Maths

Maths at Harris Primary Academy Beckenham Green

Our curriculum will teach the following mathematical concepts, taught as discrete units throughout the year.: 

• Number
• Statistics
• Geometry
• Measure

Pupils will learn about the following substantive concepts through our spiral curriculum, units will return to these same big ideas year on year. 

Intent: Introduction, Vision and Philosophy

The purpose of this document is to clarify the how, why and what of maths teaching at Harris Primary Academy Beckenham Green. This is to be used by staff to clarify expectations, highlight the resources that we have access to, and to ensure that a high-quality maths curriculum is being taught to all pupils in our academy. At Beckenham Green, we want our children to be confident, fluent mathematicians, as well as problem solvers. We teach maths for mastery. This means that we are teaching our children to have a deep conceptual understanding as opposed to teaching children to answer correctly. Being able to explain how they got an answer, why that answer is correct, and what might happen if a particular variable was changed are the hallmarks of a mathematician – simply getting the correct answer ought to be a given.

We emphasise:

Retrieval practice - Knowing more- remembering more! Daily retrieval practice to consolidate prior learning and practice.

Language – communicating ideas, proof, clarity and development of mathematical concepts.

Thinking – questioning and task design to promote mathematical thinking.

Understanding – using the concrete, pictorial and abstract approach to deepen conceptual understanding and making connections to previous learning, to other subjects.

Problem Solving – to be mathematical is to solve mathematical problems. Problem solving is both why and how we learn mathematics.

Implementation:

What does maths look like at HPABG?

At Beckenham Green we teach maths in units, usually for a couple of weeks per unit. We aim to develop children’s understanding from the Concrete (actual physical manifestation of the maths), on to the Pictorial (being able to approach maths using pictures rather than physical resources), and finally onto the Abstract (being able to approach mathematics without the physical or pictorial resources). A typical two-week unit might have 2-4 concrete, practical lessons (photo recorded with follow-up next step questions) as well as 6-8 lessons focussing more on the pictorial and abstract (recorded using stickers followed by further extension sticker where necessary).

White Rose at Harris Primary Academy Beckenham Green

For our pupils:

Harris Primary Academy Beckenham Green has opted for the White Rose Maths scheme of learning from EYFS to Year 6 to ensure a robust, comprehensive, and high-quality approach to the teaching and learning of mathematics. The decision to adapt this scheme was guided by a desire to foster maths mastery, improve conceptual understanding, and to align with Ofsted's standards for effective teaching and learning.

White Rose Maths adheres to the concrete, pictorial, abstract (CPA) approach, a three-step pedagogical strategy that aids in developing a deep and sustainable understanding of maths. Beginning with 'concrete' experiences, where pupils engage with physical, manipulatives, learners are then introduced to 'pictorial' representations, followed by 'abstract' symbols. This gradual approach aids pupils in visualising mathematical concepts and contextualising abstract ideas, thereby nurturing mastery learning.

The systematic nature of the White Rose Maths scheme underscores the importance of conceptual understanding. Rather than rushing to provide quick fixes or rote learning methods, White Rose allows our pupils to understand the ‘why’ and ‘how’ of mathematical concepts. This aligns with Ofsted's emphasis on deep learning, wherein pupils should understand and apply the underlying principles and connections within their learning.

Each White Rose Maths unit provides a 'small steps' progression framework, ensuring a pedagogically sound sequence of mathematical learning that we at Harris Primary Beckenham Green have adapted to best fit the needs of our pupils. This approach allows concepts to be broken down into manageable chunks, giving learners the opportunity to fully grasp each new skill or concept before moving on. This fits within Ofsted's recommendation that schools offer a curriculum with appropriate sequencing, which provides a strong foundation for cumulative learning.

The White Rose Maths scheme comprehensively covers the breadth of the national curriculum. It provides a coherent, structured and detailed scheme of learning that ensures all necessary topics are covered systematically. This aligns with Ofsted's requirement that the school curriculum should be broad, balanced and provide the requisite knowledge and skills for future learning and employment.

