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Maths
Knowledge Organisers - for the attention of parents and students
Thamesview Curriculum Intent and Implementation
As a community we have the highest aspirations for all our students, regardless of their background, and are ambitious in the breadth and depth of knowledge we want our students to gain in their subjects.
Our Curriculum has been designed using a Trivium framework encouraging students to Know Well, Think Well and Communicate Well. Students need to develop rich foundational knowledge, be able to think and deepen their understanding through questioning, discussion and debate. Be able to communicate and express their learning in a variety of forms.
As Tom Sherrington states in The Learning Rainforest, “Knowledge is key in a curriculum but so too is the ability to develop capacity to question and challenge, to engage in dialect of the trivium*, to contribute to debate and conversation.”
Thamesview seeks to go beyond a curriculum based on knowledge alone, to a curriculum that builds thought, expression and character.
The Trivium as outlined by Martin Robinson has three parts for students;
Knowledge (AKA Grammar):
Learning involves connecting new information with what is stored in our long-term memory. Therefore, limited prior learning can limit our future learning. Development of a rich knowledge base essentially makes us more intelligent by creating more branches for new learning and ideas to connect with. Without much foundational knowledge of a topic it is difficult for learners to form their own ideas and to work independently. Teachers have a vital part to play in leading the learning process to ensure that conceptual understanding progressively builds over time. The curriculum must be coherently constructed and sequenced across subject disciplines to achieve this. The development of a broad vocabulary is also a key part of this pillar. Thamesview places high importance on every subject area having a coherent and strong approach to successfully improving and strengthening disciplinary literacy within our school. This work is based on the research of the EEF and Alex Quigley.
Elements of Teaching & Learning related to Knowledge:
- Clarity through explanations & modelling
- Responsive teaching strategies
- Repetition & spaced retrieval practice
- Regular low level stakes assessment to identify and close gaps & address misconceptions.
- Disciplinary Literacy strategies to secure and cement knowledge for learners.
- Relevant Rosenshine principles of effective implementation – Thamesview School expects all staff to know and implement Rosenshine principles in curriculum implementation.
Exploration (AKA Dialectic):
Simply knowing things is insufficient. Encouraging our students to think, debate and consider alternative views is a vital part of the education we provide. Knowing things without the skill to explore knowledge further is of limited value to our students in the wider world. We encourage our students at Thamesview to be respectful of others, to be resilience when learning or when ideas are challenging, to be ambitious for themselves, seeking to take knowledge beyond the just knowing and retaining of facts.
Elements of Teaching and Learning related to Exploration:
- Real world experience, challenges and experimentation
- Debate, critical thinking & deep questioning
- Problem solving & reflection
- Character Education
- Relevant Rosenshine principles of effective implementation – Thamesview School expects all staff to know and implement Rosenshine principles in curriculum implementation.
Communication (AKA Rhetoric):
We want our students to leave Thamesview confident communicators. Explaining ideas publicly strengthens knowledge. This pillar is not, however, limited to public speaking. Any performance involves communication, whether it be a Sporting or creative performance, essay, speech or exhibition of work. These performances help to develop a range of qualities that prepare our learners well for their future lives. Ensuring all our learners can communicate in a clear, articulate and convincing manner, in a variety of ways, is vital.
Elements of Teaching & Learning related to Communication:
- Public performance & extended writing
- Presentations, exhibitions and displays.
- Demonstrating Thamesview Character values.
- Relevant Rosenshine principles of effective implementation – Thamesview School expects all staff to know and implement Rosenshine principles in curriculum implementation. At Thamesview we aim to build our curriculum around five key principles.
- A curriculum that has Coherence for students – explaining to them what they are learning and when and why.
- A curriculum that provides all students with a wide and deep range of Experience(s).
- A curriculum that equips students with Knowledge and the ability to use it, develop it and be inspired by it.
- A curriculum that Expands horizons for students.
