# Mathematics curriculum

Introduction

The aim of the Mathematics curriculum is to provide pupils with the critical knowledge and problem-solving skills they need to develop in their chosen career and lead a successful life. The curriculum encompasses mathematics that pupils can apply to real life situations through a range of mathematical reasoning as well as equipping pupils with skills that can be used across other curriculum areas.

Key Stage 3

At KS3, all pupils follow a series of key topics which are then differentiated to suit the needs of the pupils. The KS3 curriculum has been designed to ensure pupils explore topics and reasoning within mathematics to a greater depth to ensure they are prepared for KS4.

Year 7 curriculum:

 Autumn 1: Place value, addition and subtraction (1a) Place value (including decimals), (1b) Add and subtract (inc. decimals), (1c) Estimation, (1d) Perimeter Autumn 2: Place value, multiplication and division (2a) Factors, HCF, multiples, LCM, (2b) Multiply and divide (including decimals), (2c) Area of rectangle and triangle, (2d) Calculate the mean Spring 1: Geometry: 2D shape in a 3D world (3a) Draw, measure and name acute and obtuse angles, (3b) Find unknown angles (straight lines, at a point, vertically opposite), (3c) Properties of triangles and quadrilaterals Spring 2: Fractions (4a) Equivalent fractions, (4b) Compare and order fractions and decimals, (4c) Change mixed numbers to improper fractions and vice versa, (4d) Fraction of a quantity, (4e) Multiply and divide fractions Summer 1: Applications of algebra (5a) Order of operations, (5b) Substitution, (5c) Simplify algebraic expressions, (5d) Solve word problems with expressions, (5e) Sequences (term-to-term, not nth term) Summer 2: Percentages and pie charts (6a) Construct and interpret statistical diagrams including pie charts, (6b) Convert between percentages, vulgar fractions and decimals, (6c) Percentage of a quantity, (6d) Find the whole given the part and the percentage

Year 8 curriculum:

 Autumn 1: Number (1a) Primes and indices, (1b) Prime factorisation to find LCM, HCF, squares, cubes, (1c) Venn diagrams, (1d) Enumerating sets, (1e) Add and subtract fractions Autumn 2: Algebraic expressions (2a) Negative numbers and inequality statements, (2b) Formulate and evaluate expressions, (2c) Linear equations, (2d) Expressions and equations from real-world situations, (2e) Linear sequences: nth term Spring 1: 2-D geometry (3a) Draw accurate triangles and quadrilaterals (ruler, protractor, compasses), (3b) Find unknown angles (including parallel lines), (3c) Conversion between length units and between area units, (3d) Areas and perimeters of composite figures, (3e) Areas of parallelograms and trapeziums Spring 2: Proportional reasoning (4a) Convert between percentages, vulgar fractions and decimals, (4b) Percentage increase and decrease, finding the whole given the part and the percentage, (4c) Ratio (equivalent, of a quantity) and rate, (4d) Speed, distance, time Summer 1: 3-D geometry (5a) Rounding, significant figures and estimation, (5b) Circumference and area of a circle, (5c) Visualise and identify 3-D shapes and their nets, (5d) Volume of cuboid, prism, cylinder, composite solids Summer 2: Statistics (6a) Collect and organise data, (6b) Interpret and compare statistical representations, (6c) Mean, median and mode averages, (6d) The range and outliers

Key Stage 4

At KS4, all pupils at Platanos College follow the curriculum outlined below. It is the case that pupils will cover a range of topics which span both the foundation and higher specifications. In Year 9, pupils begin the GCSE course and the KS4 curriculum builds on KS3 content. It is challenging and the complexity is designed to ensure pupils are exploring a range of reasoning and problem-solving questions.

 Year 9 Foundation: Number 1.1 Calculations, 1.2 Decimal numbers, 1.3 Place value, 1.4 Factors and multiples, 1.5 Squares, cubes and roots, 1.6 Index notation, 1.7 Prime factors Algebra 2.1 Algebraic expressions, 2.2 Simplifying expressions, 2.3 Substitution, 2.4 Formulae, 2.5 Expanding brackets, 2.6 Factorising, 2.7 Using expressions and formulae Graphs, tables and charts 3.1 Frequency tables, 3.2 Two-way tables, 3.3 Representing data, 3.4 Time series, 3.5 Stem and leaf diagrams, 3.6 Pie charts, 3.7 Scatter graphs, 3.8 Line of best fit Fractions and percentages 4.1 Working with fractions, 4.2 Operations with fractions, 4.3 Multiplying fractions, 4.4 Dividing fractions, 4.5 Fractions and decimals, 4.6 Fractions and percentages, 4.7 Calculating percentages 1, 4.8 Calculating percentages 2Equations, inequalities and sequences 5.1 Solving equations 1, 5.2 Solving equations 2, 5.3 Solving equations with brackets, 5.4 Introducing inequalities, 5.5 More inequalities, 5.6 More formulae, 5.7 Generating sequences, 5.8 Using the nth term of a sequence Angles 6.1 Properties of shapes, 6.2 Angles in parallel lines, 6.3 Angles in triangles, 6.4 Exterior and interior angles, 6.5 More exterior and interior angles, 6.6 Geometrical patterns Averages and range 7.1 Mean and range, 7.2 Mode, median and range, 7.3 Types of average, 7.4 Estimating the mean, 7.5 Sampling Perimeter, area and volume 1 8.1 Rectangles, parallelograms and triangles, 8.2 Trapezia and changing units, 8.3 Area of compound shapes, 8.4 Surface area of 3D solids, 8.5 Volume of prisms, 8.6 More volume and surface area

