# Mathematics

The teaching of Mathematics at Watford Grammar School for Boys aims to encourage students, reflecting their Key Stage, to

• develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment;
• develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs;
• extend their range of mathematical skills and techniques and use them in unstructured problems;
• develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected;
• recognise how a situation may be represented mathematically and understand the relationship between ‘real world’ problems and standard and other mathematical models and how these can be refined and improved;
• use mathematics as an effective means of communication;
• acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations;
• develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general;
• take increasing responsibility for their own learning and the evaluation of their own mathematical development.

Key Stage 3 Mathematics

At Key Stage 3 pupils consolidate their existing mathematical understanding from Key Stage 2 and extend their knowledge of number, algebra, geometry and statistics as detailed below. Students are taught Mathematics in sets by ability level and the lower ability students follow a moderated curriculum. There are half termly progress tests for assessment and setting purposes along with end of year tests.

Year 7 Units of Study

•  Pythagoras’ Theorem
•  Number and patterns
•  Order of operations
•  Parts of a whole
•  Introducing geometry
•  Fractions and decimals
•  Probability and sets
•  Parallel Lines
•  Area
•  Multiplication and division of decimals
•  Metric and imperial units
•  Directed numbers
•  Formulae
•  Handling data
•  Grouping data
•  Equations
•  Solids
•  Straight Line graphs

These topics are taught in the order shown. Only applicable for sets 1-7. Other sets follow a modified scheme of work.

Year 8 Units of Study

•  Working with numbers
•  Multiplication and division of fractions
•  Fractions and percentages
•  Polygons
•  Ratio
•  Areas of triangles and parallelograms
•  Scatter graphs
•  Circumference and area of a circle
•  Formulae
•  Reflections, translations and rotations
•  Linear equations
•  Pythagoras’ Theorem
•  Straight line graphs
•  Curved graphs
•  Enlargement
•  Continuous data
•  Simultaneous equations
•  Solving equations
•  Volumes
•  Scale drawing
•  Travel graphs

These topics are taught in the order shown. Only applicable for sets 1-7. Other sets follow a modified scheme of work.

Key Stage 4 Mathematics

Key Stage 4 is a three-year course following the Edexcel Exam Board, Higher Linear 1MA1.  In May/ June of year 11 there are 3 exam papers (one calculator and two non-calculator) with an emphasis on problem solving and showing mathematical method.  Students are taught Mathematics in sets by ability level. The top 3 sets follow an accelerated course to include an additional AQA Further Mathematics (Level 2) course which is two exams ( a calculator and a non-calculator) in the summer term of Year 11.

The lower sets follow the same curriculum and sit the Edexcel exams but with a moderated pace and expectation to match their ability. Some students will sit the Foundation papers instead of the Higher papers.

There are half termly Progress Tests and Mock GCSE exams in Year 11. The course can be summarised as follows:-

Year 9 Units of Study

•  Working with numbers
•  Probability
•  Sets (not in text book)
•  Percentages
•  Ratio and proportion
•  Algebraic products
•  Inequalities
•  Algebraic factors
•  Organising and summarising data
•  Formulae
•  Simultaneous equations
•  Graphs
•  Areas and volumes
•  Transformations
•  Similar figures
•  Trigonometry: Tangent of an angle
•  Sine and cosine of an angle
•  Loci
•  Solids
•  Geometric Proof
•  Congruent triangles

These topics are taught in the order shown. Only applicable for sets 1-6. Other sets follow a modified scheme of work.

Year 10 TERM 1

• Number 1 and 2
• Percentages
• Using a calculator
• Standard form
• Substitution
• Measures
• Measurements and Bounds
• Algebra 1
• Simplifying and solving equations
• Solving problems
• Trial and improvement
• Sequences
• Linear graphs
• Real-life graphs
• Simultaneous equations (various methods)
• Shape, Space and Measures 1
• Angles and properties of shapes
• Congruent shapes
• Locus and construction
• Pythagoras' theorem - 3D

TERM 2

• Three-dimensional co-ordinates
• Area
• Circles, arcs, sectors and segments
• Volume and surface area
• Similar shapes
• Algebra 2
• Changing the subject of a formula
• Inequalities and regions
• Direct and Inverse proportion
• Curved graphs
• Graphical solution of equations

TERM 3

• Shape, Space and Measures 2
• Drawing 3-D shapes, symmetry
• Trigonometry
• Transformations
• Vectors
• Sine, cosine, tangent for any angle
• Sine and cosine rules
• Circle theorems

