# Mathematics

The teaching of Mathematics at Watford Grammar School for Boys has the following 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**

Four rules for whole numbers

Handling data

Number and patterns

Parts of a whole

Sets

Addition and subtraction of decimals

Multiplication and division of decimals

Metric and imperial units

Introducing geometry

Symmetry

Triangles and quadrilaterals

Probability

Sets and Venn Diagrams

Area

Parallel lines

Coordinates and quadrilaterals

Directed numbers

Formulae

Straight line graphs

Solids

Equations

**Year 8 Units of Study**

Working with numbers

Probability

Multiplication and division of fractions

Fractions and percentages

Ratio

Polygons

Areas of triangles and parallelograms

Scatter graphs

Circumference and area of a circle

Formulae

Reflections, translations and rotations

Linear equations

Straight line graphs

Curved graphs

Continuous data

Simultaneous equations

Solving equations

Volumes

Enlargement

Scale drawing

Pythagoras’ Theorem

**Year 9 Units of Study**

Working with number

Probability

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

Set notation and Venn Diagrams

**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 2 exam papers (Calculator and Non-calculator) with an emphasis on problem solving and showing mathematical method. Students are taught Mathematics in sets by ability level. The top 2 sets follow an accelerated course to include an additional AQA Further Mathematics (Level 2) course which is two exams again 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

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

Problem-solving 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 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

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 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 Mathematics**

The department currently offers the following mathematics courses in the sixth form:

AS mathematics GCE (OCR course code 3890)

A2 mathematics GCE (OCR course code 7890)

AS mathematics is completed in the lower sixth form by studying the following modules:

Core Mathematics 1 (C1) – indices and surds, polynomials, coordinate geometry and graphs, differentiation;

Core Mathematics 2 (C2) – trigonometry, sequences and series, algebra, integration;

Probability and Statistics 1 (S1) – probability, discrete random variables, bivariate data

A2 mathematics is then completed in the upper sixth form by studying:

Core Mathematics 3 (C3) – algebra and functions, trigonometry, differentiation and integration, numerical methods;

Core Mathematics 4 (C4) – algebra and graphs, differentiation and integration, first order differential equations, vectors;

Mechanics 1 (M1) – force as a vector, equilibrium of a particle, kinematics of motion in a straight line, Newton’s laws of motion, linear momentum.

Further module details are available here in the OCR specification document

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 external written examination of duration 1 hour 30 minutes in each module, with no coursework.

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 or prefer students who have studied Further Mathematics to at least AS level.

In the Lower Sixth Further Mathematics and Mathematics are offered as ONE option. In the upper sixth, if a student wishes to continue with his Further Mathematics studies, the course is offered as a separate option to Mathematics (i.e. two out of his three or four A2 levels will be Maths). As an alternative, there is an option to complete A2 Mathematics and Further Mathematics AS.

We offer the OCR Courses (3892 AS level, 7892 A2 level)

Modules studied in the Lower Sixth are: C1, C2, FP1, S1, M1, D1

Modules studied in the Upper Sixth are: C3, C4, FP2, S2, S3, M2, M3

A brief outline of the additional modules available follows:

Further Pure Mathematics 1 (FP1) – algebraic proofs, complex numbers, matrices

Further Pure Mathematics 2 (FP2) – numerical methods, calculus, hyperbolic functions

Mechanics 2 and 3 (M2, M3) – moments, impulse, momentum, centres of mass, motion, forces

Decision 1 (D1) – algorithms, linear programming, graphs and networks

Statistics 2 and 3 (S2, S3) – continuous random variables and associated distributions, Poisson distribution, hypothesis testing, confidence intervals, testing for population differences

Further module details are available here in the OCR specification document

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 external written examination of duration 1 hour 30 minutes in each module, with no coursework.