- A curriculum that represents all creating a sense of Belonging
Thamesview Sixth Form Curriculum Intent and Implementation
Intent:
At Thamesview 6th Form, our goal is for all students, staff, parents and carers to develop a sense of a shared ambition for success, and the resilience to achieve that ambition. Our shared vision is for all students to leave Thamesview 6th Form as knowledgeable, respectful global citizens who are fully prepared to overcome all challenges that come their way in a rapidly changing society. In achieving this, we consider that wider opportunities in the 6th form are essential to the holistic development of our students. Students have the opportunity to become part of the Student Leadership Team as well as being part of an active academic and pastoral mentoring programme that supports students in the lower school.
At KS5 we offer a varied curriculum made up of A levels, Vocational courses, and the Extended Project Qualification. Students are able to commence a Foundation Pathway should they fail to meet the Level 3 pre-requisites. This breadth of choice allows students to specialise and focus their learning on three key areas of study and provides access to higher education, apprenticeships and straight-to-work options. In the 6th Form, we provide high quality careers guidance and experiences to ensure that students embark on the correct programme of study or employment pathway for them. All students will be exposed to advice and guidance from our Careers Advisor.
We aim to map our values and vision across the KS5 curriculum. To support this, each department has a clear statement of its curriculum intent, implementation and impact; additionally, each department has its own curriculum map.
“Students are mature in how they work and behave. They are keen to go to university and, with good careers advice, have begun to think carefully about their futures. They are good role models for younger pupils.” (Ofsted, 2018)
At Thamesview 6th Form, our intent is trivium. As outlined by educationalist Martin Robinson, we expect all students to “know well, think well, communicate well”.
Know well: To achieve this, all 6th Form students will be exposed to the best knowledge in their curriculum. Schemes of Work have been carefully designed to ensure that students are able to build on prior learning and knowledge. In most cases, this will be done through ‘do it now’ activities that are prominent in lessons at KS5. Core knowledge is identified and embedded in the fabric of teaching and learning so that students are able to articulate what needs to be retained in their long-term memory. Where possible, hinterland, substantive and procedural knowledge will be utilised to support the core knowledge taught; this will often include trips outside of the classroom, processes and narratives to reinforce understanding. As a member of the 6th Form, students are encouraged to build their resilience for their chosen subjects and read outside of the curriculum; all students will be given a core reading list and a wider reading list for their chosen subject area; this will enable the application of subject terminology to specific tasks and case studies where applicable.
Think well: At Thamesview 6th Form, questioning is planned in line with the curriculum and the core knowledge required. As preparation for life after 6th Form, students at KS5 are encouraged to critically explore ideas and concepts beyond the recollection of facts. To demonstrate ambition, students are encouraged to ignite debate and discussion amongst their peers and demonstrate that they are aware of other perspectives and viewpoints. Often, teachers will use pedagogic models that encourage students to be more independent in their thinking and learning, this will often include working on the foundations of Vygotsky’s Zone of Proximal Development and Bruner’s scaffolding techniques.
Communicate well: At KS5, assessments are either low stake demonstrating retrieval of knowledge or cumulative end of unit assessment. At level 3, assessments will tend to be extended pieces of writing that require analytical and evaluative skills. Schemes of work have been carefully developed to ensure that any mis-conceptions are planned for. Furthermore, communication is also done in the form of articulate debates which enthuse and stimulate discussion around a specific topic area.
Our shared vision is for all students to leave Thamesview 6th Form as knowledgeable, respectful global citizens who are fully prepared to overcome all challenges that come their way in a rapidly changing society- whether that be for Higher Education or the workplace. We deem it important that students can leave with the necessary skill set to analyse, evaluate and communicate effectively. In achieving this, we consider that wider opportunities in the 6th form are essential to the holistic development of our students. Students have the opportunity to become part of the Student Leadership Team as well as being part of an active academic and pastoral mentoring programme that supports students in the lower school.
Implementation:
At Thamesview 6th Form, students can expect a high quality education that is centred on the individual needs of each student. We believe passionately that every young person, regardless of social background or previous experiences, deserves the chance to succeed in education and that is why we expect high standards of effort and behaviour from all of our students. Our curriculum implementation ensures that each student is able to access a curriculum pathway that enables them to make the best progress.