The White Rose scheme is a progressional model that consolidates, builds upon and extends our children's maths learning. It provides a carefully crafted journey, where children continuously build on their previous learning, ensuring readiness for the next steps in their mathematical education. This complies with Ofsted’s expectations of effective progression and curriculum planning, helping pupils to deepen their knowledge and understanding over time.

By adapting the White Rose Maths scheme, Harris Primary Academy Beckenham Green demonstrates a commitment to a high-quality mathematics education that is personalised for the needs of all our pupils. White Rose equips our pupils with the necessary mathematical skills, knowledge and understanding to excel in their future academic and personal endeavours and develop a love of mathematics.

For our staff:

Harris Primary Academy Beckenham Green has made the decision to adapt the White Rose Maths scheme of learning, an initiative supported by a myriad of compelling reasons. Our objective is to ensure that our staff are empowered with comprehensive teaching resources, pupils are provided with engaging and challenging mathematical learning, and that our collective commitment to staff wellbeing and manageability of workload is maintained.

Firstly, the White Rose Maths scheme offers an integrated, robust and holistic curriculum for mathematics, providing an expansive body of pedagogical research, concrete, pictorial and abstract teaching methods, and a track record of successful implementation in numerous educational institutions including across most of the primary academies in the Harris Federation. Its meticulous curriculum design aids teachers in understanding the progression of each mathematical topic, its foundational knowledge, and its trajectory for future learning. This coherence and structure equip our staff to deliver mathematical instruction with confidence, precision, and effectivity.

The investment in the White Rose on demand package is another strategic step that we have taken to support our staff. This package includes video content for every maths unit, detailing the teaching process, from concrete examples to pictorial representation, to the abstract understanding of each mathematical concept. This is an effective tool to reinforce our teachers' understanding of subject matter, pedagogical methods and lesson execution.

Furthermore, White Rose on demand provides valuable CPD for our staff, focusing on key pedagogical strategies that have been backed by research to effectively bolster children's learning in mathematics. Examples of these strategies include the bar model method and partner talk, each serving to encourage deep understanding and active participation from our pupils.

The resources provided by White Rose are comprehensive, efficient, and tailored to assist our staff in planning and teaching outstanding maths lessons. The vast array of resources and schemes of learning that White Rose offers aligns with our commitment to ensure that our staff's workload remains manageable. They provide teachers with ready-made, high-quality resources, reducing planning time and relieving workload pressure.

Harris Primary Academy Beckenham Green has also adapted the White Rose year overview to a more specific, week-by-week overview. This initiative gives staff a clear and comprehensive view of the objectives for each week, fostering an understanding of the yearly progression of learning across the school.

Lastly, our commitment to the continuous professional development of our staff is reflected in our regular CPD sessions on the White Rose Maths scheme. These sessions enable our staff to stay abreast of new strategies and resources, continually improving their teaching practices and thereby our pupils' learning experiences.

In conclusion, the adoption of the White Rose Maths scheme of learning and the investment in the White Rose on demand package are in line with Harris Primary Academy Beckenham Green's commitment to providing our staff with the best tools to deliver high-quality mathematics instruction, support their professional growth, and ensure their wellbeing.

Unit Overview

When planning a unit, teachers will have access to a range of different resources and areas to support the lessons that are outlined in our teaching overview. Generally, teachers will follow the recommended progression delivered in staff CPD sessions as well as the order of the slideshows in White Rose. However, additional slides are added to promote vocabulary and partner practice. If a specific teaching tool or representation is not available on White Rose, then teachers have the freedom to make their own resource to best suit the needs of their class.

Adapt not Adopt

At Harris Primary Academy Beckenham Green, we have long recognised the value of the White Rose Maths scheme of learning for its comprehensive approach to teaching Mathematics. This scheme's well-structured approach is lauded for the depth and breadth it provides in each unit of learning. However, we have also recognised the necessity to go beyond simply adopting schemes and sought to tailor this scheme to more accurately meet the unique needs of our children.

