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:

- 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.

- 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.

- 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.

### At KS4 pupils are taught in order to:

- 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.

- 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.

- 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.