# 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.

##### Subject Overviews

#### 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.

**Number and Calculation** – To solve increasingly complex number and practical problems by applying understanding of all 4 operations including decimal and negative numbers.

**Percentages** – Calculate percentages without a calculator and calculate the new amount after a percentage increase or decrease.

**Probability** – To demonstrate a secure understanding of theoretical probability and experimental probability.

**Statistics** – To calculate summary statistics, including mode, median and mean from a list. Represent raw data using a range of statistical diagrams.

**Geometry** – To describe, classify, analyse and investigate two and three dimensional objects by their properties and apply knowledge of these to solve increasingly complex geometric problems

##### 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** – Manipulate algebraic expressions and solve a range of multi-step algebraic equations, where the solution may not be a whole number.

**Ratio and Proportion** – To solve problems involving direct and inverse proportions and ratio.

**Graphs** – To accurately plot, interpret and use straight line graphs.

**Geometry** – To describe, analyse and construct 2d and 3d objects with or without curved surfaces.

**Sequences** – To describe patterns algebraically and use known elements within the pattern to make predictions.

**Geometry** – To calculate the volume and surface area of prisms.

**Transformations** – To accurately describe and complete transformations of 2D shapes using reflection, rotation, translation or enlargement.

##### 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

**Geometry**– To solve complex angle problems, involving parallel lines and polygons.

**Algebra 1 **– To understand inequalities; solving inequalities and represent solutions on a number line.

**Number** – To round numbers appropriately and use rounding to estimate the answer to complex questions.

**Algebra 2** – To rearrange formulae and substitute positive and negative values in formulae. To plot and use quadratic graphs.

**Geometry **– Use Pythagoras’s Theorem to find missing sides in right-angled triangles.

**Ratio** – To solve problems involving direct and inverse proportion.

**Statistics** – To calculate averages from a range of data, including tables. To produce and interpret scatter graphs.

**Geometry** – To use trigonometry to find missing sides and angles in right angled triangles.

**Number** – To freely convert numbers from standard form to ordinary form and to use the four operations with numbers written in standard form.

**Probability** – To produce and use a range of probability diagrams, including sample space diagrams, Venn diagrams, frequency trees and two-way tables.

#### KS4 Curriculum Map

##### KS4 Overview

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

**Number** – To solve problems involving factors, multiples and primes and apply this to real life problems including ‘best value’ problems.

**Algebra 1 **– Manipulate linear and quadratic algebraic expressions. Use and rearrange formulae.

**Geometry 1 – **To calculate the area and perimeter of shapes involving rectilinear shapes.

**Percentages – **Calculate percentages both with and without a calculator. Solve complex compound percentage problems and reverse percentage problems.

**Algebra 2 **– Solve a range or linear, quadratic and simultaneous equations.

**Ratio **– Recap ratio and proportion and solve complex problems algebraically.

**Statistics** – Accurately produce and use statistical charts and diagrams.

**Fractions **– Calculate with numerical and algebraic fractions.

**Graphs – Plot and interpret linear, quadratic and cubic graphs.**

**Sequences** – Continue and describe linear and quadratic (H) sequences, recognise and continue geometric and Fibonacci sequences.

**Geometry 2** – Recognise and describe shapes using their properties. Draw accurate plans and nets. Use Pythagoras’s Theorem in 2D and 3D (H) triangles.

##### 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

**Inequalities** – Represent inequalities on a coordinate grid. Solve quadratic inequalities.

**Histograms** – Construct and interpret histograms for grouped data.

**Probability** – Calculate the probability of independent and dependent events using tree diagrams.

**Polygons** – Deduce and use the angle sum in any polygon.

**Geometry** – Know and apply the rules of trigonometry to find unknown lengths and angles in 2D and 3D shapes.

**Constructions** – Use compass and ruler to construct figures and solve loci problems.

**Vectors** – Use vectors to construct geometric arguments and proofs.

**Functions** – Recognise and sketch transformations of a given function.

#### 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.

**Trigonometry** – Solve trigonometric equations within a given interval.

**Integration** – Integrate x^n (excluding n = −1), and related sums, differences and constant multiples. Evaluate and use definite integrals to find the area under a curve.

**Logs** – Use the functions a^x, e^x and ln x and their graphs. Use the laws of logarithms. Use logarithmic graphs to estimate parameters.

**Vectors** – Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form. Use vectors to solve problems in pure mathematics and in context.

**Sampling** – Understand, use and compare sampling techniques.

**Location and Spread** – Calculate measures of location, mean, median and mode. Calculate measures of variation, standard deviation, variance, range and interpercentile range.

**Representing data** – Interpret diagrams for single-variable data.

**Modelling** – Introduction to mathematical modelling and standard S.I. units of length, time and mass.

**Acceleration** – Graphical representation of velocity, acceleration and displacement.

**Forces** – Know and apply Newton’s first law.

**Correlation** – Use and interpret scatter diagrams and regression lines.

**Probability** – Use mutually exclusive and independent events.

**Statistical distribution** – Use discrete distributions to model real-world situations. Identify the discrete uniform distribution. Calculate probabilities using the binomial distribution.

**Hypothesis** – Understand and apply the language of statistical hypothesis testing. Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results.

**Forces** – Know and apply Newton’s second and third laws.

**Acceleration** – Use calculus to determine rates of change for kinematics. Use integration for kinematics problems.

##### 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.

**Trigonometry** – Understand and use double angle formulae and geometrical proofs of these formulae.

**Integration** – Integrate more complex expressions, including trig functions and exponential functions. Find the area under a curve and the area between two curves. Use integration by substitution and by parts. Integrate using partial fractions. Understand and use trapezium rule.

** Parametric Equations** – Understand and use the parametric equations of curves and conversion between Cartesian and parametric forms.

**Vectors** – Use vectors in three dimensions.

** Numerical Methods** – Locate roots of f(x) = 0. Solve equations approximately using iterative methods. Solve equations using the Newton-Raphson method and other recurrence relations.

**Statistics** – Use a regression line. Calculate the PMCC. Conduct a statistical hypothesis test and interpret the results in context.

**Forces** – Find the forces acting on a particle and resolve a force into components. Understand frictional force and calculate called the coefficient of friction.

**Moments** – Know and use the formula for moment of a force and draw mathematical models to represent horizontal rod problems.

**Normal Distribution** – Understand and use the Normal distribution to find probabilities. Find the mean and variance of a binomial distribution.

**Conditional Probability** – Understand and use tree diagrams, Venn diagrams and two-way tables. Use the conditional probability formula.

**Further Kinematics** – Find the time of flight, range and maximum height of a projectile.