The rationale behind this decision is multi-faceted. Firstly, the inherent diversity amongst our pupils necessitates a more personalised approach. Our children come from a wide array of backgrounds with different learning styles, capabilities, and experiences, which must be factored into our teaching methods. We believe that a "one-size-fits-all" approach to Mathematics does not effectively cater to the individual needs and strengths of our pupils, hence the decision to adapt the White Rose scheme.

By unpicking the units of the White Rose scheme, we have gained a deeper understanding of the content and how best to deliver it. This has enabled us to decide which units will be implemented, in what order, and for how long, depending on our pupils' readiness and interest. We aim to set high expectations for all pupils, but these expectations need to be reasonable and achievable, given each child's unique learning journey. This flexibility allows us to meet these expectations while also maintaining an engaging and motivating learning environment.

Our goal is to foster an understanding and appreciation of Mathematics that goes beyond mere rote learning. By adapting the scheme, we can emphasise the areas where our pupils excel, and dedicate more time to the areas where they may struggle. This approach reinforces their strengths and addresses their weaknesses, creating a balanced, comprehensive Mathematics education that sets them up for success.

Lastly, we believe that this personalised approach to Mathematics, which combines the high-quality units of learning from the White Rose scheme with our own knowledge of our pupils, leads to more meaningful and enjoyable learning experiences. Children are more likely to be engaged and motivated when learning is relevant to their needs and interests, which ultimately leads to improved academic outcomes.

In conclusion, Harris Primary Academy Beckenham Green has adapted the White Rose Maths scheme not as a critique of its effectiveness, but rather as an enhancement to better meet the needs of our pupils. By doing so, we provide a tailored, high-quality Mathematics curriculum that not only caters to the diverse needs of our pupils but also sets high expectations for their academic achievement.

Where we have adapted White Rose:

Why we have adapted White Rose

Autumn

Rationale for adapting the White Rose Maths Scheme at Harris Primary Academy Beckenham Green in Autumn Term:

Extending the Geometry Unit in Year 1: By extending the geometry unit on shapes by one week, the aim is to provide pupils in Year 1 with more time to explore the properties of 2D shapes through manipulatives and physical representations. This hands-on approach allows pupils to engage with shapes in a tangible way, fostering a deeper understanding of their characteristics and properties. By giving them additional time to manipulate and interact with shapes, pupils can develop a stronger foundation in geometry, which will benefit their mathematical understanding as they progress to more complex concepts in the future.

Extending the Number Place Value Unit in Year 3: Year 3 is the first time pupils are introduced to numbers up to 1000. To ensure their success in the rest of the number curriculum, it is crucial for pupils to have a secure understanding and conceptual knowledge of numbers to 1000. By extending the number place value unit by one week, pupils are provided with more time to work with concrete resources such as base 10 and place value counters. These hands-on materials allow pupils to visualize and manipulate numbers, helping them develop a strong foundation in place value. Furthermore, incorporating pictorial representations such as part-part-whole models allows pupils to bridge the gap between concrete and abstract methods, facilitating a smoother transition in their learning.

Extending the Multiplication and Division Unit in Year 4: Multiplication and division are fundamental operations in mathematics, and in Year 4, pupils are introduced to more advanced concepts within these operations. By extending the multiplication and division unit by one week, pupils have additional time to focus on mastering their multiplication facts up to 12 x 12 and their inverse facts. This extended period of practice ensures that pupils have a solid foundation in these basic facts, which is essential for their success in more complex mathematical problems. Additionally, introducing the short-written method for multiplying 3 digits by 1 digit allows pupils to develop their conceptual understanding of this method. By using place value counters and base 10 materials, pupils can visualize and manipulate numbers, facilitating a deeper understanding of the multiplication process.

