Maths

Intent

Maths is an essential part of the curriculum at Maidwell Primary School and the teaching of the subject is supported by the belief that all children need a deep understanding of the maths they are learning. It is our intention that we provide an engaging and ambitious, knowledge-rich curriculum that both supports and challenges all of our pupils; establishing a solid foundation for the subject whilst also inspiring a sense of enjoyment, curiosity and appreciation for maths in everyday life. We want our children to reach their full potential and this is achieved when key concepts and the fundamentals of the subject are revisited and reviewed regularly to allow sufficient practise to embed learning and develop a deeper understanding.

Maths at Maidwell Primary School is driven by a methodical and coherent curriculum designed by White Rose Education and is supported by carefully sequenced lessons and resources which enables children to build on, and embed, their prior knowledge of the fundamentals of maths. This is achieved through:

Quality teaching of key concepts and processes in different ways, including physical concrete objects, pictorial diagrams and abstract representations (a CPA approach);
A variety of opportunities to apply knowledge and become fluent in these concepts and processes through embedded reasoning and problem solving;
Recall of key number facts e.g. number bonds and timetables with speed and accuracy and use them to calculate and work out unknown facts.

We believe that being able to talk about maths is vital for our pupils to be able to reason and problem solve. Through discussion, active teaching approaches and reflection on learning, all of our children will achieve; their learning will be deep and sustainable because their learning will build on prior knowledge and they will leave us as confident, resilient mathematicians, with the ability to combine concrete and abstract methods appropriately and fluently, with effective reasoning and explanation abilities to be able to successfully problem solve.

Implementation

Our teaching of maths across all key stages follows the National Curriculum through the White Rose Scheme of Learning which outlines in year groups when mathematical knowledge will be taught:

Our progression overview shows the development of concepts across the primary years. These allow subject leaders to have an overview of the progression of concepts over time and allow class teachers to know what children have learnt previously and how the learning continues subsequently.
Our calculation policies outline in more detail which concepts and procedures / strategies will be introduced and then developed. Subject leaders have adapted the White Rose scheme when it does not teach the methods according to our calculations polices.
Our planning is based on White Rose Maths which is tailored to the needs of our children. The progression of ‘small steps’ are used to structure each unit of work being taught that are developed through explicit teacher modelling, worked examples, guided practice, partner work and independent practice.
Pupils are provided with a variety of resources throughout the school to ensure they are exposed to multiple representations of a concept. This is part of our CPA (Concrete, Pictorial and Abstract) approach, where children move towards working in the abstract.
Whole year group / class teaching is in mixed attainment classes / year groups.
Talk for maths is very important and we focus on key mathematical vocabulary and language in an age-appropriate way using Never Heard The Word Grids (NHTW grids) and toolkits to support children’s understanding where appropriate. Children are encouraged to verbalise their thinking; our teachers ensure that pupils build secure foundations by using discussion to justify their answers and misconceptions.

Challenge and Deepening Understanding in Maths:

We ensure that all pupils can achieve a high standard in mathematics and the majority will move through the curriculum around the same pace. However, based on effective and continuous assessment of the children’s needs, our teachers make decisions about when to progress children, and how best to fill gaps in learning for the children who require more support, including for our children who join Maidwell Primary School part way through a key stage. All of this is achieved in the following ways:

Pupils gain understanding of the mathematics relevant to their year group so that is it built upon in subsequent years;
Pupils who grasp concepts quickly are challenged through rich and more complex reasoning problems;
Differentiation is through the same concept, posing different questions and problems for children working above age-related expectations to extend their thinking. This may be through mastery strategies such as ‘Prove it; Compare; True or False’;
Those who are not sufficiently fluent with earlier concepts will consolidate their understanding, including through additional practice and targeted interventions.

Maths in Early Years:

From the beginning of EYFS, children have a daily maths session where 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.

Maths at KS1:

In KS1, our main priority is to ensure that our children are developing an appropriate understanding and fluency of place value 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 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 ÷.)

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 methods such 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 as soon as children are ready to.

Maths at 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:

(i) Halving to make the calculation easier;

(ii) Dividing 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.

Maths at 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 of 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.

Intervention

Any child whose mathematical understanding is below age-related expectations has additional interventions. In KS1, children have additional place value and number bond sessions to ensure they make effective progress in their understanding of these vital mathematical elements. In KS2, children work on key instant recall facts including place value, number bonds, doubles and near doubles as part of their additional intervention sessions.

Impact

The impact of how we teach our children to become efficient mathematicians is demonstrated through:

Regular retrieval practice (including flashbacks, mental maths and arithmetic);

End of unit assessment quizzes (hot tasks);

Assessment for learning within each lesson through skilful questioning and live feedback;
Mathematics summative assessments to measure pupil progress and QLAs to identify next steps;
KS1 and KS2 SATS;
Regular times tables and calculations checks.

By the time our children leave Maidwell, our children will have acquired a deep understanding of maths and by us promoting the importance of maths and ensuring it is taught to a greater depth, our pupils will make at least good progress in maths from their last point of statutory assessment or from their starting point in EYFS and will be able to know, retain and understand more which will only benefit their future opportunities.

At the End of EYFS at Maidwell Primary School:

Children at the expected level of development will achieve the ELGs in Number and Shape, Space and Measure. They will:

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;
Solve problems, including doubling, halving and sharing;
Use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems;
Recognise, create and describe patterns;
Explore characteristics of everyday objects and shapes and use mathematical language to describe them;
Have positive attitudes and interests in mathematics.

At the End of Key Stage 1 at Maidwell Primary School:

Children at the expected level of development will:

Have developed their confidence and fluency with whole numbers, counting and place value;
Work fluently with number facts to 20 including working with numerals, words and the four operations;
Describe properties of shapes;
Compare and describe different quantities such as length, mass as well as time and money.

At the End of Lower Key Stage 2 at Maidwell Primary School:

Children at the expected level of development at the end of Year 4 will:

Become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value;
Have developed efficient written and mental methods and perform calculations accurately with increasingly large whole numbers;
Have developed their ability to solve a range of problems, including with simple fractions and decimal place value;
Have memorised their multiplication tables up to and including the 12x multiplication table and show precision and fluency in their work.

At the End of Upper Key Stage 2 at Maidwell Primary School:

Children at the expected level of development at the end of Year 6 will:

Extend their understanding of number and place value involving larger integers;
Develop connections between fractions, decimals, percentages and ratio;
Develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic;
Use efficient written and mental methods for calculation when solving problems;
Use mathematical vocabulary correctly, when articulating and explaining how they solved the problem;
Be introduced to the language of algebra as a means of solving a variety of problems.