Maths

Maths Intent

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 most forms of employment. A high-quality mathematics education 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.

The national curriculum for mathematics aims 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 non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are organised into distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects. The expectation is that the majority of pupils will move through lesson sequences at broadly the same pace. However, decisions about when to progress should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly are challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material consolidate their understanding, including through additional practice, before moving on.

Maths Implementation

At Garfield, we teach using White Rose Maths which utilises a CPA approach and Maths Mastery, to consolidate the building blocks children need to study maths successfully. 

We are developing our mastery approach in Maths, with excellent support from the NCETM (National Centre for Excellence in the Teaching of Mathematics) and our local Maths Hub. Behind all NCETM teaching for mastery work are 5 Big Ideas, informed by research evidence and classroom experience. This diagram helps bind these ideas together: 5_Big_Ideas_Maths_NCETM.pdf

White Rose Maths and the teaching for mastery approach helps children develop their conceptual understanding of mathematics by using concrete manipulatives, pictorial representations and abstract thinking. This uses the principles of cognitive psychology and child development.

Concrete - the “doing” stage involves physically manipulating objects to solve a Maths problem.

Pictorial - the “seeing” stage involves using images to represent objects to solve a Maths problem.

Abstract - the “symbolic” stage involves using only numbers and symbols to solve a Maths problem.

The CPA stages are interlinked within maths lessons - the aim is to remove the need for concrete manipulatives so children do the maths using the abstract number system. Manipulatives are there to represent a maths idea and help children 'see' the structure of the maths behind the problem - rather than using manipulatives to 'do' the maths.

Incorporating the use of concrete resources, problem solving and group work, the White Rose curriculum is child-centred and fun to teach. In lessons, teaching focuses on the use of visualisation, finding patterns and exploring mental strategies. Tasks and activities have problem-solving approaches, enabling children to apply increasingly fluent calculation skills and encouraging higher-level thinking. Pupils practise reasoning, supported by sentence stems and using journaling techniques to demonstrate understanding and show their methods. Challenge is welcomed through key and specific questioning, with pupils aware of next steps. Our children enjoy and do well in Maths. 

EYFS

In the Early Years, Maths involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measure.

Pupils are taught:

Number

• count reliably with numbers from 1 to 20
• place them in order and say which number is one more or one less than a given number
• add and subtract two single-digit numbers and count on or back to find the answer using quantities and objects
• solve problems, including doubling, halving and sharing

Shape, space and measure

• 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
• use mathematical language to describe them.

Key Stage 1

The National Curriculum (2014) states that:

The principal focus of maths teaching in KS1 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 [for example, 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.

Lower Key Stage 2

The National Curriculum (2014) states that:

The principal focus of maths teaching in LKS2 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 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 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.

Upper Key Stage 2

The National Curriculum (2014) states that:

The principal focus of mathematics teaching in UKS2 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.

Maths Impact

We want children to become confident and successful Mathematicians, with an understanding of what the subject will bring to their lives and the maths links within their local and wider community. Throughout each lesson formative assessment takes place and feedback is given orally and through marking to ensure pupils are meeting the learning objective. Teachers use assessment to aid planning and ensure lessons support each child to progress. Maths is monitored termly through book scrutinies, learning walks, listening to pupils’ opinions and lesson observations. Each term children from Year 1 and above complete NTS summative standardised assessments to demonstrate their understanding of the topics covered. Results from both formative and summative assessments are used to determine children’s progress and attainment.

By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes in their programme of study. Children in the EYFS are assessed within Maths and progress is tracked termly. Age related expectations are reported to parents at the end of Reception. In KS1 and KS2, assessment takes place throughout the year and at the ends of topics. Teachers record progress in Maths against National Curriculum expectations for each year group. Teachers use this information to inform future lessons, ensuring children are supported and challenged appropriately. Assessment data is analysed to inform and address any trends or gaps in attainment. Further information is gathered through pupil voice activities, highlighting strengths and achievements and any recommendations for improvements, knowledge and skills that need to be embedded. Each part of the Maths curriculum is reviewed termly by the subject leader.