YEAR 11 TERM 1

• Algebra 3 -
• Indices
• Algebraic fractions
• Transformation of curves
• Data Handling
• Averages and range
• Data presentation
• Comparing sets of data
• Scatter diagrams
• The handling data cycle
• Sampling and bias
• Cumulative frequency
• Histograms
• Probability
• Relative frequency
• Working out probabilities
• Probabilities of exclusive events
• Probabilities of independent events
• Tree diagrams
• Conditional probability

TERM 2

MOCK EXAM

PROOF & CONJECTURES

• Algebraic
• Geometric

REVISION

•  Revision exercises non-calculator
•  Revision exercises calculator

TERM 3

GCSE EXAMS

The following topics are covered for the AQA Further Mathematics (Level 2) course

• Function notation
• Domain & range of a function
• Graphs of functions
• Graphs of linear functions
• Finding the equation of a line
• Graphs of functions with up to three parts to their domains
• The gradient of a curve
• Differentiation
• Differentiation using standard results
• Tangents and normals
• Increasing and decreasing functions
• Stationary points
• Factor theorem
• Multiplying matrices
• Transformations
• Identity matrix
• Transformations of the unit square
• Combining transformations
• Solution of trigonometrical equations
• Trigonometrical identities

Key Stage 5 Mathematics

The department offers the following A Level Mathematics course: Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)

This two-year course builds directly on the foundation of the GCSE Higher Level syllabus. It pre-supposes skills in basic algebraic manipulation and the ability to work logically through multistage problems to further develop mathematical understanding. Students are encouraged to think, act and communicate mathematically, providing them with the skills to analyse situations in mathematics and elsewhere. The mathematical knowledge gained will be broad and widely applicable, preparing students for a range of destinations in Higher Education and employment.

The A level specification has 3 components:

 Component Outline Content Weighting 1 Core Pure Mathematics 1  Indices and surds, polynomials, coordinate geometry, trigonometry, sequences and series, algebra and functions, differentiation and integration, numerical methods, exponentials and logarithms, proof, vectors 33 1/3% 2 Core Pure Mathematics 2 Any pure maths content as above 33 1/3% 3 Statistics and Mechanics Sampling, interpretation in context, standard deviation, binomial and normal distributions, hypothesis testing, use of large data sets, conditional probability. (50% of paper) Newton’s laws of motion, kinematics of motion in a straight line and under gravity, equilibrium of a particle, force as a vector and resolving forces, projectile motion, moments (50% of paper) 33 1/3%

Regular assessment takes place, usually half termly, to ensure students remain on top of their studies, with mock exams taking place in the Spring Term. Final assessment is by 3 external written examinations of duration 2 hours each at the end of the Upper 6th, with no coursework. Further details are available in the Edexcel specification document here.

Key Stage 5 Further Mathematics

The study of further mathematics adds breadth and depth to the topics covered in A level Mathematics. It introduces new topics, for example matrices and complex numbers. Such topics form an important part of maths-rich degrees in areas such as the sciences, engineering, statistics, economics and computing in addition to mathematics itself. Some prestigious universities now require a Further Mathematics qualification.

The department currently offers Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0).

The specification has 4 components:

 Component Outline Content Weighting 1 Mandatory Core Pure Mathematics 1  Proof, complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar co-ordinates, hyperbolic functions, differential equations, trigonometry. 25% 2 Mandatory Core Pure Mathematics 2 : Any of the pure mathematics above. 25% 3 Further Statistics 1 : Discrete probability distributions, Poisson and binomial distributions, geometric and negative binomial distributions, hypothesis testing and central limit theorem 25% 4 Further Mechanics 1: Work, energy and power, elastic strings and springs and elastic energy, elastic collisions in one dimension, elastic collisions in two dimensions, impulse and momentum 25%

Regular assessment takes place, usually half termly, to ensure students remain on top of their studies, with mock exams taking place in the Spring Term. Final assessment is by 4 external written examinations of duration 1.5 hours each at the end of the Upper 6th, with no coursework. Further details are available in the Edexcel specification document here

KS5 Core Mathematics

The Department also offers the AQA Level 3 Certificate in Mathematical Studies, which is equivalent to an AS Level.  The course is designed for students for whom an A Level in Mathematics may not be suitable, but who recognise the benefit of strengthening and developing the mathematical knowledge and skills they have learnt at GCSE.  The skills gained are readily applicable to the problems that they will encounter in their A Level courses, further study, life and employment.

The course is assessed by two 90 minute papers and has the following content:

 Compulsory content: Analysis of data, Maths for personal finance, Estimation, Critical analysis of given data and models Optional content (at least three of these must be studied): The normal distribution, Probabilities and estimation, Correlation and regression, Critical path and risk analysis, Expectation, Cost benefit analysis, Graphical methods, Rates of change, Exponential functions