## Intent

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The intent of the department curriculum is to ensure that all pupils are able to gain sufficient wide and extensive knowledge so that they are well prepared for the next stage of their education and can apply their mathematical knowledge in many subjects across the curriculum such as science, geography and computing. The Scheme of Work at Key Stage 3 is organised into distinct domains, but pupils should build on Key Stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems.

Decisions about progression are based on the security of pupils’ understanding and their readiness to progress to the next stage of their education. Pupils who grasp concepts rapidly will be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for the next stage of their education. Those who are not sufficiently fluent will be given the opportunity to consolidate their understanding, including through additional practice, before moving on. At KS3 pupils are taught in order to:

### Develop fluency

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots.
• Select and use appropriate calculation strategies to solve increasingly complex problems.
• Use algebra to generalise the structure of arithmetic, including formulating mathematical relationships.
• Substitute values in expressions, rearrange and simplify expressions, and solve equations.
• Move freely between different numerical, algebraic, graphical and diagrammatic representations.
• Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.
• Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

### Reason mathematically

• Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
• Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
• Identify variables and express relations between variables algebraically and graphically.
• Make and test conjectures about patterns and relationships; look for proofs or counter-examples
• Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
• Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
• Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

### Solve problems

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems.
• Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
• Begin to model situations mathematically and express the results using a range of formal mathematical representations.
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

The key concepts are extended further at KS4, so pupils are taught in order to:

Develop fluency

• Consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots {and fractional indices}.
• Select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π {and surds}, use of standard form and application and interpretation of limits of accuracy.
• Consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, {and expressions involving surds and algebraic fractions}.
• Extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities.
• Move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic, reciprocal, {exponential and trigonometric} functions.
• Use mathematical language and properties precisely.

Reason mathematically

• Extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically.
• Extend their ability to identify variables and express relations between variables algebraically and graphically.
• Make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments {and proofs}
• Reason deductively in geometry, number and algebra, including using geometrical constructions.
• Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
• Explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally.
• Assess the validity of an argument and the accuracy of a given way of presenting information.

Solve problems

• Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts.
• Make and use connections between different parts of mathematics to solve problems.
• Model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions.
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem.

Together, the mathematical content set out in the KS3 and KS4 scheme of work covers the full range of material contained in the GCSE Mathematics qualification. Wherever it is appropriate, given pupils’ security of understanding and readiness to progress, pupils are taught the full content set out in this programme of study for KS4. The more able pupils are offered an extra qualification which is called GCSE Further Mathematics. This qualification places an emphasis on higher order technical proficiency, rigorous argument and problem-solving skills. It gives high achieving students an introduction to AS level topics that will help them to develop skills in Algebra, Geometry, Calculus, Matrices, Trigonometry, Functions and Graphs.

These skills are taken much further at KS5 when they start their A Level course in Mathematics and Further Mathematics. This increase of knowledge and understanding of mathematical techniques and their applications also support the study of other A levels, provide excellent preparation for a wide range of university courses, lead to a versatile qualification that is well-respected by employers and higher education. Students taking Further Mathematics overwhelmingly find it to be an enjoyable, rewarding, stimulating and empowering experience. It is a challenging qualification, which both extends and deepens pupils’ knowledge and understanding beyond the standard A Level Mathematics. Students who study it often say it is their favourite subject. For someone who enjoys mathematics, it provides a challenge and a chance to explore new and more sophisticated mathematical concepts. As well as learning new areas of the compulsory units of core pure mathematics, the pupils are given the opportunity to deepen their understanding further of the more challenging applications of mathematics units in mechanics and statistics. Their understanding of the overall combinations of the Further Mathematics units make the standard A Level topics seem easier and the challenge of solving some of the complicated problems help to develop areas of the brain untouched by other subjects. Some of the new topics such as matrices and complex numbers are vital in many STEM degrees. Some prestigious university courses require the pupils to have a Further Mathematics qualification and others may adjust their grade requirements more favourably to students with Further Mathematics. The options we select for the students will put them even in a stronger position.

The Mathematics curriculum has been designed to ensure that it is accessible to all students. Teachers ensure that the needs of pupils with SEN are met to enable them to access the Mathematics curriculum and make the most of their abilities. All staff are aware of the SEN pupils they teach and have made provisions for them in their lessons. SEN pupils in the Mathematics department perform well relative to their peers. There have been some notable SEN pupils who have performed at the highest possible level, achieving Grade 9 at GCSE Mathematics and A* at A-Level Mathematics and Further Mathematics. SEN pupil’s needs are met in the department and they are able to achieve their best.

