts and procedures, ultimately building a deeper, more robust conceptual understanding.
Key Topics taught
EYFS
The Early Years Foundation Stage (EYFS) Mathematics curriculum focuses on establishing the essential bedrock of mathematical understanding, primarily centered around Number and Numerical Patterns. The goal is to build genuine mastery by ensuring children develop a strong sense of 'number-ness' through hands-on, playful, and practical activities. The curriculum emphasises the crucial skill of subitising (recognising a small quantity without counting) and building a secure knowledge of composition of number up to 10. Lessons are structured to utilise the Concrete-Pictorial-Abstract (CPA) approach from the very start, using physical objects and manipulatives to support early concepts and link them directly to mathematical language. This systematic approach ensures children develop fluency in counting, compare quantities accurately, and recognise patterns, laying a secure foundation that progresses smoothly into the structured planning used in Year 1.
Key Stage 1 - Years 1 and 2
The main focus in these early stages of learning is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This involves working with numerals, words and the four operations, including using practical resources. At this stage, pupils will develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching involves using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. In these early stages of a child's Mathematical education, we follow the 'Mastering Number' programme from the NCETM. This project aims to secure firm foundations in the development of good number sense for all pupils from Reception through to Year 2. The aim over time is that pupils will leave Key Stage 1 with fluency in calculation and a confidence and flexibility with number which will provide the firm foundations needed for later work in Mathematics.
Lower Key Stage 2 - Years 3 and 4
The main focus is to ensure that pupils become increasingly fluent with whole numbers and the 4 operations, including number facts and the concept of place value. This will ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils will develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching will ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. Children will use measuring instruments with accuracy and make connections between measure and number. By the end of Year 4, pupils will have memorised their multiplication tables up to and including 12 x 12. In order to support this, we utilise the TTrockstars website and create regular competitions to keep children motivated. We also teach the children how to build, recall and apply their multiplication facts on a regular basis.
Upper Key Stage 2 - Years 5 and 6
The main focus is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This will help develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. At this stage, pupils will develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures will consolidate and extend knowledge developed in number. Teaching will also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them. By the end of year 6, pupils will be fluent in written methods for all 4 operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils will read, spell and pronounce mathematical vocabulary correctly.
Substantive and Disciplinary Knowledge
At William Shrewsbury, in Maths we focus on teaching children Substantive Knowledge, which is the "what" of the subject—the essential building blocks like times tables, number bonds, and the steps for column addition. Once children have these "tools" in their kit, we teach them Disciplinary Knowledge, which is the "how." This is where children learn to think like mathematicians by spotting patterns, explaining their reasoning, and applying what they know to solve tricky real-world problems. By balancing both, we ensure children aren't just memorizing rules, but truly understanding how to use them with confidence and creativity. Below is a document which shows how both substantive and disciplinary knowledge progresses in different areas of Maths from Early Years all the way through into Year 6.
Substantive and disciplinary knowledge at WSPS
Road maps
To show when each key topic is taught, year groups 1 to 6 have their own individual road maps which plot out each key focus across the year. These are then broken down further into individual lessons.
Progression documents
To show how each key concept develops between year groups, the following documents illustrate how each progresses from Year 1 to Year 6.
Maths and Oracy
As part of our Maths curriculum, the use of specific vocabulary and mathematical talk is planned for at every stage of learning. Children work in talk partners to discuss ideas and use given vocabulary, ready to share with the class. Stem sentences are used for the children to build model answers upon and to support their mathematical understanding.
- “There are ___ equal groups of ___.”
- “The whole is ____. It has been divided into ___ equal parts.”
Children are also able to use generalisation statements to support their explanation as well.
- "even numbers are divisible by two...therefore..."
- "If a number ends in a digit less than 5, it rounds down to the nearest 10; if it ends in 5 or more, it rounds up."
Year Group Targets
Knowledge Organisers
Below are our knowledge organisers which include the key learning goals and strategies for each half-term and for each year group.
Useful websites
The following links will help you to support your child's learning at home.
Key Stage 1
Key Stage 2
Key Stage 1 and 2
Maths Subject Knowledge Practice Questions
Mathematics Calculation Videos
Addition:
Subtraction:
Multiplication:
Division:
Year 1 Division