In summary, the adaptations made to the White Rose Maths Scheme in Autumn Term at Harris Primary Academy Beckenham Green are aimed at providing pupils with additional time and resources to deepen their understanding of key mathematical concepts. By extending units in geometry, number place value, and multiplication and division, pupils are given the opportunity to engage with manipulatives, physical representations, and pictorial models, fostering a strong conceptual foundation in these areas. This approach ensures that pupils develop a secure understanding of fundamental mathematical principles, which will support their future learning and success in mathematics

Spring

Rationale for adapting the White Rose Maths Scheme at Harris Primary Academy Beckenham Green in Spring Term:

Introducing Number Fractions in Year 2: The academy has carefully evaluated its existing curriculum and identified areas where targeted sequencing of topics would aid in a smoother understanding of key mathematical concepts. Spring has been deemed an appropriate time to introduce fractions. This timing follows lessons on division, doubling and halving, allowing pupils to transfer their understanding of these concepts to fractions. Fractions are taught as parts, with pupils recognising halves and quarters, to build on knowledge acquired in the previous academic year where fractions of a quantity were introduced. This progression, from recognising fractions of objects to confidently finding fractions of numbers, is an essential step that requires substantial instruction using concrete, pictorial, and abstract approaches.

Extending the Decimal and Percentage unit in Year 5: The decision to extend the number unit (decimals and percentages) by one week has been taken to reinforce the conceptual understanding of percentages. This is the first exposure pupils have to percentages, and this additional time ensures they can relate percentages with decimals effectively.

Moving Ratio, Algebra and Extending the Fractions, Decimals and Percentage unit in Year 6: For Year 6, the academy has chosen to move the ratio topic to week 6, as this naturally follows learning fractions, decimals, and percentages. Furthermore, the year 6 pupils concluded the previous term with learning fractions. Teaching decimals next builds on this understanding by introducing another way of representing these parts of a whole. Decimals provide a practical extension of place value understanding from whole numbers to include numbers less than one. After grasping the concept of fractions as part of a whole, children will more easily comprehend the idea of a decimal as another representation of parts of a whole, now with a greater emphasis on the place value system. After understanding the separate concepts of fractions and decimals, pupils are well-prepared to learn about the interconnections between fractions, decimals, and percentages. The understanding that fractions, decimals, and percentages are different ways of expressing the same part-whole relationship is easier to grasp once the individual concepts are firmly understood. One major part of achieving mastery in these areas is the ability to convert fluently between fractions, decimals, and percentages. The progression from fractions to decimals and then to percentages helps reinforce the necessary skills to perform these conversions. Extending the fractions, decimals, and percentages unit by an extra week allows for an embedded knowledge base to be established. This understanding is fundamental for comprehending the concept of ratio, as it involves comparing parts to other parts and proportion, which compares parts to the whole. We have opted to move the algebra unit to the summer term due to its complexity and the necessity to provide a solid foundation before pupils transition into the KS3 curriculum. This rearrangement allows pupils ample time to grasp the intricate nature of algebra, aiding in their ability to engage with higher-level mathematics effectively.

In conclusion, the adaptation of the White Rose Maths scheme of learning is a well-thought-out approach to support pupils' progression and understanding of crucial mathematical concepts. It demonstrates Harris Primary Academy Beckenham Green’s commitment to providing high-quality maths education that is cognizant of the learning needs and capabilities of its pupils.

Summer

Rationale for adapting the White Rose Maths Scheme at Harris Primary Academy Beckenham Green in Summer Term:

Extending the Fraction Unit in Year 1: In Year 1, extending the unit on fractions by focusing more on finding fractions of a quantity will help build a stronger foundation in our pupils' understanding of this key concept. This progression from recognising fractions of objects or shapes to identifying fractions of quantities strengthens mathematical comprehension at an early age and helps to ensure that the learning objectives are effectively met.

Introducing Problem Solving and Consolidation in Year 2: For Year 2, reducing the measure unit on time by one week has allowed us to introduce a problem-solving and consolidation unit. This key shift will reinforce our pupils' grasp on vital concepts before they sit for the KS1 SATs examinations, thereby providing them with an integrated understanding and improving their performance.

Accommodating Assessment weeks in Year 3 and Year 4|: Similarly, modifications in Year 3 and 4 have been made to coincide with our assessment week. Reducing the measure unit on money by one week in Year 3 and rescheduling the consolidation unit in Year 4 allows us to conduct a comprehensive review of our pupils' progress and learning, ensuring that they are on track with the curriculum.