Mathematics department staff model the correct Mathematical vocabulary in lessons and ensure that the students use the correct Mathematical vocabulary whenever it is required. If students make spelling or grammatical errors, these are corrected and explained to the students to ensure the highest possible standards of literacy are met. When talking to our pupils regarding Mathematics, they will tend to use the correct Mathematical terminology in their explanations. This shows that it has become embedded learning from the curriculum they have followed and the teaching and assessment they have received.

## Implementation

At Key Stage 3 schemes of work are based upon the new Key Stage Curriculum for Mathematics.  The Mathematics department has implemented the new changes to the National Curriculum and has a large number of resources in addition to the published text books to enrich students’ learning of mathematics. As a result, the department decided to:

• Invest on new quality textbooks and other electronic resources for all students in KS3. Each student has a textbook in class and has access to the electronic versions at home. My Maths and other commercial packages are very well used by most teachers and students.
• To change the termly assessments in Years 7 to 9 in order to meet the new changes.
• Use the new GCSE grading system from Year 7 to Year 11 from 2015.
• Encourage the students to be more independent and more resilient.
• Focus on depth of understanding rather than working through content.
• Teach pupils how to connect new knowledge with existing knowledge in order to develop their understanding further. To ensure that pupils develop fluency and unconsciously apply their knowledge. To nurture confidence and raise achievement we constantly focus on the 10 Key Principles of Progress in Mathematics at KS3 and beyond. They are:
• Fluency
• Mathematical Reasoning
• Multiplicative Reasoning
• Problem Solving
• Progression
• Concrete-Pictorials-Abstract
• Relevance
• Modelling
• Reflection

The department puts a great emphasis on KS3, as explained above, and its importance for students to be successful in mathematics later. The assessments and grading system used make the transition from KS3 to KS4 very smooth, almost unnoticed! We decided to increase the number of classes in Year 9 from 6 to 8 and the number of periods from 7 to 8. Year 7 and 8 classes have seven periods and the length of a period is 1 hour. We also decided to increase the curriculum time at KS4 time from 6 periods a fortnight to 7 and then to 8 for GCSE Mathematics prior to the start of the new GCSE in September 2015. This increase was essential for the delivery of the new syllabus due to increase in content and level of challenge. We also increased the number of classes from 6 to 8 allowing learning to be structured and paced most appropriately.

Current topics taught are:

Year 7

Analysing and displaying data, number skills, equations, functions and formulae, fractions, angles and shapes, decimals, equations, multiplicative reasoning, perimeter, area and volume and sequencing and graphs

Year 8

Factors and powers, working with powers, 2D shapes and 3D solids, real life graphs, transformations, fractions, decimals and percentages, constructions and loci, probability, scale drawings and measure and graphs

Year 9

Powers and roots, quadratics, inequalities, equations and formulae, collecting and analysing data, multiplicative reasoning, non-linear graphs, accuracy and measures, graphical solutions, trigonometry and mathematical reasoning.

Year 10 and 11

Number, algebra, interpreting and presenting data, fractions, ratio and percentages, angles and trigonometry, graphs, area and volume, transformations and constructions, equations and inequalities, probability, multiplicative reasoning, similarity and congruence, equations and graphs, proof, vectors and geometric proof and proportion and graphs.

Year 12 and 13 (A Level Mathematics)

Pure Mathematics – Algebraic methods, functions and graphs, circles, exponentials and logarithms, sequences and series, the binomial expansion, trigonometry and modelling, parametric equations, calculus, numerical methods and vectors.

Statistics – Data collection, measures of location and spread, representations of data, probability, statistical distributions, hypothesis testing, regression and correlation and the normal distribution.

Mechanics – Modelling in mechanics, constant and variable acceleration, forces and motion, moments, projectiles and application of forces.

Year 12 and 13 (Further Maths)

In addition to the A Level Mathematics units, the Further Mathematics pupils will study:

Core Pure Mathematics – Complex numbers, roots of polynomials, volumes of revolution, matrices, linear transformations, proof by induction, series, methods in calculus, polar coordinates, hyperbolic functions and differential equations.

Further Mechanics 1 – Impulse and momentum, work, energy and power, elastic strings and springs, elastic collisions in one and two dimensions.

Decision Mathematics 1 – Algorithms, graphs and networks, algorithms on graphs, the route inspection problem, the travelling salesman problem, linear programming, the simplex method and the critical path analysis.