We offer three pathways:
- Pathway A that is made up of Level 3 courses and the Extended Project Qualification (2 years)
- Pathway B mirrors Pathway A but allows students to resit their Math and English in dedicated timetabled lessons.
- Pathway C is a foundation year, best suited for those that have not met the pre-requisites of the Level 3 courses (1 year)
We aim to shape and evolve our students to be as independent in their studies as they can possibly be and prepare them for life after the 6th Form. It is imperative that students are able to take responsibility for their own learning and complete all activities that are required in class and also sat as homework. All lessons will be planned in line with the school’s teaching and learning policy and teachers will plan for regular summative and formative assessment points. As a member of the 6th Form, students will be required to abide by the school rules (where applicable) and adhere to the dress code.
All students will be given the chance to partake in Year 12 work experience. Additionally, students will be given plenty of opportunities to attend University open days and career/ apprenticeship fairs. These experiences will help prepare our students for life after Thamesview 6th Form.
“I’m very impressed with the standard of lessons being delivered with a variety of tasks” (Parental feedback, 2021)
At Thamesview 6th Form, implementation is centred around Rosenshines ‘Principles of Instruction’. It is important that in all lessons, a review of previous learning takes place; in most cases this will be done in line with low stake assessments and the ‘do it now’ activities. New material will be presented in small, manageable steps in line with the scheme of work and the specification, whereby questions will be asked to ensure that any misconceptions are addressed. At KS5, questions will tend to be analytical and evaluative in nature so that the student is able to reflect on cause and consequences. At Thamesview 6th Form staff and students have many resources available to enable them to model key concepts and pieces of work, whether this be technological or pedagogic, students can use these processes to help guide them through their work. As previously mentioned, scaffolding techniques are used to enable students to reach their full potential. Where possible, independent practice is encouraged whether this be in the form of wider reading, peer teaching or research specific tasks.
Impact:
Results have been improving year on year since opening in September 2017. We have achieved a 100% pass rate for each cohort and surpassed Kent averages. 100% of our students who made University applications received entry to their first choice universities. This is due to the hard work and dedicated of both students and staff where we strive for excellence on a daily basis.
From a Teaching and Learning perspective, at Thamesview 6th Form there are a range of measures used to evaluate the impact of the curriculum. These include:
- Progress measures using formative and summative assessment
- Observation of pupil engagement during drop-ins, lessons observations and learning walks
- Deep Dives carried out in conjunction with partner Gravesham Schools
- Director led work scrutiny
- Reviewing attendance data
- Student/ parental surveys
- Destination data and follow up calls to students, parents and carers to ensure transition to University, apprenticeship or employment has been successful.
We aim to map our values and vision across the KS5 curriculum. To support this, each department has a clear statement of its curriculum intent, implementation and impact; additionally, each department has its own curriculum map. Schemes of Work will be reviewed year on year so that necessary amendments can take place if need be.
Student success stories (2020):
“Nga Siene received the equivalent of two A* and one A at A-Level is studying International Business at Greenwich University”
“Alex Austin received the equivalent of two A* and one A at A-Level is studying Film and Screen Arts at Plymouth College of Art”
“Jamie Ward received the equivalent of two A* and one A at A-Level is studying Law at Canterbury University”
“Jamie Rafferty received the equivalent of one A*, one A and one B at A-Level is studying Digital Music and Sound Art at the University of Brighton”
“Molly Maxted received the equivalent of two A* and is studying Law at Greenwich University”
Subject Curriculum Intent and Implementation
