Mathematics Subject Overview
Philosophy for Teaching Mathematics
At St Mary’s the mathematics department equip students with the mathematical and numerical skills they need to be successful academically, whilst preparing them for life beyond the classroom. We believe that every student can be successful in mathematics and our goal is to ensure the best outcomes for all learners.
We have an ambitious mathematics curriculum which is rich in skills and knowledge. Our curriculum is under pinned by three key principles. In line with the aims of the KS3 National Curriculum, we believe all students should be able to reason mathematically, solve problems and be fluent with facts.
At St Mary’s we create mathematicians who think, act and speak with purpose and confidence. Teachers promote oracy and develop confidence by encouraging pupils to talk openly about mathematics and to explain their thinking. Staff and students use complex mathematical vocabulary to communicate their ideas and create arguments and conjectures.
We believe it is essential that students are fluent in the fundamentals of mathematics. We promote fluency through varied and frequent practice and by introducing increasingly complex problems over time. We use low floor, high ceiling tasks that enable students to be successful whilst stretching the more able. Students should feel confident in tackling both familiar and unfamiliar problems by using their knowledge and skills to break problems down into smaller steps. This approach is used in order to build resilience, deepen understanding and develop conceptual understanding.
Our pedagogy is underpinned by a mastery approach meaning we teach for understanding. We have a challenging spiral curriculum which bases future teaching on previous learning. Teachers clearly model mathematical procedures with consistency as agreed within the scheme of learning and calculations policy. This approach is consistent with the latest educational research.
Where applicable, teachers make links across units of work in order to emphasise the many connections between different mathematical facts, procedures and concepts to create a rich network of understanding. Lessons are well structured and teachers use carefully selected examples in order to model methods for pupils to practice. They ensure milestones, which lead to excellence, are broken down into smaller steps for each unit of work. Proportional time is spent developing deep knowledge of the key ideas that are needed to underpin future learning (progression of skills), guided by the scheme of learning. Pedagogy is based on the best available evidence (supported by Blackpool Research School) with a variety of teaching strategies used. Teachers predict difficulties learners may have in advance and plan to address potential misconceptions before they arise. If there are further difficulties within the lesson misconceptions are uncovered and addressed rather than sidestepped. Carefully selected manipulatives and representations are used to support mathematical understanding of concepts, enabling pupils to deepen understanding and use the mathematics independently.
All teachers have strong mathematical knowledge and have a clear understanding of our schemes of learning; they are knowledgeable of the mathematical journey pupils have already been on and continue to build on it, leading to success at GCSE and beyond. Teachers work towards the defined excellence for each unit of mathematics. The approach ‘find out what they don’t know and teach them it’ is embedded. Summative data is analysed at a fine grain size during DAFITAL which provides formative information, which is then used to inform further teaching. Alongside this, an efficient and continuous assessment for each unit or milestone are carried out with marking and feedback that informs future planning and addresses misconceptions.
Mathematics Video Help for Parents/Carers
KS3 Curriculum Map
Year 7 Overview
In Year 7 students will consolidate their numerical and mathematical capability from Key Stage 2. They will extend their understanding of the number system and make connections between number relationships and their algebraic and graphical representations.
Year 7 Topics
Numeracy – To ensure students are fluent in numerical calculations and problem solving to allow learners to be ready for the demands of the mathematical curriculum
Algebra – Model perimeter and area problems by translating them into algebraic expressions and simple equations. Use specific values to evaluate these expressions.
Year 8 Overview
Students will build on their Year 7 knowledge and begin to move freely between different numerical, algebraic, graphical and diagrammatic representations. They will begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Year 8 Topics
Number and Calculation – To apply knowledge of percentage multipliers, standard form and indices to solve increasingly complex number and practical problems.
Algebra – To draw straight line graphs and use them to solve algebraic equations, where the solution may not be a whole number.
Year 9 Overview
Students begin Year 9 with “crossover topics” which appear on both higher and foundation tier papers with students on a higher pathway engaging in more complex problems. Students build on their learning for GCSE to establish firm foundations for either tier at GCSE.
Year 9 Topics
Probability – To represent and interpret numerical data in two-way tables, frequency trees and Venn diagrams.
Number 1 – To use the product of primes to find HCF and LCM of two or more numbers. To solve money problems using exchange rates and reason mathematically to determine best value.
Algebra 1 – To solve any linear equations and manipulate equations to change the subject.
KS4 Curriculum Map
Over the next two years of studying the GCSE syllabus, students will investigate, discover, develop and consolidate their understanding of Mathematics. Students will explore key areas of mathematics such as: Number; Algebra; Ratio, Proportion and Rates of Change; Geometry and Measures; Statistics and Probability.
Year 10 Topics
Algebra – Solve linear inequalities and represent the solution set on a number line. Solve quadratic equations. Plot and interpret quadratic and cubic graphs.
Geometry (Triangles) – Find missing sides/angles using Pythagoras’ Theorem and Trigonometry.
Geometry (Circles) – Find the area and perimeter of circles, sectors and compound shapes.
Year 11 Topics
Proportion – Solve problems involving direct and inverse proportion, including graphical and algebraic representations.
Circle Theorems – Solve geometric problems and proofs using circle theorems.
Transformations – Use and describe multiple transformations. Understand congruence and similarity.
Graphs – Identify parallel and perpendicular lines
A Level Curriculum Map
Year 12 Topics
Indices – Use the laws of indices and perform essential algebraic manipulations.
Surds – Use and manipulate surds.
Quadratics – Solve a quadratic equation using various methods. Work with quadratic functions and their graphs.
Inequalities – Solve linear and quadratic inequalities. Interpret and represent linear and quadratic inequalities graphically.
Simultaneous Equations – Solve linear and quadratic simultaneous equations.
Graphs – Understand and use the equation of a straight line and other functions, including polynomials. Work with parallel and perpendicular lines. Use graphs to solve equations. Sketch the result of a simple transformation given the graph of any function y = f(x).
Circles – Understand and use the equation of a circle. Use the properties of chords and tangents for circle problems.
Algebraic Methods – Use algebraic division. Apply the factor theorem. Use proof by deduction and exhaustion.
Binomial Expansion – Use the binomial expansion. Find an unknown coefficient of a binomial expansion.
Trigonometry – Use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. Use the sine and cosine rules.
Differentiation – Differentiate from first principles. Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points.
Year 13 Topics
Functions – Sketch graphs of functions involving modulus functions. Solve equations and inequalities involving modulus functions. Work out the composition of two functions and the inverse of a function and sketch its graph. Transform functions.
Sequences – Work with a range of linear and quadratic sequences. Understand and work with arithmetic and geometric sequences and series.
Binomial Expansion – Understand and use the binomial expansion.
Radians – Work with radian measure, including use for arc length and area of sector. Know and use exact values of sin, cos and tan and be able to use the standard small angle approximations for sine, cos and tan.
Trigonometry – Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan.
Differentiation – Differentiation from first principles for sin x and cos x. Understand and use the second derivative. Differentiate using the product rule, quotient rule and chain rule. Construct simple differential equations.