In Year 7 pupils are taught Mathematics as a form. In Years 8 and 9 there are four sets in each half grouped based on Mathematical ability.  In Years 10 and 11 pupils are divided into two parallel groups set according to their Mathematical ability. All groups are studying GCSE Mathematics and the more able will study GCSE Further Mathematics too.  The sets into which pupils are placed are dependent upon their work throughout the year and their performance in the end of year examinations.  No setting takes place in Years 12 and 13.

Whilst there is no prescribed model of teaching, teachers explain clearly, support independence through worked examples and assess regularly, providing feedback on how to improve through a variety of mechanisms. Knowledge and Skills are transferred to pupils’ long term memories, through the activities undertaken, through over-learning that takes place and through the structures and sequencing of learning over time.  This will allow pupils to become better at thinking logically and analytically. Through solving problems, pupils develop resilience and are able to think creatively and strategically. The writing of structured solutions, proof and justification of results help them to formulate reasoned arguments. The pupils will have as a result excellent numeracy skills and the ability to process and interpret data. Homework and class work is regularly scrutinised to ensure a pupil is progressing appropriately and acted upon accordingly. Investigational work is used too to assess individual and group work and the ability to present communicate mathematical ideas, understanding and results.

There are termly assessments for all year groups from Year 7 to Year 13 which are taken under examination conditions. This is to ensure that pupils regularly retrieve the information learned. Thorough feedback is given to pupils to check understanding effectively, and identify and correct any misconceptions. Extension tasks for all, but in particular for the more able are used to ensure that pupils embed key concepts in their long-term memory and apply them fluently. There are also end of year examinations for all year groups. The results of these assessments are used to help pupils embed knowledge and use it fluently and assist teachers in producing clear next steps for all pupils.

All pupils in Year 7, about 60 pupils in each of Years 8 to 11 and all the pupils who study A Level Mathematics in Years 12 and 13 participate in the yearly UK Maths Challenges. These mathematical enrichment activities which are organised by the UKMT give the opportunity for Years 7 to 13 pupils to participate in three individual national challenges. A number of students from each challenge usually qualify to a follow-on Olympiad round and take part in mentoring schemes and summer schools which are aiming at high performing pupils. Trips are organised for some pupils from each challenge to participate in regional competitions.

The department plays a key role in the school’s engagement with several different partner schools across Europe through Erasmus+ projects to create an array of interesting international learning opportunities for our pupils. We place a strong emphasis on delivering international education across a broad curriculum, raising students’ awareness of different cultures and social conditions through well-planned activities, some of which draw global learning into STEM based projects. This involves taking pupils in trips to visit our partner schools and welcoming students to visit our school and participating in a variety of activities.

## Impact

• Students in all Key Stages enjoy studying Mathematics, which is evident through their behaviour and attitude in lessons, quality of work in their books, lesson observations and the regular pupil surveys.
• The curriculum helps the students to understand mathematics and mathematical processes in ways that promote confidence, foster enjoyment and provide a strong foundation for progress to further study.  It extends their range of mathematical skills, techniques and enhances their understanding of the coherence and progression in mathematics and how different areas of mathematics are connected.
• The impact of the curriculum will be seen through pupils gaining an extensive amount of knowledge and skills which enable them to access the next steps in their education and life. This is evidenced through the excellent results in public examinations. The GCSE results for the first examination of the new curriculum put the Mathematics Department in the top 1% nationally with a Progress 8 of 1.17. The average Progress 8 has 0.95 in the last three years.  This is clear evidence about the successful teaching strategies used by the department to embed key concepts and knowledge to pupils’ long-term memory and apply them fluently including SEND and disadvantaged pupils.
• The impact of the curriculum is also seen through the popularity of the subject at Key Stage 5. A large number of students study A Level Mathematics as well as A Level Further Mathematics many of whom go on to study the subject or subject related disciplines at some of the top universities. In 2018, 10 students decided to study Mathematics, 11 decided to study Engineering, 8 decided to study Accounting and Finance, 5 decided to study Computing and 13 decided to study Economics at university. In total, 47 (over 27%) of the students went on to study mathematics or related subjects at university. This is due to students’ attitudes towards mathematics, their on-going engagement with the subject and the quality of increasing mathematical competence at GCSE.
• The Mathematics curriculum also helps the students to take increasing responsibility for their own learning and the evaluation of their own mathematical development.  They are encouraged to become responsible citizens; this is achieved through applying mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general.

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