Curriculum Intent for Mathematics. We believe that Mathematical intelligence is expandable, and that every child can learn Mathematics, given the appropriate learning experiences within and beyond the classroom. Every pupil is entitled to master the key mathematical content for their age, by receiving the support and challenge they specifically need. Our intent is to deliver an ambitious, connected curriculum that is accessible to all pupils allowing them to become fluent in the fundamentals of mathematics and to be able to reason and to solve problems. Our curriculum embraces these National Curriculum aims, ensuring they have the necessary skills and knowledge for them to reach their highest potential beyond the time they spend with us. In our KS3 curriculum, we start with Algebra as this is key to the secondary curriculum as well as being comparatively new for pupils. The skills are carefully ordered, embedding the use of previous skills and using them to build new ones, making sure that topics are covered so pupils experience variety as well as consolidation. This is in line with our objective to develop pupils to think well. The fundamental idea behind our curriculum design is to support pupils to be able to perform simpler tasks so they can then move on to perform more complex tasks. Following on from that, every unit is taught in blocks and broken down further into small steps which are again sequenced in order of difficulty and dependency. We combine the best of both ‘mastery’ and ‘spiral’ approaches in our curriculum. It certainly follows many of the mastery principles – spending longer on topics to help gain deeper understanding, making connections, keeping the class working together on the same topic and a fundamental belief that, through effort, all pupils are capable of understanding, doing and improving at mathematics. But we also recognise that just spending a good chunk of time on a topic doesn’t mean that all pupils will ‘master’ it the first time they see it, and that they need to see it again and again in different contexts and in different years to help them truly develop their understanding on their journey to mastery, so we’ve built in the revisiting and reinforcing features of spiral curricula too. |
Links to Whole School Intent. When teaching Mathematics at Thamesview, we incorporate sustained levels of challenge through varied and high quality activities with a focus on fluency, reasoning and problem solving. This keeps us in line with the following three key principles:
Our practice highlights the importance of using core knowledge to embed the importance of deep understanding, by allowing pupils to represent concepts with concrete, pictorial and abstract forms wherever suitable.
We want students to think like mathematicians, not just do the maths. We believe that during the learning experience students should explore, wonder, questions, conjecture, experiment and make theories in order to guide their own journey. We believe that it is essential for pupils to develop mathematical thinking in and out of the classroom to fully master mathematical concepts.
We encourage pupils to use mathematical language throughout their maths learning to deepen their understanding of concepts. Each class is required to explore Mathematics in depth, using Mathematical vocabulary to reason and explain their workings. In order for this to be successful, we ensure that pupils are taught how to work with concrete, pictorial and abstract forms wherever suitable, thus teaching them to think well. In addition to this, they are taught to communicate well by explaining their choice of methods and showcase their reasoning skills. We teach that ambition, resilience and respect are often necessary steps in learning. We understand that the way pupils speak and write about mathematics has been shown to have an impact on their success in the subject. |
Curriculum Implementation for (List Department or subject here). At KS3 pupils take part in six one-hour lessons per fortnight and at KS4 it is eight one-hour lessons per fortnight, all taught but teachers who show a high level of skill, knowledge and enthusiasm for their subject. Interventions are offered for those pupils who need additional help, tailored to them by Math specialists. Learning is encouraged through a variety of teaching styles which is bespoke to individual classes and how they learn best. After any training, best practice is shared across the department to ensure pupils are making progress. We as a team are continuously developing the curriculum and the lessons and to use our SharePoint for any resources within our curriculum and also share any additional resources that they find. Tasks and lessons are well designed to meet the needs of pupils and all pupils are able to access and be successful in their learning. The department offers many enrichment opportunities for pupils to develop skills and enjoy Mathematics outside of the usual classroom timetable. These include: MathsWatch, Half-Term revision sessions and afterschool revision sessions. Throughout the curriculum, there are opportunities to link Maths to ‘real life’ applications and build the foundation for college, apprenticeship and further career opportunities. Pupils at Thamesview are set challenging but achievable targets. Throughout the year, KS3 are assessed on two formal occasions, but we also make use of informal assessments to monitor pupils’ understanding. Throughout KS4, pupils are formally assessed once every half term with two data points in the year. In all year groups students will complete a topic evaluation every six lessons. These are then followed by a feedback session where positive praise is highlighted in relation to what they’ve just studied, any misconceptions are addressed and a live model answer is presented before students can move on with a stronger understanding of their weaknesses. Achievements are well celebrated with golden tickets awarded to students which creates an atmosphere of success and high aspirations within the department. High expectations of achievement are evident and the quality of pupil work and steps of progress made at KS3 and 4 are relative to the pupils’ behaviour and effort put in. |
