Our mathematics curriculum develops all students into confident and fluent mathematicians, equipped with strong reasoning and problem-solving skills and able to navigate successfully the numerical world around them.

We are ambitious for, and have high expectations of, all of our students and know that every student can experience success in mathematics through careful sequencing of the curriculum and high-quality, research-informed teaching and learning. We believe that every student at Paddington, regardless of prior or current attainment, has the right to access the centuries-old, rich body of mathematical knowledge, from Pythagoras’ theorem through to proportional reasoning. Our consistent use of explicit instruction and systematic retrieval practice across all classes ensures all students make progress in mathematics.

We recognise that rapid and accurate recall and application of mathematical knowledge and standard techniques (‘fluency’) forms the foundation of student success and confidence in the subject. Therefore we ensure that our students systematically acquire declarative and procedural knowledge so that they are set up for long-term success in mathematics. Our curricular sequencing provides opportunities to revisit concepts in mathematics and our lessons provide opportunities for students to go beyond fluency towards applying their conditional mathematical knowledge to more complex problem solving and conjecture. Through the development of strong reasoning and problem-solving skills, we want our students to appreciate the beauty and power of mathematics. Extension opportunities such as the UKMT Maths Challenges are provided at all key stages.

Mathematics is essential to everyday life and almost all forms of employment. Our mathematics curriculum therefore also aims to equip our students with the strong financial literacy and the confidence to engage with data needed to lead a well-informed and fulfilled life. It also empowers our students to work in a diverse range of fields including engineering, physics, architecture, medicine and business.

**Year 7**

Much of Year 7 focuses on developing students’ proficiency in number and basic geometry and algebra. When students join Paddington, they start by looking at place value and our base 10 number system, including rounding and working with the four operations. Students then have the opportunity to apply the four operations to problems involving the area of rectangles, triangles and parallelograms. We prioritise developing students’ automaticity of number facts at the start of KS3, which supports them with topics including calculating with decimals, working with fractions and negative numbers. Students continue their exploration of geometry by looking at angles and measure, including the properties of 2D shapes and symmetry. Students are also introduced to algebra, with a focus on manipulating expressions, and basic probability.

**Year 8**

At the start of Year 8, students look at the properties of numbers, including prime factors, square and cube numbers, and roots. They build on their work in Year 7 by applying negative numbers and fractions to the four operations, with increased focus on the order of operations. Students revisit their knowledge of algebra and have the opportunity to build on this by solving equations. Students expand their awareness of place value, rounding and estimation by looking at significant figures, before learning about angle properties and angles in parallel lines. Having learnt about the area of rectilinear shapes in Year 7, students go on to look at circle geometry and the area of compound shapes in Year 8, including unit conversion. Towards the end of Year 8, students learn about speed and distance-time graphs, percentages, ratio, proportion, volume, surface area and comparing and analysing data.

**Year 9**

Students begin Year 9 learning about coordinates and linear graphs. They revisit and build on their knowledge on angle rules and parallel lines by learning about angles in polygons. They look at place value in greater depth when converting to and from standard form. Students also look at more complex expansion and factorising, as well as forming and solving simultaneous equations, working with inequalities and the laws of indices. Students extend their geometrical reasoning, learning about Pythagoras’ Theorem and transformations, before finally developing their knowledge of probability.

**Year 10**

In Year 10, students build on knowledge and skills developed at Key Stage 3 in a range of fundamental mathematical topics, allowing them to develop their reasoning and problem-solving skills. For example, understanding of worded proportion problems at Year 8 and Year 9 supports students’ ability to solve algebraic proportion in Year 10. Other algebraic content taught in Year 10 includes graphs, algebraic fractions, rearrangement of formulae, sequences, simultaneous equations and indices. Success with percentages in Year 8 leads to fluency with compound growth and decay in Year 10. Students also look at ratio in greater depth including with algebra, as well as compound measures, surds, bounds, trigonometry, probability, Venn diagrams and averages.

**Year 11**

In addition to a core body of content taught to all students, more highly attaining students in Year 11 are taught additional mathematical content on the Higher tier; more advanced topics, such as estimating gradient and area under a curve, form a solid foundational understanding for calculus in Key Stage 5. Students in Year 11 begin by looking at geometry, including area, volume, constructions, loci, bearings, similarity, transformations and circle theorems. With circle theorems, for example, students have the opportunity to revisit concepts they have learned in previous years, such as angles, in greater depth and complexity. Students learn how to solve quadratic equations and inequalities, as well as looking at complex vector problems, non-right-angled trigonometry, functions, proof and graph transformations – all of which support their learning at Key Stage 5. An additional Level 2 Further Maths qualification is also taught to the highest attaining students.

**Year 12**

Mathematics in Year 12 and Year 13 at Paddington builds on students’ prior knowledge gained at Key Stage 4 such as coordinate geometry, trigonometry and sequences and series, deepening their understanding and connecting different aspects of mathematics. Fundamental new concepts are introduced such as calculus. There is a strong emphasis on the use of logical deduction to solve problems, and the course is embedded with opportunities to apply their knowledge to the real world. The course is divided into pure and applied mathematics, providing students with statistical and mechanical methods. There are significant opportunities for extension provided to students, along with preparation for university admissions tests requiring MAT and STEP papers.

Students in Year 12 study a wide range of topics including coordinate geometry (straight lines, quadratics and circles), vectors, binomial expansion, trigonometry, circles, exponentials and logarithms, and sequences. Many of these topics are developed from the Key Stage 4 curriculum, but are studied in much more depth. In applied mathematics, students are introduced to various new concepts, such as hypothesis testing and variable acceleration problems which rely on their pure knowledge of binomial expansion and calculus respectively.

**Year 13**

Students in Year 13 deepen their knowledge of certain pure topics such as advanced trigonometry, numerical methods, calculus and functions. In mechanics, they build on Year 12 foundations to study static and dynamic bodies in more depth, and in statistics will study regression, conditional probability and the normal distribution.

Further mathematics (an additional A level) introduces new branches of mathematics within which students begin to learn the deeper connections underlying mathematics, and to provide students with more sophisticated tools to understand the world around them. Students taking A Level further mathematics study all the single maths content in Year 12 and then all the further maths content in Year 13. In Year 13 they study a significant amount of advanced pure mathematics, including complex numbers, differential equations, polar coordinates, matrices and hyperbolic functions. In further statistics they widen their awareness of different distributions (binomial, Poisson, geometric, negative binomial, normal) and use these to test and evaluate real-world hypotheses. Finally in further mechanics they study more varied situations such as elastic and inelastic collisions in one and two dimensions.

Throughout both pure and applied maths there is a consistent focus on modelling. For example, students apply their knowledge of trigonometric functions to model wave-like behaviour such as a daily tide pattern. This provides ample opportunity for students to learn advanced mathematics and simultaneously see how what they are learning applies in their everyday life. Our maths and further maths curricula in Key Stage 5 are therefore both academically rigorous and highly rewarding for our students.