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Our Approach to Maths

Intent
 
Our whole curriculum is shaped by our school vision which aims to enable all children, regardless of background, ability, additional needs, to flourish to become the very best version of themselves they can possibly be.

Our Maths teaching is underpinned by the belief that all children need a deep understanding of the mathematics that they are learning. We ensure that all pupils have access to mathematical concepts and the rich connections between them.

We teach the National Curriculum, supported by a clear skills and knowledge progression. This ensures that skills and knowledge are built on year by year and sequenced appropriately to maximise learning for all children. This allows for the development of depth and sufficient practice to embed learning with an ambitious Maths curriculum for all.

 

Devoting time to key concepts enables us to:

  • Represent concepts in lots of different ways (multiple representations).

  • Teach the processes and then allow the children to apply their knowledge, increasingly rapidly and accurately.

  • Commit key facts to children’s long-term memory.

 

Therefore, at an age-appropriate level, we expect the vast majority of our children to be able to:

  • Use mathematical concepts, facts and procedures appropriately, flexibly and fluently

  • Have a sufficient depth of knowledge and understanding to reason and explain mathematical concepts and procedures and use them to solve a variety of problems.

  • Recall key number facts e.g. number bonds and times tables, with speed and accuracy and use them to calculate and work out unknown facts.

Useful Links

Implementation

 

How we ensure challenge:

We ensure that the majority of pupils will move through the curriculum at broadly the same pace. However, based on effective AfL, our teachers make decisions about when to progress children, based on the security of each pupils’ understanding and their readiness to progress to the next stage. This does not mean that we hold children back or that all children access the same questions and same activities all of the time. Pupils who grasp concepts rapidly are challenged by ‘going deeper’, being offered rich and more sophisticated problems before any acceleration through new content. Adaptive teaching allows appropriate levels of scaffold and challenge to ensure appropriate support for all learners. Mastery strategies such as ‘Prove it; Compare; True or False are used. ‘Deepening’ through differentiation is important in all year groups, but of paramount importance in our mixed age classes. Those who are not sufficiently fluent with earlier material, consolidate their understanding, including through additional practice, before moving on. A ceiling is not put on children’s learning and flexible grouping is adopted based on pre-assessments.

How we ensure a well sequenced, progressive curriculum:

We teach the National Curriculum (2014). Pupils gain understanding of the mathematics relevant to their year group so that is it built upon in subsequent years.

  • Our long-term map outlines in year groups / phases when mathematical knowledge, in unit blocks of work, will be taught and revisited. This is the basis for our well sequenced and progressive curriculum.

  • Our Calculation Policy outlines in more detail which concepts and procedures / strategies will be introduced and then developed.

 

Whilst we teach Maths in progressive distinct domains (units of work) we recognise that Maths is an interconnected subject. Therefore, we encourage children to make connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. Children also apply their mathematical knowledge across the curriculum, and particularly in science, where relevant.

We regard talk in Maths as important and introduce mathematical vocabulary in an age-appropriate way. We encourage children to verbalise their thinking; our teachers ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.

 

We make time to teach Maths:

Children in EYFS have a daily mathematical focus based on acquiring knowledge of basic mathematical facts and concepts within the EYFS Curriculum. Mathematical concepts are also woven throughout their continuous provision.

Children in KS1 and 2 have a daily Maths session lasting 1 hour.

We also implement daily sessions focussing on the recall of identified key facts. These progressive, specific facts are non-negotiables that every child should know by the end of each year group. In addition to this all KS1 and KS2 children access arithmetic practice within daily lessons, to consolidate mental maths skills.

If children are not reaching the expectations outlined below, we intervene quickly by giving extra support. We give catch up support by utilising post teach and precision teach for short term rapid progress. The content of these sessions is determined by on-going gap analyses and our in depth knowledge of each child. These sessions are additional to our daily Maths session and form part of an identified intervention.

We build a skilled team who can teach Maths:

Many members of our teaching staff have accessed  training provided by our local Maths Hub, which they have disseminated school wide. This has focussed on Maths subject knowledge and pedagogical subject knowledge. Our Maths Subject Leader has also accessed Maths hub CPD this academic year. We carry out regular (at least termly) in house CPD sessions based on the aforementioned training and have carried out 1:1 coaching for identified staff. Leaders in our school prioritise the teaching of Maths. Leaders monitor the provision of Maths through learning walks in Maths sessions, work and planning scrutiny and the impact of this provision through the analysis of:

  1. end of year cohort data (end of KS1and 2 Maths)

  2. individual pupil attainment and progress throughout the year (on going assessments).

Implementation & Impact

 

Early Years

From the beginning of EYFS (third week) we prioritise the five principles of counting:

(i) The one-to-one principle: A child knows that we only count each item once.

 

(ii) The stable order principle: A child knows that the order of the number names always stays the same. We always count by saying one, two, three, four, five….in that order.

 

(iii) The cardinal principle: A child knows that the number they attach to the last object they count gives the answer to the question how many….?

 

(iv) The abstraction principle: A child knows that we can count anything – they do not all need to be the same type of object.