Links to Whole School Implementation. In line with the Rosenshine principles of effective instruction, we focus more on conceptual understanding as a department instead of procedural fluency. In order to do this, we present new material in small steps with student practise after each step. This method of teaching for mastery with the aim that pupils will acquire a deep, long-term, secure and adaptable understanding of mathematical concepts. Providing modelling is a key aspect of our day-to-day practise as well as being used to provide feedback to students after each assessment. After effective modelling, it is vital that we check pupils understand what has been taught and this is often done through asking a large number of questions to check responses of all students. We continuously strive to better ourselves and frequently share ideas and things that have been particularly effective. We take part in training opportunities and regional networking events such as PiXL, our local Maths Hub as well as with the Maths Advisor from The Education People. |
How Impact is measured within the department We aspire that a Thamesview Mathematician will have developed a bank of efficient and accurate skills that can be used effectively in their future endeavours. These will have been underpinned by the trivium concept so children understand rather than just do, and they are able to communicate effectively. Summative assessments are used as a diagnostic tool to ensure that teachers are adapting learning to meet the needs of all pupils and ensure any necessary interventions are targeted specifically to meet the needs of children. As a department we carry out various monitoring exercises to ensure that intent and implementation is being well met in all lessons. This can be in the form of pupil voice, through discussion and feedback, they can talk enthusiastically about their maths lessons and speak about how they love learning about maths. They can articulate the context in which maths is being taught and relate this to real life purposes. We also carry out book monitoring sessions were we look at the work that is produced in each class as well as visiting each class in action in order to share good practice and any developmental advice when it is needed. |
Schemes of work
Subject Core Knowledge Maps
Under Construction
Homework
Year |
Set Day |
Due Day |
Year 7 |
Wednesday |
Wednesday |
Year 8 |
Wednesday |
Wednesday |
Year 9 |
Wednesday |
Wednesday |
Year 10 |
Wednesday |
Wednesday |
Year 11 |
Wednesday |
Wednesday |
What is being studied each term
Assessment
Mathematics Department Assessment and Feedback Policy 22-23
Year 7
|
H1, H2, T1, T2 |
H3, T3, I band |
Term 2 |
Autumn Core Assessment (Set A) |
Autumn Foundation Assessment (Set A) |
Term 4 |
Spring Core Assessment (Set A) |
Spring Foundation Assessment (Set A) |
Term 6 |
Summer Core Assessment (Set A) |
Summer Foundation Assessment (Set A) |
Year 8
|
H1, H2, T1, T2 |
H3, T3, I band |
Term 2 |
Autumn Core Assessment (Set A) |
Autumn Foundation Assessment (Set A) |
Term 4 |
Spring Core Assessment (Set A) |
Spring Foundation Assessment (Set A) |
Term 6 |
Summer Core Assessment (Set A) |
Summer Foundation Assessment (Set A) |
Year 9
|
Paper |
Term 1 |
Calculator |
Term 2 |
Calculator |
Term 3 |
Non-Calculator |
Term 4 |
Calculator |
Term 5 |
Calculator |
Term 6 |
Non-Calculator |
Year 10
|
Paper |
Term 1 |
GCSE Paper Calculator |
Term 2 |
GCSE Paper Calculator |
Term 3 |
GCSE Paper Non-Calculator |
Term 4 |
GCSE Paper Calculator |
Term 5 (Mock) |
GCSE Papers Calculator & Non Calculator |
Year 11
|
Paper |
Term 1 |
GCSE Paper Calculator |
Term 2 (Mocks) |
GCSE Mock Set |
Term 3 |
GCSE Paper Non-Calculator |
Term 4 (Mocks) |
GCSE Mock Set |
Literacy
Year Group |
Objective |
Activities |
---|---|---|
Year 7 |
Develop mathematical vocabulary |
1. Vocabulary Building: Introduce and reinforce key mathematical terms through interactive activities such as word walls, vocabulary games, and discussions. |
Improve reading comprehension of math problems |
2. Problem-solving Tasks: Provide a variety of math problems that require reading comprehension skills, such as interpreting word problems, identifying key information, and formulating mathematical solutions. |
|
Enhance communication skills in mathematical reasoning |
3. Mathematical Discussions: Engage students in group discussions where they explain their reasoning behind mathematical solutions, justify their answers, and communicate mathematical concepts effectively to peers. |
|
Year 8 |
