# Mathematics

#### Curriculum Intent

The Mathematics department encourages students to build fluency, the ability to reason mathematically and solve complex multi-stage problems. Mathematics is a discipline which has intrigued the most brilliant minds for centuries. Mathematical concepts are essential to every walk of life, central to many other areas of the curriculum and pivotal to further education and the world of work. We aim to:

• develop students’ understanding in each of the key foci of Number (numeracy), Algebra, Geometry and Statistics

• develop a desire to become independent and competent problem solvers and the ability to communicate mathematically

• appreciate the link between Mathematics and other subjects

• enable students to become mathematically aware in preparation for life beyond school. #### Curriculum Mapping

Topics Studied in Year 7

 Topic Brief Description Being a Mathematician A series of lessons introducing pupils to various areas of Mathematics that they will meet in KS3, whilst learning about some key mathematical skills Place value Adding, subtracting, multiplying and dividing whole numbers and decimals. Rounding & estimation Angles Constructions with a ruler and protractor, bearings, angle facts and angles in polygons Factors and Multiples Factors, multiples, index notation and prime factorisation Directed Number & Expressions Using letters to represent unknown amounts, simplification, using brackets and solving equations. Four operations involving negative numbers Ratio & Measure Understanding ratio notation, simplifying ratios and sharing in ratios. Metric conversions, interpreting scales & scale drawing Classifying Shapes, Area & Perimeter Area and Perimeter of rectangles, triangles, parallelograms, trapeziums and circles. Classifying shapes including by symmetry and parallel lines Fractions Equivalent, fractions, using mixed numbers, four operations involving fractions, Sequences Generating sequences, linear and quadratic sequences, geometric progressions

Topics Studied in Year 8

 Topic Brief Description Sequences Generating sequences, linear and quadratic sequences, geometric progressions Discrete data project Interpreting data, calculating mean, median, mode and range, frequency tables and frequency graphs Proportion Understand notation, Solving problems with proportional quantities using the unitary method, the double number line and ratio tables, scale drawing 3D Shapes Properties of 3D Shapes, understand nets, plans and elevations. Volume and surface area of cuboids and, volume of prisms More Complex Equations & Expressions Factorising, expanding double brackets, creating setting up and solving equations Percentages Using multipliers to find Ppercentages of quantities, percentage increase and decrease, reverse percentages Construction, Loci & Pythagoras Know and apply Pythagoras’ theorem, constructing with a pair of compasses, loci problems Graphs Coordinates, Real life graphs, plotting linear graphs, solving simultaneous equations using graphs

Topics Studied in Year 9

 Topic Brief Description Probability Probability of single and, combined events, estimating probability, using sample spaces and venn diagrams Equations, Expressions & Inequalities Solving equations with unknowns on both sides. Solving inequalities, solving simultaneous equations using substitution and elimination. Trigonometry, Pythagoras & Angle Reasoning Pythagoras, and trigonometry for right-angled triangles. Solving complex problems using angle facts Bounds, Standard Form & Compound Units Converting between standard form and ordinary numbers. Calculating compound measures such as speed, rates of pay, density. Error Intervals. Formulae & Graphs Word Formulae, substitution, rearranging formulae. Identify the gradient and intercept of a linear graph. Plotting quadratic and cubic graphs. Percentages Revision of percentage change using multipliers, finding percentage increase and decrease, reverse percentages. Repeated percentage increase & decrease Transformations Rotation, reflection, translation, enlargement, describing transformations. Continuous data project Grouped frequency tables and diagrams, scatter diagrams and lines of best fit.

Topics Studied in Year 10 & 11 Foundation

 Topic Brief Description Year 10 Expressions, Formulae & Sequences Expanding brackets and factorising, sequences, formulae Place Value, Rounding, Standard Form & Indices Rounding, multiplying and dividing decimals, index notation, prime factorisation. Writing numbers in standard form and calculating with standard form, calculating roots, working with indices Angles Bearings, scale drawing, angles in polygons and parallel lines Fractions, Decimals & Percentages Four operations with fractions, converting between fractions, decimals and percentages, reverse percentages, repeated percentages Probability Probability of single and combined events, estimating probability, using sample spaces, venn diagrams and tree diagrams Equations & Inequalities Setting up and solving equations with x on both sides, solving linear inequalities Ratio & Proportion Dividing into ratios, solving problems involving direct and inverse proportion Transformations & Vectors Rotation, reflection, translation, enlargement, describing transformations, vectors Area & Volume Circumference and area of circles, nets, plans and elevations, volume and surface area of prisms Year 11 Grouped Data Project Scatter diagrams, pie charts, calculating the mean from grouped frequency tables Graphs Gradient and intercept of linear graphs, finding the equation of straight lines, plotting cubic, quadratic and reciprocal graphs Pythagoras & Trigonometry, Loci & Construction Pythagoras, and trigonometry for right-angled triangles, exact trigonometric values for special angles, proof of congruent and similar triangles. Loci & construction Simultaneous Equations Solving pairs of equations by elimination and substitution Complex Area & Volume Surface area and volume of spheres, cones, pyramids and composite solids, calculating arc lengths and areas of sectors Quadratics Factorising quadratics, solving equations by factorisation, identifying and deducing roots and turning points

Topics Studied in Year 10 & 11 Higher

 Topic Brief Description Year 10 Expressions, Equations & Sequences Linear simultaneous equations, quadratic sequences, expanding double brackets and factorising, rearranging complex formulae. Trigonometry Revision of right angled trigonometry, cosine and sine rule, congruent triangles, similarity. Indices, Surds & Standard Form Converting between recurring decimals and fractions. Surds, negative fractional indices, calculating with standard form. Probability Probability of single and combined events, estimating probability, conditional probability. Using sample spaces, two-way tables, venn diagrams and tree diagrams. Graphs Equations of straight lines, parallel and perpendicular lines. Plotting and interpreting quadratics, cubics, reciprocal graphs, exponential graphs and circular functions. Percentages & Proportion Reverse percentages, repeated percentages, growth and decay. Direct and inverse proportion. Complex Areas & Volumes, Accuracy Area and volume of spheres, pyramids & cones. Arcs and sectors, upper and lower bounds. Transformations Combinations of rotation, reflection, translation and enlargement (including negative enlargement). Year 11 Quadratics Solving quadratics by factorising, completing the square and using the formula. Solving simultaneous equations involving quadratics. Solving quadratic inequalities. Data Project Scatter diagrams, cumulative frequency graphs, histograms. Circle Theorems & Trigonometry Identify, apply and prove circle theorems. Pythagoras and trigonometry for right-angled triangles, exact trigonometric values for special angles. Apply and use sine rule and cosine rule. Recognise, sketch and interpret graphs of trigonometric functions. Vectors Add and subtract vectors, multiplying by scalars, vector proofs. Functions Inverse and composite functions. Calculating, estimating and interpreting gradients of graphs and area under curves. Transformations of functions. Algebraic Fractions & Proof Iteration. Simplifying, manipulating and solving questions involving algebraic fractions. Using algebra to construct proofs.