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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

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
Coordinates
Metric and imperial units
Directed numbers
Formulae
Handling data
Grouping data
Equations

These topics are taught in the order shown. Only applicable for sets 1-4. 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
Straight Line graphs

These topics are taught in the order shown. Only applicable for sets 1-4. Set 5 follows a modified scheme of work.

Key Stage 4

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 non-calculator and two 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
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
Geometry and proof
Congruent triangles
Area volume and 3D
Introduction to statistics

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

YEAR 10

TERM 1
Surds
Arithmetic without a calculator
Fractions
Ratio
Standard form
Compound measures
Percentages
Bounds
Algebraic manipulation
Linear equations
Numerical methods
Sequences

TERM 2
Straight line graphs
Linear simultaneous equations
Angles
Area and perimeter
Pythagoras’ Theorem
Rearrange formulae
Trigonometry
Quadratics
Inequalities
Similar shapes
Volume

TERM 3

END OF YEAR EXAM
Transformations
Real life graphs
Curved graphs
3D drawings
Construction and Loci

YEAR 11

TERM 1

Indices
Algebraic proportion
Functions
Further trigonometry
Circle theorems
Stats
Probability

TERM 2

MOCK EXAM
Transformations of curves
Circles and Tangents
Vectors
Algebraic fractions
Proof

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 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 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

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

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, as determined by the Maths Department):

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 (Core Mathematics)

 

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 & Extra-curricular

The Maths department regularly takes 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 y13 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 8-13 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.