# Maths

## What is Maths?

Maths is an essential part of everyday life. Our intention for Maths at Appleton CE Primary School is to support children to: develop an ability to solve problems, reason, think logically, and work systematically and accurately. Therefore, mathematics forms an important part of our broad and balanced curriculum where we endeavour to ensure that children develop an enjoyment and enthusiasm for maths that will stay with them beyond their time at Appleton and empower them in future life.

### Aims of Maths

It is our belief that our pupils should:

• Become fluent in the fundamentals of mathematics, so that they:
•  Have a well-developed sense of number values.
• Know by heart key number facts (in line with the programme of study): e.g. number bonds, times tables and related division facts.
• Apply knowledge of the above to work out connected facts.
• Reason mathematically, so that they:
• Can follow a line of enquiry.
• Provide generalisations and proof of findings around their investigations.
• Can justify their thinking, e.g. as to why a particular calculation strategy is the most efficient.
• Solve problems by applying their understanding of mathematics, so that they:
• Encounter a variety of both routine and non-routine problems.
• Can select a specific maths skill and/ or operations.
• Persevere with a line of enquiry, breaking down increasingly complex problems into a series of smaller steps.

### How is Maths taught?

Teaching and Learning

Big Ideas

Our mathematics teaching is underpinned by the NCETM’s Five Big Ideas:

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

Teaching Principles

• Teachers believe in the importance of mathematics and the value of deep understanding of mathematics as a life skill.
• Mastery of mathematics is not a fixed state, but a continuum where children are always striving to move their learning forwards. It is built continually throughout school and is a valuable tool for life.
• Staff have high expectations for all pupils.
• Challenge is provided by going deeper, within a pupil’s own year group, rather than accelerating to new content.
• The whole class is taught mathematics together. The learning needs of individuals are addressed through careful scaffolding, questioning and appropriate rapid intervention where necessary, to provide the appropriate support and challenge.
• It is important that children have the time and opportunity to master new facts, procedures, and concepts in mathematics. Teachers target time appropriately and in response to the needs of the pupils.
• The reasoning behind mathematical processes is emphasised. Teacher/ pupil interaction explores how answers were obtained as well as why the method worked and what might be the most efficient strategy.
• Precise mathematical language is used by teachers so that mathematical ideas are conveyed with clarity and precision. Mathematical talk is valued and encouraged.
• Conceptual variation and procedural variation are used throughout teaching. This helps to present the mathematics in ways that promote deep, sustainable learning.

The Maths Learning Environment

Our mathematics learning environment includes:

•  Maths working walls in all classrooms. This resource is built up over time by the class as they move through the different areas of learning.
•  Freely accessible resources, including concrete manipulatives (e.g., multilink, shapes counters), available in all classrooms.
• Opportunities for cross-curricular learning, which provide tangible demonstrations as to the relevance and importance of maths to daily life and the broader educational curriculum.
• For Reception and Year One, appropriate child-led and carefully planned adult initiated maths activities, which build confidence and mathematical skills.

### Assessment

Teachers use a range of informal, formal, and statutory assessments to monitor pupil progress and attainment. These help teachers to set targets for groups and individuals. At key points in the year, children are assessed against the National Curriculum standards. We carry out regular and purposeful formative assessment of mathematics. This aids the teacher in identifying key gaps in understanding, which are providing a barrier to progress. These gaps are then addressed in class and/ or through rapid intervention.

Suitable summative assessment enables teachers to monitor pupil’s progress and attainment. It should not be an expectation that next-steps or targets be written into pupils’ books; the next lesson should be designed to take account of the next steps. Analysis of the outcomes of the summative assessments inform teachers’ planning for mathematics teaching and targeted interventions. Where necessary, they also inform Maths Leaders’ strategic planning for the provision of mathematics across the school.

### Parents and Carers

The role of parents and carers in helping to develop their child’s mathematical knowledge and understanding is incredibly important. We encourage parents and carers to support their child to develop good number sense and to help support fluency development such as through learning times table facts. Parents and carers can also help by discussing maths in everyday life such as using maths in activities such as shopping, cooking, or telling the time.

### Intent

We believe that unlocking mathematical fluency is an essential life skill for all learners and is a pre-requisite to being able to reason and solve problems mathematically. Our aim is to develop a positive culture of deep understanding, confidence and competence in maths that produces strong, secure learning. As a school, we recognise that the key to unlocking the potential in our children is through the development of basic mathematical skills and the understanding of mathematical concepts. We therefore place great emphasis on the use of concrete resources and pictorial representations at all ages, to enable children fully to understand the concepts and principles, when presented with abstract calculations and questions. Our maths curriculum is progressive and helps to prepare children for their learning in future years.