 

(v) The order irrelevance principle: A child knows that we count a group of objects in any order and in any arrangement and we will still get the same number.

 

We also prioritise:

Subitising: the ability to recognise how many there are in a small group of objects without counting them. This allows children to see that numbers can be represented in different ways.

Unitising: one object can have a value of more than one (equivalence). e.g. using Base 10 equipment, Numicon, coins.

By the end of EYFS, we expect the vast majority of our children to achieve the ELGs in Number and Shape, Space and Measure.

Number ELG: Count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

Shape, Space and Measure ELG: Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

By the end of EYFS, we expect the vast majority of our children to achieve the ELGs in Number and Shape, Space and Measure.

Number ELG: Count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

Shape, Space and Measure ELG: Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

KS1

In KS1 our main priority is to ensure children are developing an appropriate, deep understanding and fluency of place value and the four operations. By the end of KS1 we expect the vast majority of our children to have developed confidence and mental fluency with whole numbers, counting and place value including working with numerals, words and the four operations.

We focus on:

  • Using the CPA approach (Concrete, Pictorial and Abstract) as a way to introduce children to a range of representations. Each year group / class has a toolkit of concrete resources.

  • Practice to aid fluency at this early stage.

  • Early Addition and Subtraction strategies which include:

 

(i) Addition and Subtraction facts to 10

 

(ii) Recording when appropriate, using the word ‘and’ progressing to = .

 

(iii) Including putting the ‘answer’ at the front e.g. 10 = 4 + 6 and including missing numbers 4+ _ = 10

 

(iv) Exploring commutative 4 + 6 = 6 + 4

 

(v) Exploring balanced sides e.g. 4 + 6 = 3 + 7

Progressing to:

 

(vi) Subtraction and addition facts to 20

 

(vii) Recording of balanced sides e.g. 8 + 5 = 10 + 3

 

(viii) Including missing numbers e.g. 8 + _ = 10 + 4; 9 + _ = 10 + _

 

(ix) Structured progression to addition of larger numbers:

e.g. How does making 10 help to solve

- 2 digit and 1 digit (with a 1 in the tens column, bridging ten) e.g. 14 + 7 = 10 + 10 +1

- 2 digit and 2 digit (with a 1 in both the ten columns) e.g. 14 + 17 = 20 + 10 + 1

- 2 digit and 2 digit e.g. 27 + 18 = 30 + 10 + 5

  • Partitioning in different ways.

  • Early multiplication and division strategies which include:

(i) Repeated addition

(ii) Counting in multiples

(iii) Arrays

(iv) Progressing from division as sharing to grouping. (Division as sharing becomes an inefficient strategy as soon as numbers become larger. Division as grouping also enables the connection to be made between x and ÷.)

(See detailed progression in our Calculation Policy.)

 

In addition, we aim for children to:

  • Develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary.

  • Use a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.

We develop visualisation by:

• Using equipment

• Seeing equipment but not using it

• Visualising using a jotting.

• Introducing such methods as bar modelling to visualise mathematical concepts and solve problems.

We build in opportunities for verbalisation of thinking in younger years leading to written explanations of thinking / reasoning by Year 5/6.

 

Lower KS2

In Lower KS2 our main priority is to ensure children are becoming increasingly fluent with the four operations (including efficient methods), number facts and place value (including simple fractions and decimals) and are able to problem solve.

We focus on:

  • Continuing to use the CPA approach (Concrete, Pictorial and Abstract) as a way to develop children’s conceptual understanding.

  • Encouraging the most efficient strategies for calculation. Children are taught a range of strategies; they are taught to look at the calculation as a whole to encourage thinking about what the numbers mean rather than just the digits and using one strategy.

  • Progressing understanding of multiplication by looking for linked / connected calculations:

  • Progressing understanding of division by e.g.:

 

(i) By halving to make the calculation easier:

 

(ii) By diving the dividend and the divisor by any number to make the calculation easier

 

(iii) Divide by partitioning in different ways.

 

(See detailed progression in our Calculation Policy.)

 

In addition, we aim for children to:

  • Draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them.

  • Use measuring instruments with accuracy and make connections between measure and number.

 

By the end of Year 4 we expect the vast majority of our children to have:

  • Become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value.

  • Developed efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

  • Developed their ability to solve a range of problems, including with simple fractions and decimal place value.

  • Memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.

 

Upper KS2

In Upper KS2 our main priority is to ensure that children are:

  • Extending their understanding of the number system and place value to include larger integers.

  • Developing connections between multiplication and division with fractions, decimals, percentages and ratio. Developing 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.

  • Introduced to the language of algebra as a means for solving a variety of problems.

 

In addition, we aim for children to:

  • Consolidate and extend their knowledge developed in number in geometry and measures.

  • Classify shapes with increasingly complex geometric properties and learn the vocabulary they need to describe them.

 

By the end of Year 6, we expect the vast majority of our children to:

  • Be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

  • Have deep conceptual understanding and the ability to recall and apply mathematical knowledge rapidly and accurately.

  • Reason mathematically by following a line of enquiry, using their knowledge of relationships and generalisations, and justify using mathematical language.

  • Solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

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