 Year 9 Higher: Number 1.1 Number problems and reasoning, 1.2 Place value and estimating, 1.3 HCF and LCM, 1.4 Calculating with powers (indices), 1.5 Zero, negative and fractional indices, 1.6 Powers of 10 and standard form, 1.7 Surds Algebra 2.1 Algebraic indices, 2.2 Expanding and factorising, 2.3 Equations, 2.4 Formulae, 2.5 Linear sequences, 2.6 Non-linear sequences, 2.7 More expanding and factorising Interpreting and representing data 3.1 Statistical diagrams 1, 3.2 Time series, 3.3 Scatter graphs, 3.4 Line of best fit, 3.5 Averages and range, 3.6 Statistical diagrams 2 Fractions, ratio and percentages 4.1 Fractions, 4.2 Ratios, 4.3 Ratio and proportion, 4.4 Percentages, 4.5 Fractions, decimals and percentages Angles and trigonometry 5.1 Angle properties of triangles and quadrilaterals, 5.2 Interior angles of a polygon, 5.3 Exterior angles of a polygon, 5.4 Pythagoras’ theorem 1, 5.5 Pythagoras’ theorem 2, 5.6 Trigonometry 1, 5.7 Trigonometry 2 Graphs 6.1 Linear graphs, 6.2 More linear graphs, 6.3 Graphing rates of change, 6.4 Real-life graphs, 6.5 Line segments, 6.6 Quadratic graphs, 6.7 Cubic and reciprocal graphs, 6.8 More graphs Area and volume 7.1 Perimeter and area, 7.2 Units and accuracy, 7.3 Prisms, 7.4 Circles, 7.5 Sectors of circles, 7.6 Cylinders and spheres, 7.7 Pyramids and cones

In Year 10, pupils continue with the GCSE course. The curriculum builds on many topics introduced in year 9.

 Year 10 Foundation: Graphs 9.1 Coordinates, 9.2 Linear graphs, 9.3 Gradient, 9.4 y = mx + c, 9.5 Real-life graphs, 9.6 Distance-time graphs, 9.7 More real-life graphs Transformations 10.1 Translation, 10.2 Reflection, 10.3 Rotation, 10.4 Enlargement, 10.5 Describing enlargements, 10.6 Combining transformations Ratio and proportion 11.1 Writing ratios, 11.2 Using ratios 1, 11.3 Ratios and measures, 11.4 Using ratios 2, 11.5 Comparing using ratios, 11.6 Using proportion, 11.7 Proportion and graphs, 11.8 Proportion problems Right-angled triangles 12.1 Pythagoras' theorem 1, 12.2 Pythagoras' theorem 2, 12.3 Trigonometry: the sine ratio 1, 12.4 Trigonometry: the sine ratio 2, 12.5 Trigonometry: the cosine ratio, 12.6 Trigonometry: the tangent ratio, 12.7 Finding lengths and angles using trigonometry Probability 13.1 Calculating probability, 13.2 Two events, 13.3 Experimental probability, 13.4 Venn diagrams, 13.5 Tree diagrams, 13.6 More tree diagrams Multiplicative reasoning 14.1 Percentages, 14.2 Growth and decay, 14.3 Compound measures, 14.4 Distance, speed and time, 14.5 Direct and inverse proportion Constructions, loci and bearings 15.1 3D solids, 15.2 Plans and elevations, 15.3 Accurate drawings 1, 15.4 Scale drawings and maps, 15.5 Accurate drawings 2, 15.6 Constructions, 15.7 Loci and regions, 15.8 Bearings Quadratic equations and graphs 16.1 Expanding double brackets, 16.2 Plotting quadratic graphs, 16.3 Using quadratic graphs, 16.4 Factorising quadratic expressions, 16.5 Solving quadratic equations algebraically Perimeter, area and volume 2 17.1 Circumference of a circle 1, 17.2 Circumference of a circle 2, 17.3 Area of a circle, 17.4 Semicircles and sectors, 17.5 Composite 2D shapes and cylinders, 17.6 Pyramids and cones, 17.7 Spheres and composite solids

