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At Bilton, as per the National Curriculum, we aim to ensure that all pupils:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice 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 nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

We do this – develop fluency, reasoning and problem solving - by adopting a mastery approach.

Teaching for mastery in maths

Putting number first: a significant amount of time is spent reinforcing number in order to build competency and ensure children can confidently access the rest of the curriculum.

Pupils work towards endpoints for their key stage – objectives that we would expect most pupils to be able to achieve by certain points in their maths education.

Rather than accelerate through lots of different curriculum endpoints, those who grasp the mathematical concepts more quickly will be challenged through rich and more sophisticated problems. For example, once a Year 2 child has reached their endpoint of being able to ‘recognise the place value of each digit in a 2-digit number (tens, ones)’, rather than moving quickly on to objectives from subsequent years such as ‘recognise the place value of each digit in a 4-digit number (thousands, hundreds, tens, ones)’ they will ‘master’ the different ways in which they can apply their knowledge of recognising the place value of 2-digit numbers through reasoning and problem solving. This means that pupils acquire a depth of knowledge in each maths topic. If pupils take longer than expected to grasp mathematical concepts, they will be given additional support and ‘scaffolding’ (resources/strategies to help them) and further opportunities to develop their fluency through deliberate practice (in sessions additional to their daily maths lessons).

To further deepen this understanding, the curriculum is designed in such a way so that there are regular opportunities to revisit previously learned skills and use their connected knowledge (knowledge that they already have) to support their understanding of new concepts. For example, a Year 3 pupil being introduced to calculating the perimeter of shapes in Spring Term, will be taught that perimeter is the total distance around the outside of a 2D shape. They could use this new knowledge alongside their connected knowledge of squares having four sides all of the same length (introduced in Autumn term of Year 2) and of their multiples of 4 (from Autumn term of Year 3) to solve the problem, “The length of one side of a square is 3, what is its perimeter?”.

If you have any questions regarding Maths at Bilton Grange, please do not hesitate to contact your child’s class teacher or our Maths Lead, Mr Guyan.

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Concrete, Pictorial, Abstract (CPA)

Research shows that all children, when introduced to a new concept, should have the opportunity to build competency by following the CPA approach. This features throughout our curriculum.

Concrete: Children should have the opportunity to work with physical objects/concrete resources, in order to bring the maths to life and to build understanding of what they are doing.

 concrete 1

Pictorial: Alongside concrete resources, children should work with pictorial representations, making links to the concrete. Visualising a problem in this way can help children to reason and to solve problems.

concrete 2

Abstract: With the support of both the concrete and pictorial representations, children can develop their understanding of abstract methods.

concrete 3

White Rose Maths

White-Rose-logoOur teaching is based on the recommended National Curriculum and is then personalised to meet the needs of our learners.

To support consistency of our mastery approach, we follow the White Rose Maths schemes of work from Early Years, through to Year 6. This has helped to sequence the objectives for each individual year group and to ensure pace and progression within skills throughout school. However, the learning suggested by White Rose Maths can – and should – be adapted if the teacher sees fit. It may be, for example, that the worksheet provided by White Rose Maths is seen to move on to quickly from fluency to reasoning, or have too many different types of problem for pupils to cope with in regard to their working memories. In such cases, teachers will use different resources (or make their own) in order to create a lesson that they feel most appropriate for their pupils.  

To ensure consistency, we follow adapted White Rose Maths calculation policies for Addition and Subtraction and Multiplication and Division

Calculation Policy Addition and subtraction

Calculation Policy Multiplication and division

Assessment in Maths

Formative assessment – as outlined in more detail in our assessment policy – is ongoing and forms the basis for our teaching and learning in maths.

In addition to the statutory Early Learning Goals, Multiplication Tables Check (MTC), Standard Assessment Tests (SATs) in Years 2 and 6, further scheme-specific, summative assessments are conducted prior to a scheme of learning being delivered and after its completion. This allows teachers to accurately evaluate where pupils are in their learning, pupil progress in maths, and to address any misconceptions that arise.   

Ready to Progress

Should a pupil make less than expected progress or have regular misconceptions that need addressed, they may be invited to additional, regular, small-group Ready to Progress (RTP) interventions to do so.