Expand understanding of mathematical notation |
1. Notation Exercises: Introduce new mathematical symbols and notation through guided exercises and practice activities. |
Develop skills in interpreting mathematical texts |
2. Text Analysis: Provide students with mathematical texts, such as proofs, theorems, and mathematical articles, and guide them through the process of interpreting and understanding the content, including identifying main ideas and supporting details. |
|
Foster critical thinking through mathematical literature |
3. Mathematical Literature Study: Introduce students to mathematical literature, including biographies of mathematicians, historical accounts of mathematical discoveries, and books on mathematical concepts, to promote critical thinking and deepen understanding of mathematical concepts. |
|
Year 9 |
Strengthen writing skills in mathematics |
1. Writing Tasks: Incorporate writing tasks into mathematics assignments, such as explaining mathematical concepts in written form, writing mathematical proofs, and composing reflections on problem-solving strategies. |
Enhance comprehension of mathematical concepts |
2. Concept Mapping: Use concept mapping techniques to help students visualize and organize mathematical concepts, relationships, and processes. |
|
Introduce mathematical research skills |
3. Research Projects: Assign research projects where students investigate real-world applications of mathematics, explore mathematical history, or delve into topics of personal interest, and present their findings in both written and oral formats. |
|
Year 10 |
Develop technical writing skills for mathematics |
1. Technical Writing Tasks: Guide students in writing technical mathematical explanations, and formal mathematical arguments, focusing on clarity, precision, and adherence to mathematical conventions. |
Enhance interpretation of mathematical diagrams |
2. Diagram Analysis: Provide opportunities for students to analyse and interpret mathematical diagrams, graphs, charts, and geometric figures, emphasizing the connection between visual representations and mathematical concepts. |
|
Encourage independent reading in mathematics |
3. Independent Reading: Encourage students to explore mathematics beyond the classroom by providing access to mathematical literature, including textbooks, articles, and online resources, and facilitating discussions on their reading experiences. |
|
Year 11 |
Prepare for standardized assessments |
1. Exam Practice: Provide practice materials for standardized assessments, including past exam papers, sample questions, and revision guides, and guide students through strategies for approaching exam-style questions effectively. |
Consolidate mathematical literacy skills |
2. Review and Reflection: Review key literacy skills covered in previous years and provide opportunities for reflection on growth and improvement. Encourage students to identify areas for further development and set goals for ongoing improvement in mathematical literacy. |
|
Apply literacy skills in real-world contexts |
3. Real-World Applications: Engage students in projects and activities that require the application of mathematical literacy skills to real-world problems, such as financial planning, data analysis, and decision-making in various contexts. |
Contacts for the department
Nomsa Tshuma | n.tshuma@thamesview.kent.sch.uk |
We understand that supporting your child's mathematical learning journey can sometimes feel challenging, especially if you're not feeling confident in your own mathematical skills. That's why we've compiled a list of helpful websites to assist you in supporting your child's mathematics education at home. You'll also find a detailed table outlining specific ways you can help your child flourish in mathematics, organised by year group and aligned with the White Rose Maths system.
These websites offer a wide range of resources, including instructional videos, practice exercises, interactive games, and printable worksheets, all designed to make learning mathematics enjoyable and accessible for both you and your child. Whether your child is struggling with a specific topic or simply looking for additional practice, these websites provide valuable tools to reinforce classroom learning and build confidence in mathematics.
We encourage you to explore these resources together with your child, taking advantage of the step-by-step explanations, interactive activities, and personalized learning features available. Additionally, the accompanying table provides specific guidance on how you can support your child's mathematical development at home, tailored to their year group and curriculum.
Remember, learning mathematics is a journey, and every step forward, no matter how small, is a step in the right direction.
If you have any questions or need further assistance, please don't hesitate to reach out to your child's teacher or school's mathematics department. We're here to support you and your child every step of the way.
Happy learning!
Warm regards,
Thamesview Mathematics Department