All children are challenged and encouraged to excel in maths. Through quality first teaching, all children, including those with SEND, will have access to teaching and learning. New mathematical concepts are introduced using a ‘Concrete, Pictorial and Abstract’ approach; enabling all children to experience hands-on learning when discovering new mathematical topics and allowing them to have clear models and images to aid their understanding. Arithmetic and basic math skills are practised daily to ensure key mathematical concepts are embedded and children can recall this information to see and utilise the links between topics in maths.

Children are encouraged to make mistakes in a safe and supportive environment. They are encouraged to discuss mathematical misconceptions with their peers and staff alike. We place oracy at the heart of our learning, through shared work and class discussions. Use of appropriate vocabulary is modelled throughout lessons by both staff and children, allowing everyone to ‘talk like a mathematician’. Once a child can articulate their understanding of a concept, can they truly begin to make connections within their learning.

### Implementation

Maths at Appleton Primary School:

• Fundamental maths skills are taught daily, focussing on key areas including place value, the four cornerstone operations (addition, subtraction, multiplication, division) and fractions.
• A range of reasoning resources are used to challenge all children and give them the opportunity to reason with understanding.
• Techniques such as pre-teaching are used to support children to ensure they are ready for their next maths lesson.
• Children are taught through mixed ability whole class lessons, with rapid intervention where required.
• Lessons use a Concrete, Pictorial and Abstract approach to guide children through their understanding of mathematical processes.
• Where possible, links are made with other subjects across the curriculum.

Our Maths curriculum provides breadth and balance, is relevant and engaging, and is differentiated to match needs and abilities to ensure that all pupils can excel.

To help structure and plan our lessons, we use White Rose Maths Hub schemes of learning to ensure firm foundations and sequence our learning. Alongside this, we use a range of rich resources to enhance our lessons and deepen understanding. Our teaching is informed by the NCETM Five Big Ideas underpinning Teaching for Mastery: Fluency, Variation, Representation and Structure, Mathematical Thinking and Coherence.

From Reception to Year 6, we adhere to our calculation policy which outlines the progression of strategies and methods to be taught along with the relevant maths vocabulary. We have created our medium-term plans in line with White Rose small steps but can alter the order to suit and benefit the needs of our children, so that connections between units of learning are easier to recognise. From Reception to Year 6, children follow the scheme of ‘White Rose’ which supports children in learning the fundamentals behind the meanings of numbers and exploring other key mathematical areas. White Rose use ‘small steps’ to break down the teaching sequence into small achievable steps. Where children require additional support, ‘scaffolds’ are used to support children further to ensure that they have secured the small step before moving on. These ‘scaffolds’ may be in the form of returning to concrete resources or pictorial representations. For children who understand a concept quicker, challenges are used to deepen thinking and understanding within the topic area. Progression documents are carefully used to ensure that children are not being stretched outside their year group but rather deepened within it.

Reception and KS1 also follow the NCETM Mastering Number Programme which supports the development of good number sense for all children with the aim that children will leave KS1 with fluency in calculation and a confidence and flexibility with number.

Times tables play an important part in our maths learning, with children developing their fluency in rapid recall of tables up to 12 x 12 by the end of Year 4. While the rapid recall of times tables is being developed, children are also learning how to apply and manipulate their understanding of this to reason and solve problems.

Times Table Rockstar homework is set in KS2. This platform has been developed with the view of making the learning of times tables fun and has been shown to increase speed and accuracy of recall. The progressive and structured approach to learning times tables is adapted to meet each child where they are at, and the platform allows teachers to review learning and support pupils as needed.

Termly assessments are used as a diagnostic tool to ensure that teachers are adapting learning and targeting interventions to meet the needs of all children .

### Impact

As a result of our Maths teaching at Appleton CE (A) Primary School you will see:

• Engaged children who are all challenged.
• Confident children who can all talk about maths, their learning, and the links between mathematical topics.
• Children who have fluency and automaticity with key facts and concepts
• Lessons that use a variety of resources to support learning.
• Different representations of mathematical concepts.
• Learning that is tracked and monitored to ensure all children make at least good progress.

By the end of Year 6, transitioning to secondary school, we aspire that our pupils will have developed a bank of efficient and accurate skills that can be used to calculate effectively. These will have been underpinned by the Concrete, Pictorial, Abstract  process so children understand rather than just do, which ultimately will allow children to identify when answers do not make mathematical sense.  Children will be able to apply calculation skills both to examples that they have been taught, and broader mathematical problems for which they have been able to see appropriate links. We aim for our children to transition to secondary school as confident and resilient problem solvers, with the ability to reason and articulate their ideas mathematically.

### The Four Operations: Calculation Methods

These documents detail the progression of addition, subtraction, multiplication, and division methods, both mental and written, from Year 1 to Year 6. The methods should be considered as a continuum that children gradually work their way through, some children may spend longer on one method or even skip methods as they progress.

Ultimately, children need to decide which method to use for any given calculation, this will vary depending on the difficulty and context of the question and their own preferences. The key outcome is for the method to be successful and to be completed in a reasonable time.