Maths
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
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

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
These topics are taught in the order shown. Only applicable for sets 14. Set 5 follows 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 14. Set 5 follows a modified scheme of work.

Straight Line graphs
Key Stage 4
Key Stage 4 is a threeyear course following the Edexcel Exam Board, Higher Linear 1MA1. 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 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 17. 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

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

Algebraic

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

Exams & Assessment
GCSE
Edexcel Exam Board, Higher Linear 1MA1
AS Level
AQA Level 3 Certificate in Mathematical Studies
A Level
A Level Mathematics course: Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)
A Level Further Mathematics course: Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0)
Enrichment & Extracurricular
The Maths department regularly take part in country and national level competitions and challenges with recent accomplishments including winning the Maths Challenge Hertfordshire Maths Challenge in 2021 with Year 8.
A group of year 13 students reached the finals of the M3 challenge in New York and were awarded the ‘best team for presentation’ as well as 3rd place in technical computing (Outstanding use of programming)  2024
 Many students participate in the Junior, Intermediate and Senior Maths Challenge from the UK Mathematics Trust and many achieve medals, with a significant number qualifying for the subsequent rounds.
 Hans Woyda Prep Club for years 813 takes place each Monday lunchtime. Hans Woyda is a prestigious maths competition which takes place each year and students from the school have been very successful over the years.
 ‘Maths in Motion’ lunch time club for all year groups takes place on Tuesday lunchtime.