Mathematics

Mathematics at Pomphlett

Rationale- What has informed our curriculum design in mathematics?

Mathematics is essential to everyday life. At Pomphlett, we place great importance in learning this life skill and developing a sense of enjoyment and curiosity about the subject. Our aim is that learners in our community will see mathematics as a subject that is relevant to their lives now and in the future. They will see that learning mathematics is more than simply learning to calculate. Through the study of mathematics, we want pupils to become quick computational mathematicians who are able to apply their reasoning skills and solve problems across the curriculum. Furthermore, we believe that learning in this way equips children with the ability to think creatively, understand that there are many ways to view a challenge, and as a manifestation of our school moto, believe that they can succeed. In essence, successful teaching and learning in maths should positively impact teaching and learning across the curriculum.

Intent- What are our aims?

Our mathematics curriculum aims for pupils to become fluent in the fundamentals of maths and provides children with rich mathematical experiences. It is built on the key aims of the National Curriculum which are to ensure that all learners:

• 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 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.

We encourage pupils to make significant links between mathematics as a discreet subject and using their mathematical knowledge in other subjects, as well as within real life problems.

Implementation - How do we teach mathematics?

At Pomphlett Primary School, our mastery approach to the teaching and learning of mathematics aims to ensure that the mathematics curriculum foregrounds cores skills as essential elements for success whilst also explicitly teaching children how to apply these in problem-solving situations by scaffolding the development of effective reasoning skills.

 This teaching approach can be broken down into the National Centre for Excellence in the Teaching Mathematics’ (NCETM) five big ideas that underpin mathematics lessons across the school:

Big Ideas

NCETM’s 5 Big Ideas are as follows. Opportunities for Mathematical Thinking allow children to make chains of reasoning connected with the other areas of their mathematics. A focus on Representation and Structure ensures concepts are explored using concrete, pictorial and abstract representations, the children actively look for patterns as well as specialise and generalise whilst problem solving. Coherence is achieved through the planning of small connected steps to link every question and lesson within a topic. Teachers use both procedural and conceptual Variation within their lessons and there remains an emphasis on Fluency with a relentless focus on number and times table facts.

We use Big Maths across the school to structure the small steps in the teaching of these ideas and to revisit them each term. It is not a scheme, but is a way of breaking down steps in learning.  All learning in maths is planned to carefully build an understanding of concepts, with reasoning skills and problem-solving developing alongside mathematical fluency.

Please use the following link to find out more about Big Maths: http://www.bigmaths.co.uk/

Every day, children in KS1 and KS2 also work on their own mental arithmetic book. We began this programme in January 2016 and alongside Big Maths, as a result of daily practice, children secure the ability to manipulate number and calculate accurately; understand mathematical vocabulary; and apply reasoning skills in problem solving.

Further information on the mental arithmetic books can be found here:https://www.schofieldandsims.co.uk/mental-arithmetic/

Alongside Big Maths and the National Curriculum, White Rose Maths https://whiterosemaths.com/ and the NCETM progression materials (which support the 2020 DfE non-statutory mathematics guidancehttps://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/954510/Maths_guidance_introduction.pdf ) are also used to inform planning and promote links between children's fluency, reasoning and problem-solving.  

Impact: How will we know this?

An overview of the learning expected for different age-groups is given below. We assess children’s understanding using a variety of strategies to build a broad picture of this learning. These include summative assessments (tests) and formative assessment through the daily teaching of mathematics.

The Main Areas of Early Years Maths

There are six main areas that collectively underpin children’s early mathematical learning, and which provide the firm foundations for the maths that children will encounter as they progress through primary school.

They are:

• Cardinality and Counting: understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents
• Comparison: understanding that comparing numbers involves knowing which numbers are worth more or less than each other
• Composition: understanding that one number can be made up from (composed from) two or more smaller numbers
• Pattern: looking for and finding patterns helps children notice and understand mathematical relationships
• Shape and Space: understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
• Measures: comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later.

The principal focus of mathematics teaching in Key Stage 1 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.

The principal focus of mathematics teaching in lower key stage 2 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 that 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 that 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.

The principal focus of mathematics teaching in upper key stage 2 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.

As a result of our high quality maths provision, we have a community of enthusiastic mathematicians who enjoy showcasing their developing numeracy knowledge and skills. Standards of mathematics across the curriculum, and through cross-curricular links, are of a consistently high standard and our learners take pride in the work they produce. They are confident to take risks in their mathematics, and love to discuss and share their ideas.

We hope you find the information provided useful. If you have any questions about mathematics at Pomphlett, please do not hesitate to get in touch with Mrs Skuse, the Mathematics Subject Leader. Please follow the links below to find further information regarding what maths is learned at different stages in your child's education.