Moving the Number (Decimal) and Measure (Converting Units) in Year 5: In Year 5, the rescheduling of the Numbers (decimals) unit to week 3 ensures that pupils have a solid understanding of this pivotal concept before progressing to Converting units of measure unit in week 6. By reducing the geometry shape unit by one week, we have been able to maintain our focus on core learning while accommodating the assessment week.

Introducing Algebra in Year 6: In Year 6, the inclusion of the Spring unit of Algebra in week 3 has been executed to provide access to this complex topic after most of the White Rose curriculum has been covered. This will not only enhance the pupils' understanding but also act as a robust transition to Key Stage 3 Maths.

Overall, these adaptations aim to create a more effective, targeted learning environment that prioritises student progress, catering to their needs and ensuring a more enriching and comprehensive educational experience.

Typical Daily Lesson

Individual classes all have different needs, and teachers often have individual styles therefore they need to be responsive to this in their teaching approach. Each lesson should begin with an arithmetic starter (times tables, counting, mental calculation strategies). Plenaries should be used where necessary to build on children’s understanding or in order to respond when and where misconceptions occur.

A typical lesson across the school might look like this:

Teach and partner talk: (20 minutes) – Here the teacher uses the teaching slides or other resources to give the children input, with plenty of opportunity to practise and discuss questions with their partners, apply their learning and understanding to mini-tasks, and clarify misconceptions (the teacher isn’t talking for 20 minutes!).

Extended partner practise: (15 minutes) – Here the children get the opportunity to have a go at the day’s new learning in what might be a game, a sheet with the same layout as your teaching, but with different numbers, some sort of physical resource that they will use to solve a problem. At this point, the teacher can move around the room, and assess how well the children have understood the learning. Include mini-plenaries where necessary.

Written task: (22 minutes) – Here the children are working independently to complete the task stickers, which, after the teach and talk, and partner practice, are accessible and understood by the children. Include mini-plenaries where necessary.

Impact: Task

When teaching a practical theory lesson, record the learning on a sheet with the LO, Date, Summary, Photo and PPQ (purple pen question). When children are completing a written task, this will typically be presented on four stickers for a lesson. Some units, like statistics, might need another format. Not all children will complete all stickers (sticker four is aimed at the top 3-4 children in the class). Early on in year 1, most will only complete one or two stickers. For ideas and support on making task stickers use the ‘primary task stickers’ folder. The lowest 20% should be carefully planned for – pre-empting any misconceptions they may have during the lesson – in order that they are able to access the learning through the use of manipulatives, TA and teacher support. The highest 20% should be appropriately challenged through higher level questioning (which should be evident on lesson plans) as well as through greater depth questioning, using mastery resources from NTETM and white Rose.

The stickers should follow a clear progression.

Problem solving

At the end of each unit of work, children’s understanding will be further assessed with a problem-solving task within a problem solving lesson, which will link to the skills they have acquired during the unit.

How will we judge the impact of the mathematics curriculum?

Teachers will use formative assessment during the lessons to inform them of what they should do next with their pupils and the progress they are making, which will allow them to understand how to support and extend the pupils appropriately.

Teaching staff recognise the difference between performance and learning and understand that pupil performance in the lesson today does not necessarily translate into the type of learning that will be evident tomorrow. As a result, the use of low stakes tests (in the form of spaced retrieval practice) enable staff to regularly assess what learning has been retained by pupils over longer periods of time. This also provides pupils with the regular opportunity of retrieving information from memory, which consequently facilitates learning.

This includes:

• Assessment of learning
• Pupil voice (WIL about maths)
• Challenge tasks
• End of unit assessment (Low Stakes Testing)
• Standards of learning in books
• Spaced retrieval practice (see below)
• WIL

Interrupting the forgetting- Making learning stick!

Children will take three standardised tests over the course of the year where gaps can be analysed, and trends identified on a class, academy and federation level. These assessments will address three elements of the curriculum: fluency, reasoning and problem solving.

Times Tables