Let's Work It Out!

If your child practises number facts for 10 minutes a day, they could have an extra 70 minutes per week or 3,640 minutes each year developing their mental maths skills!

Intent - What are we trying to achieve?

Rationale

Mathematics equips pupils with the uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways. Mathematics is important in everyday life, critical to science, technology and engineering, and necessary in most forms of employment. It is integral to all aspects of life and with this in mind we endeavour to ensure that children develop a healthy and enthusiastic attitude towards mathematics that will stay with them.

Aim of the National Curriculum

Children who have mathematical fluency are confidently able to apply their mathematical knowledge and skills both at school and in their daily lives. 

The new national curriculum for mathematics aims that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems overtime, 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 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

Aims and objectives @ YFPS

Our school is committed to delivering a ‘Mastery Curriculum’, which ensures continuity and progression in the teaching of mathematics. Within a unit of work, the time spent on teaching a specific learning objective or set of learning objectives depends on the needs of the children.

A ‘Mastery Curriculum’ is designed to create a learning atmosphere:

• where all pupils can and will achieve

• with a focus on the development of deep structural knowledge

• developing rapid recall of key number facts

• through carefully chosen examples and representations supporting the opportunity to make connections between mathematical ideas

• keeping the class working together wherever possible

• spending longer time on key topics to ensure depth of understanding

• providing regular problem solving opportunities in familiar and unfamiliar contexts.

Implementation - How will we achieve this?

General principles

Children who have mathematical fluency are confidently able to apply their mathematical knowledge and skills both at school and in their daily lives.  

The new national curriculum for mathematics aims that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems overtime, 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 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.

Our school is committed to delivering a ‘Mastery Curriculum’, which ensures continuity and progression in the teaching of mathematics. Within a unit of work, the time spent on teaching a specific learning objective or set of learning objectives depends on the needs of the children.

A ‘Mastery Curriculum’ is designed to create a learning atmosphere:

• Where all pupils can and will achieve

• With a focus on the development of deep structural knowledge

• Developing rapid recall of key number facts

• Through carefully chosen examples and representations supporting the opportunity to make connections between mathematical ideas

• Keeping the class working together wherever possible

• Spending longer time on key topics to ensure depth of understanding

• Providing regular problem solving opportunities in familiar and unfamiliar contexts.

  Fluency involves:

• Quick recall of facts and procedures
• The flexibility and fluidity to move between different contexts and representations of mathematics.
• The ability to recognise relationships and make connections in mathematics
•  

  Representation & Structure

  Mathematical structures are the key patterns and generalisations that underpin sets of numbers – they are the laws and relationships that we want children to spot. Using different representations can help children to ‘see’ these laws and relationships.

   

  Variation

  Procedural variation – This is a deliberate change in the type of examples used and questions set, to draw attention to certain features.

  Conceptual variation – When a concept is presented in different ways, to show what a concept is, in all of its different forms.

   

  Mathematical thinking involves:

• Looking for pattern and relationships
•  
• Logical Reasoning
• Making Connections                                                                                                                                                                              Alongside all of these areas the maths must be taught as a coherent journey, using small steps to build knowledge and constantly make connections/links to previous learning to maximise retention.

Planning, learning and teaching: 

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, by necessity, 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 the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. (In line with the government’s recently released document – ‘Ready to Progress Criteria’) Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on. 

At Yealmpstone Farm Primary:                                                                                                                                                                   Lessons provide the children with opportunities to ‘talk the mathematics’ speaking in full sentences to develop their mathematical vocabulary and consolidate their understanding of the maths being taught. Children are required to provide justification and reasoning for their answers. For example, ‘I know the shape is a square because….’

• All children receive a daily maths lesson, although mathematical skills run through many other areas of the curriculum.
• Each lesson focuses on one clear learning focus which all children are expected to master; extension activities enable those children who grasp the objective rapidly to extend their learning by exploring it at greater depth.
• Each lesson can include elements of: fluency, to practise skills; reasoning, to deepen understanding; and problem solving, to apply skills depending on the objective being taught and the understanding of the children.
• Teachers use the White Rose Mastery planning and other resources to draw up medium term plans for each term, and a daily lesson plan is produced to incorporate the above elements. 
• Whole class teaching is adopted and children work in mixed ability groups. 
• Small steps of learning will be planned for and used effectively to consolidate, assess and take learning forward.
• Questioning is the key to success in all of our mathematics sessions and questions will be continuously adapted by the teacher and support staff based on assessment for learning.
• Daily ‘quick maths’ activities are taking place in each class (year 1 to year 6) to develop our pupils’ mathematical fluency. 
• Teachers’ plan of effective visual representation to support conceptual understanding is evident in each lesson.
• Pupils are given physical resources to manipulate during the lesson, hence deepening their understanding of the maths taught.
• Teachers are encouraged to teach and apply areas of mathematics, such as shapes, space, measure, handling data, ratio and percentages, in other areas of the curriculum to enable them to focus on teaching the key skills of mathematics during the formal maths lessons.  It also enables the children to make greater connections between what they learn at school and real life. 

What is the concrete pictorial approach in maths?

At Yealmpstone Farm Primary we believe it is important that children develop a deep understanding of the mathematical concepts they are learning. Therefore we have changed our teaching of maths, taking on the concrete, pictorial, abstract (CPA) approach, which is a system of learning that uses physical and visual aids to build a child’s understanding of abstract topics.

Pupils are introduced to a new mathematical concept through the use of concrete resources (e.g. fruit, Dienes blocks etc). When they are comfortable solving problems with physical aids, they are given problems with pictures – usually pictorial representations of the concrete objects they were using alongside the abstract.

Number Sense

At Yealmpstone Farm Primary School, we are currently using the Number Sense programme every day, in an additional slot to our maths lesson. The programme builds on our innate ability to process quantities visually with graphics that expose mathematical structures. With animations and exercises with visual scaffolding, and a wide range of practical activities, a deep understanding of number and quantity is developed.

At the core of the programme are the Addition and Subtraction Fact Grids.

These essential facts are the equivalent of times tables for addition and subtraction. Just as all multiplication and division calculations use root times table facts, all future addition and subtraction calculations use these root addition and subtraction facts.

The programme teaches every addition and subtraction fact systematically. Just as schools can tell you where they teach each grapheme-phoneme correspondence in phonics, the Number Sense Maths Fluency Programme systematically teaches the facts and strategies leaving nothing to chance.

Impact - What difference will this make?

 At YFPS, children:

• enjoy their maths learning
• are able to apply their mathematical skills in real life situations
• are able to integrate their understanding of maths into other aspects of their learning and lives (making connections)
• are mathematically resilient
• are more reflective and interested in exploring learning yet further
• are able to use the mathematical language to explain their ideas
• are confident in their maths learning

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