Why teach mathematics?

“Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and all forms of employment. A high-quality education in maths therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.”

National Curriculum in England, 2014

Fluency, Reasoning and Problem Solving

We follow the National Curriculum aims for mathematics, which are to ensure that all pupils:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practise with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately;
  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;
  • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.


Fluency development is developing pupil’s understanding of mathematical concepts and skills, how they link and how they ‘work’, in order for pupils to be competent and confident in using a variety of mathematical strategies and approaches independently. It is developed through regular discussion about strategies and methods, a recognition and understanding that there is not one right way of solving a calculation or problem, and regular arithmetic practice (Maths of the Day, arithmetic sessions in Key Stage Two, Times Table practice particularly in lower Key Stage Two).


Reasoning development is developing pupil's language and ability to discuss and explain their strategies, solutions and approaches to mathematical activities. It is developed through regular opportunities to reason verbally and in writing, the use and modelling of high quality mathematical language, the use of diagrams, manipulatives and calculations to support and structure pupil’s reasoning, and the use of a variety of questions, such as Why? Why not? What if? How?

Pupils across the school use APE as a strategy to structure their verbal and written reasoning. This strategy is adapted to suit the age of the pupils, and the detail and complexity of the reasoning increases through the year groups.

A= Answer. What is the answer to the question, problem or discussion prompt?

P= Prove. How do you know that the answer is correct? Explain with pictures, diagrams, calculations, manipulatives, sentences or in another way.

E= Explain. Explain their approach, strategies and thinking.

Problem Solving:

Problem Solving within mathematics refers to activities and experiences where maths is used and applied, where there is more than a simple, straightforward calculation, and where mathematical thinking is required. A variety of skills need to be developed in order for pupils to be successful in solving problems, such as:

  • selecting appropriate resources, posing and answering questions,
  • representing problems using symbols, words, diagrams or pictures, developing and choosing ways to record,
  • predicting,
  • making connections,
  • concluding and explaining,
  • identifying patterns,
  • forming generalisations in words, pictures or with resources,
  • justifying answers, solutions, methods and conclusions and supporting with examples,
  • organising work, working systematically and checking results.

Foundation Stage

All pupils are given ample opportunity to develop their understanding of mathematics through varied activities that allow pupils to use, enjoy, explore, practice and talk confidently about mathematics. Mathematics teaching and learning in Foundation Stage involves providing pupils with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and describing shape, spaces and measures.

A Guide to Maths Mastery in Reception

Key Stage One

The principal focus of mathematics teaching in Key Stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations, including with practical resources (e.g. concrete objects and measuring tools). At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. By the end of Year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency. Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at Key Stage 1.

National Curriculum in England, 2014

The Year 1 Maths Learner

The Year 2 Maths Learner

Lower Key Stage Two

The principal focus of mathematics teaching in lower Key Stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also 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. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number. By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.

National Curriculum in England, 2014

The Year 3 Maths Learner

The Year 4 Maths Learner

Upper Key Stage Two

The principal focus of mathematics teaching in upper Key Stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. At this stage, pupils should 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 should consolidate and extend knowledge developed in number. Teaching should 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 should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils should read, spell and pronounce mathematical vocabulary correctly.

National Curriculum in England, 2014

The Year 5 Maths Learner

The Year 6 Maths Learner

Calculation Strategies

Pupils are encouraged to develop and use a variety of formal and informal methods for recording their mathematical learning, appropriate to their age. Pupils are encouraged to compare and discuss different methods, and are supported in choosing an appropriate and effective strategy for the activity. Mental mathematics and arithmetic are incorporated throughout all lessons and mental calculation strategies are discussed and developed continuously. A secure foundation in mental calculation, mental strategies and recall of number facts is established, before written strategies and methods are introduced.

In order for pupils to understand and reason why concepts, approaches and strategies are true and effective, pupil's conceptual understanding is developed alongside their understanding of how strategies and concepts work. Pupils are taught new strategies using CPA approach (concrete, pictorial, abstract). This means that pupils will first use a strategy or method with concrete resources and manipulatives (such as dienes, counters or cubes), then pictorially (such as diagrams, bar model or pictures of manipulatives), and finally in their head or on paper.

Our calculation policy is currently being updated and a parent's guide will be available here soon.

Mathematics Glossary of Key Terms

Resources and Manipulatives

A wide range of resources and manipulatives are used throughout the school to develop understanding. All pupils are encouraged to use these to support their learning, and each class has similar resources to ensure progression, consistency and continuity.

Multilink Cubes

Place Value Counters


Dienes or Base Ten

Bead Strings

Tens frame

Hundred Square

Multiplication Square

Number Line

Cuisenaire Rods

Mathematics at Home

Each child in years 2-6 has an individual login to Times Tables Rockstars, a website designed to support the development of multiplication facts.

Times Tables Rockstars Login

Other useful websites may be:

MathsFrame Games

Topmarks Maths Games

Math Playground Maths Games

Family Maths Toolkit

Oxford Owl Maths at Home

Mathematics Shed

Times Tables Games

Maths Games

Useful documents for ways in which you can help your child at home:

Helping your Child with Maths

Dice and Card Games to Practice Maths Facts

Equal Opportunities

Positive attitudes towards mathematics are encouraged so that all pupils, regardless of race, gender, cultural background, ability, SEN or disability, including those for whom English is an additional language, develop an enjoyment and confidence within mathematics. All pupils receive high quality inclusive teaching, and high expectations are set for all.

A mastery approach is used within mathematics teaching and learning at St. Michael’s. A mindset that all are able to achieve is adopted by all adults and continually developed within pupils through the use of mixed ability flexible groupings and collaboration; the careful planning of tasks and activities; opportunities for pupils to reflect on their learning and understanding and choose their task, approach or resource; and the use of manipulatives for all pupils and abilities.

“The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.”

National Curriculum in England, 2014

Class teachers provide appropriately differentiated activities to ensure all pupils are challenged at an appropriate level for their current learning. Teachers use a variety of differentiation strategies, including different content of activities, different approaches to completing activities, and different use of resources. Pupils are encouraged to be reflective about their own understanding, and are given opportunities to choose the level of activity they complete, through the use of chilli challenges.