The RTP criteria is government guidance that identifies the most important conceptual knowledge and understanding that pupils need as they progress from Year 1 to Year 6. It is split into the strands:

  • Number and place value (NPV)
  • Number facts (NF)
  • Addition and subtraction (AS)
  • Multiplication and division (MD)
  • Fractions (F)
  • Geometry (G)

To give an example, if, after the Place Value scheme of learning, a Year 5 pupil was showing significant gaps in their understanding of number, they may work in a group (with up to three other pupils) with an adult through the RTP Number and Place Value criteria relevant to their ability. In these short sessions, they will work through resources developed by maths experts at NCTEM and will receive significant immediate feedback and support from an adult in attempt to address misconceptions, plug gaps in knowledge and, ultimately, improve their mathematical knowledge and understanding.

The White Rose Maths curriculum that we follow, has been mapped against both the National Curriculum and the Ready to Progress documents here: White Rose Maths progression document mapped to National Curriculum and Ready to Progress Criteria.  

Maths skills and number facts

In order to recall maths knowledge rapidly and accurately, regular deliberate practise of number facts in necessary.

Each Key Stage in school provides additional time outside of their maths schemes of learning, for such practice. For example, in a five-to-ten-minute slot before the maths lesson starts, Year 5 pupils may have a short input on mental addition in which teachers can suggest and model strategies, before spending time practising a number of such questions. In Key Stage 1, children follow the ‘Fluency Bee’ program.

Such skills and deliberate practice will also be undertaken regularly as part of homework: one aspect of this being a commitment to spending a certain amount of time per week on ‘TimesTable Rockstars’ – an interactive, competitive app that allows pupils to develop their multiplication-facts recall speed; and another being consolidation of maths skills that have been taught in maths lessons – for example, a set of 20 calculations using the formal written method for subtraction may be set the week after subtraction has been covered in maths lessons. 

Our progression of skills document - for deliberate practice in maths - outlines which skills/number facts we would like our pupils to be fluent in by the end of each year.

Number Facts Progression

More maths: outside of the classroom

Maths naturally has cross-curricular links and will therefore be seen and used in other subjects that we cover in school; this could be looking at coordinates while map-reading in Geography, differences on a timeline in History or using bar charts to analyse results in Science.

Maths reasoning problems that link to previous learning are regularly used as start of the day activities when pupils come into the classroom on a morning. These ‘Flashback 4’ questions include four questions from different areas of maths that pupils may have covered in previous weeks, terms or years. An example:


This additional, low-stakes, re-visit of fundamental concepts in maths allows pupils to remember more over time.

Maths is celebrated and championed throughout school: maths certificates are given out every week in our celebration assemblies; playing maths games – concrete and interactive – are encouraged in social times; and maths competitions, local and national, are entered each year.

Evaluation and areas for improvement

To ensure progress of Maths at Bilton, we undertake monitoring each term to evaluate: what is going well and needs to continue, and also where further improvements can be made.

This is done in a variety of ways, including: lesson observations; staff discussion/questionnaires; analysis of planning and resources; analysis of books / work; and conversations with pupils.

Successes last year:

  • New whole-school scheme successfully adopted improving consistency and coverage
  • Teachers report greater confidence in teaching Maths – Key Stage 1 teachers feel that pupils coming up from EYFS into Year 1 have a stronger start due to their exposure to White Rose Maths
  • Investment in quality Maths-related books in EYFS has led to greater enrichment and enjoyment of Maths
  • Percentage of pupils reaching the expected level in Key Stage 1 Maths significantly above national average
  • Average score on Year 4 MTC above national average
  • Significant increase in percentage of pupils reaching the expected level in Key Stage 2 compared to last year
  • Performance in Place Value above national average in Key Stage 2 Maths SAT
  • Pupils discuss their learning within Maths with greater assurance – they are clearer about what they are learning and how their teachers help them to remember

Areas for improvement:

  • Pupils’ mathematical fluency to improve. We aim to do this by having greater amount of time dedicated to the explicit teaching and deliberate practice of number-fact fluency and having a whole-school progression document outlining when we would expect pupils to be fluent in different number-fact objectives
  • Having a more consistent, whole-school approach to further support pupils with gaps in mathematical knowledge (including those in the bottom 20%). We aim to do this through a more consistent use of Ready to Progress (outlined above) as an intervention.
  • Percentage of pupils scoring full marks on the MTC. We aim to do this by increasing the opportunities that pupils have to practise their time tables in school and through more explicit teaching of strategies and methods.
  • Pupil ability to recognise Maths endpoints e.g. pupils to be aware that, while in a Year 4 lesson they may be learning to round numbers up to 100 to the nearest 10, that this is a small-step towards the end-of-year target of being able to ‘Round any number to the nearest 10, 100 and 1000’. Sharing endpoints such as this helps pupils to understand why they are learning what they are and how this fits into the ‘bigger picture’ of their mathematical learning.