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.
In years 7 and 8 for sets 1 to 4, the curriculum below is supplemented through enrichment lessons using problem solving, group work, strategic thinking and analytical skills. All year 9 are taught a series of STEM lessons in mixed ability groups in which they explore the links between mathematics, science, technology, engineering and the real world.
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
 Triangles and quadrilaterals
 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 16. 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 16. Other sets follow a modified scheme of work.
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
 Quadratic 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 16. Other sets follow a modified scheme of work.
Key Stage 4 Mathematics
Key Stage 4 is a two year course following the Edexcel Exam Board, Higher Linear 1MA0. In May/ June of year 11 there are 3 exam papers (one calculator and two noncalculator) 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 noncalculator) 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 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
 Reallife 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
 Threedimensional coordinates
 Area
 Circles, arcs, sectors and segments
 Volume and surface area
 Similar shapes
 Problemsolving tasks
 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 3D shapes, symmetry
 Trigonometry
 Transformations
 Vectors
 Sine, cosine, tangent for any angle
 Sine and cosine rules
 Circle theorems
YEAR 11 TERM 1
 Algebra 3 
 Indices
 Quadratic equations
 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
REVISION
 Revision exercises noncalculator
 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 quadratic functions
 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 currently offers the following mathematics course in the sixth form:
Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)  for first year of teaching 201718
This two year course builds directly on the foundation of the GCSE Higher Level syllabus. It presupposes 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 mathsrich 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)  for first year of teaching 201718.
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 coordinates, 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