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Church Lane, Doncaster, South Yorkshire, DN5 7EZ


Barnburgh Primary School

Learning to shine together





Teaching maths for mastery is a key plank of the Government’s education reforms and is reflected in the 2014 English national curriculum for mathematics. The NCETM, Department for Education and OFSTED have all endorsed this evidence-based approach which is a key part of the work within the Maths Hubs Programme.

Here at Barnburgh Primary school, we have worked in collaboration with the South Yorkshire Maths hub to develop our teaching and learning through a teacher research group. We have also worked with The Yorkshire and Humber Maths hub to establish the same day intervention programme.


Mathematics is a creative and highly inter-connected 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 most forms of employment. A high quality mathematics education 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 2014)


The purpose of mathematics in our school is to develop:

  • a positive attitude towards mathematics and an awareness of the relevance of mathematics in the real world
  • competence and confidence in mathematical knowledge, concepts and skills
  • an ability to solve problems, to reason, to think logically and to work systematically and accurately
  • initiative and an ability to work both independently and in cooperation with others
  • an ability to communicate mathematically.
  • an ability to use and apply mathematics across the curriculum and in real life
  • an understanding of mathematics through a process of enquiry and experiment.


At Barnburgh Primary School we have embarked on our 'journey to mastery in mathematics.'


Teaching for mastery is also characterised by:

On this basis, children are taught all together as a class and are not split into ‘ability’ groupings. Carefully structured teaching, planned in small steps provides both the necessary scaffold for all to achieve, and the necessary detail and rigour of all aspects of the mathematics to facilitate deep thinking. The small steps are connected and concepts built, leading to generalisation of the mathematics, and the ability to apply it to multiple contexts and solve problems. It is expected that those that will achieve well on a particular topic may not necessarily be the same children that achieved well on other topics. An additional short session of 10 to 15 minutes is provided on a daily basis for any pupils who do not fully grasp the lesson content, in order that they 'keep up' with the class. Our experience shows that it is not always the same pupils who require this form of intervention and this boosts the self-belief of previously low attaining pupils.

A key skill of the teacher is to be able to represent the mathematics in ways that provide access and insight for pupils. Concrete materials, contexts, drawings, diagrams, equations all play a role. These are discussed through opportunities for pupil-pupil and pupil- teacher talk, to develop reasoning, flexibility and adaptability in mathematical thinking.

Evidence from cognitive science research suggests that learning key facts to automaticity ‘frees up’ working memory to focus on more complex problem solving rather than reaching cognitive overload trying to calculate simple operations. In terms of procedural fluency and conceptual understanding, one should not be prioritised over the other, but learning is most effective when the two are fully integrated.

  • Teaching children precise mathematical language and insisting upon its use, to support children's ability to think mathematically.

Having the language and using it, empowers children’s ability to think about the concept




At Barnburgh Primary School when teaching maths for mastery, the whole class moves through topics at broadly the same pace. Each topic is studied in depth and the teacher does not move to the next stage until all children demonstrate that they have a secure understanding of mathematical concepts.



Students are given time to think deeply about the maths and really understand concepts at a relational level rather than as a set of rules or procedures. This slower pace leads to greater progress because it ensures that students are secure in their understanding and teachers don’t need to revisit topics once they’ve been covered in depth.



At Barnburgh Primary school we believe that every child deserves the chance to shine. We believe that teaching maths for mastery offers all pupils access to the full maths curriculum. This inclusive approach, and its emphasis on promoting multiple methods of solving a problem, builds self-confidence, enjoyment and resilience in pupils. This approach embodies the school's 'Learning Pit' approach across all areas of the children's learning.



Though the whole class goes through the same content at the same pace, there is still plenty of opportunity for differentiation. Unlike the old model, where advanced learners are accelerated through new content, those pupils who grasp concepts quickly are challenged with rich and sophisticated problems within the topic. Children who have grasped the fluency elements (pitched at the age related expectations) are then given the opportunity to challenge themselves by completing reasoning and problem solving challenges. Those children who are not sufficiently fluent are provided additional support to consolidate their understanding before moving on. This element is in the form of same day intervention, both in class during the lesson or as a follow up intervention.



Each week children, across KS1 and KS2, will have five maths sessions. 

Four sessions will be core maths learning, while the fifth will be a skills session.

During each core maths session children will experience:

  • Whole class input (ping-pong style teaching – I do, you do – high quality modelling)
  • Differentiation (through support, use of manipulatives and questioning)
  • Diagnostic task - AFL(questions at ARE)
  • Progress pit-stop (marking time to assess and group pupils) This is completed over morning break time.
  • Same day intervention (immediate intervention or challenging practice for pupils) or progression onto varied fluency
  • Challenge in the form of reasoning and problem solving.
  • Live marking and instant feedback and challenge.


During skills sessions children will:

  • Practise their Key Instant Recall Facts (Kirfs) challenge 
  • Arithmetic style questions or Multiplication questions
  • Extension challenge or Same Day Intervention follow up.


Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. Often referred to as the concrete, representational, abstract framework, CPA was developed by American psychologist Jerome Bruner. It is an essential technique within the Singapore method of teaching maths for mastery.


  • An essential technique of maths mastery that builds on a child’s existing understanding.
  • A highly effective framework for progressing pupils to abstract concepts like fractions.
  • Involves concrete materials and pictorial/representational diagrams.
  • Based on research by psychologist Jerome Bruner.
  • Along with bar modelling and number bonds, it is an essential maths mastery strategy.


Concrete is the “doing” stage. During this stage, students use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. With the CPA framework, every abstract concept is first introduced using physical, interactive concrete materials.



Pictorial is the “seeing” stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures, diagrams or models that represent the objects from the problem.

Building or drawing a model makes it easier for children to grasp difficult abstract concepts (for example, fractions). Simply put, it helps students visualise abstract problems and make them more accessible.



Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Students will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages of the problem. The abstract stage involves the teacher introducing abstract concepts (for example, mathematical symbols). Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols (for example, +, –, x, /) to indicate addition, multiplication or division.



Progression Document for Mathematics. Here at Barnburgh we utilise the White Rose Maths Scheme of work.

Maths Long Term Plans

Key Instant Recall Facts (KIRFs)

KIRFs are designed to support the development of the mental skills that underpin much of the mathematics work in school. They are particularly useful when calculating, be it adding, subtracting, multiplying or dividing. 

 Each year group is allocated up to six facts to focus on throughout the year, in line with age related expectations.

KIRFs will be incorporated into the weekly skills session. 

Children should be encouraged to practise these at home possibly in smaller daily bursts so that children grow in confidence to recall their facts instantly.

Each half term, children will be assessed on their year group’s KIRF. 

Key Instant Recall Facts - Click on the file to download

 kirf y1.pptmDownload
 kirf y2.pptmDownload
 kirf y3.pptmDownload
 kirf y4.pptmDownload
 kirf y5.pptmDownload
 y6 kirfs.pptmDownload
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