 Year 10 Higher: Transformations and constructions 8.1 3D solids, 8.2 Reflection and rotation, 8.3 Enlargement, 8.4 Transformations and combinations of transformations, 8.5 Bearings and scale drawings, 8.6 Constructions 1, 8.7 Constructions 2, 8.8 Loci Equations and inequalities 9.1 Solving quadratic equations 1, 9.2 Solving quadratic equations 2, 9.3 Completing the square, 9.4 Solving simple simultaneous equations, 9.5 More simultaneous equations, 9.6 Solving linear and quadratic simultaneous equations, 9.7 Solving linear inequalities Probability 10.1 Combined events, 10.2 Mutually exclusive events, 10.3 Experimental probability, 10.4 Independent events and tree diagrams, 10.5 Conditional probability, 10.6 Venn diagrams and set notation Multiplicative reasoning 11.1 Growth and decay, 11.2 Compound measures, 11.3 More compound measures, 11.4 Ratio and proportion Similarity and congruence 12.1 Congruence, 12.2 Geometric proof and congruence, 12.3 Similarity, 12.4 More similarity, 12.5 Similarity in 3D solids More trigonometry 13.1 Accuracy, 13.2 Graph of the sine function, 13.3 Graph of the cosine function, 13.4 The tangent function, 13.5 Calculating areas and the sine rule, 13.6 The cosine rule and 2D trigonometric problems, 13.7 Solving problems in 3D, 13.8 Transforming trigonometric graphs 1, 13.9 Transforming trigonometric graphs 2 Further statistics 14.1 Sampling, 14.2 Cumulative frequency, 14.3 Box plots, 14.4 Drawing histograms, 14.5 Interpreting histograms, 14.6 Comparing and describing populations

In Year 11, pupils have exposure to higher level topics and they will also review key aspects of the GCSE specification.

 Year 11 Foundation: Fractions, indices and standard form 18.1 Multiplying and dividing fractions, 18.2 The laws of indices, 18.3 Writing large numbers in standard form, 18.4 Writing small numbers in standard form, 18.5 Calculating with standard form Congruence, similarity and vectors 19.1 Similarity and enlargement, 19.2 More similarity, 19.3 Using similarity, 19.4 Congruence 1, 19.5 Congruence 2, 19.6 Vectors 1, 19.7 Vectors 2 More algebra 20.1 Graphs of cubic and reciprocal functions, 20.2 Non-linear graphs, 20.3 Solving simultaneous equations graphically, 20.4 Solving simultaneous equations algebraically, 20.5 Rearranging formulae, 20.6 Proof

 Year 11 Higher: Equations and graphs 15.1 Solving simultaneous equations graphically, 15.2 Representing inequalities graphically, 15.3 Graphs of quadratic functions, 15.4 Solving quadratic equations graphically, 15.5 Graphs of cubic functions Circle theorems 16.1 Radii and chords, 16.2 Tangents, 16.3 Angles in circles 1, 16.4 Angles in circles 2, 16.5 Applying circle theorems More algebra 17.1 Rearranging formulae, 17.2 Algebraic fractions, 17.3 Simplifying algebraic fractions, 17.4 More algebraic fractions, 17.5 Surds, 17.6 Solving algebraic fraction equations, 17.7 Functions, 17.8 Proof Vectors and geometric proof 18 Vectors and geometric proof, 18.2 Vector arithmetic, 18.3 More vector arithmetic, 18.4 Parallel vectors and collinear points, 18.5 Solving geometric problems Proportion and graphs 19.1 Direct proportion, 19.2 More direct proportion, 19.3 Inverse proportion, 19.4 Exponential functions, 19.5 Non-linear graphs, 19.6 Translating graphs of functions, 19.7 Reflecting and stretching graphs of functions

Free standing maths qualifications

In addition to GCSE Mathematics, the highest attaining pupils are offered the opportunity to gain qualifications in Further Maths (a level 2 qualification) or Additional Maths (a level 3 qualification).

 Further Maths Numbers and the number system Manipulating algebraic expressions Graphs of functions Linear and quadratic equations Algebraic proof Co-ordinate geometry Pythagoras’ theorem Trigonometric functions Trigonometrical identities Calculus Matrices Additional Maths Algebraic manipulation Polynomials, functions and equations Applications of equations and inequalities Sequences and recurrence of relationships Coordinate geometry Trigonometric functions Applications of trigonometry Permutations and combinations The binomial distribution Exponentials and logarithms Numerical methods Differentiation Integration Application to kinematics We have high expectations for all our pupils and ensure that every learner is challenged and supported to reach their full potential. 