# Mathematics

Do not worry about your difficulties in mathematics. I can assure you mine are still greater.”

Albert Einstein

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries. It is essential for everyday life, critical to science, technology and engineering and necessary for financial literacy and most forms of employment.

A high quality mathematical education therefore provides a foundation for understanding the world, the ability to reason mathematically and an appreciation of mathematics.

Our students achieve outstandingly well at all Key Stages and our results are significantly above the National Average year on year.** **

**Here at St George’s Mathematics Department we always go the extra mile for your child:**

- Reward trips for those who show dedication and progress in the subject
- Revision sessions during holidays for exam classes
- After school and Saturday revision sessions for exam classes
- Pupils across the year groups 7 and 8 are invited to Maths Puzzle Club, which takes place each week
- Every spring, our most able students take part in the UKMT Maths Challenge where they need to put their problem solving skills to the test and we are proud of the number of bronze, silver and gold certificates that pupils receive
- Students displaying strong mathematical knowledge at GCSE will be given the opportunity to take part in the mentoring scheme in year 12 where they mentor a year 11 student throughout the year

The Mathematics curriculum aims to offer our students the opportunity to develop a solid foundation in the key mathematical components: proportional reasoning, geometrical reasoning and graphical representations. This is achieved through teaching these mathematical concepts from a first principle basis to develop a deeper understanding and becoming fluent in the fundamentals of mathematics by developing their problem solving skills. Through our curriculum we aim for our students to link and master the different components to contextual real world problems, allowing students to appreciate the importance and power of mathematics in their everyday lives.

**Want to find out more?**

If you wish to find out more about Mathematics at St George’s please feel free to contact Ms C. Murden at c.murden@stgeorgesrc.org

#### Key Stage 3

The aim is to enable students to master their prior knowledge acquired from Key Stage 2, allowing students to develop their mental and written arithmetic skills. Calculators are introduced in Year 9.

Our Key Stage 3 curriculum affords our students the opportunity to explore the key concepts; Numbers and their Relations, Algebra, Shape and Space, Representing and Interpreting Data, Geometry and Measures and Ratio and Proportion through varied activities to instil the love of mathematics alongside building students' confidence in their own ability.

The aim of the Key Stage 3 curriculum is to provide the foundation of the key concepts so our students are secure and confident to apply their understanding to the more in-depth Key Stage 4 programme.

Students have four contact hours per week. Homework is set twice a week in Years 7 and 8; and three times per week in Year 9; to provide students with an opportunity to practise the skills taught in lessons and to consolidate their understanding.

End of topic assessments (approximately every two weeks) will be given by class teachers. For these assessments pupils will receive a percentage only. End of term assessments will be completed at the end of each half term. All of the above assessments will be in their exercise books with parents’ signatures and feedback.

Useful links for homework and revision:

### Year 7 Topics

**Autumn term 1:**

- Adding and Subtracting Integers
- Multiplying and Dividing Integers
- Decimals; Ordering, Adding, Subtracting, Multiplying and Dividing
- Money Questions
- Negatives in Real Life
- Four Rules of Negatives
- BIDMAS and Inverse Operations
- Factors, Multiples and Primes
- Highest Common Factor
- Lowest Common Multiple

**Autumn term 2:**

- Rounding to the nearest 10, 100, given Decimal Place and Significant Figures
- Squares, Cubes and Roots
- Estimating Answers and using Place Value
- Working with Indices
- Product of Primes
- Standard Form
- Exchanging Money
- Fractions; Equivalent, Simplifying, Comparing Fractions, Adding, Subtracting and Finding a Fraction of an Amount

**Spring term 1:**

- Introduction to Algebraic Conversions
- Function Machines
- Algebraic Manipulation - Addition, Subtraction, Multiplication and Division
- Forming Expressions
- Simple Geometric Definitions
- Polygons
- Symmetries
- Coordinates
- Angles; Names, Measuring and Drawing
- Drawing a Triangle using a Protractor
- Angles on a Given Line and at a Point

**Spring term 2:**

- Tally Charts and Bar Charts
- Pictograms
- Vertical Line Charts
- Frequency Tables and Diagrams
- Perimeter and Area of a Rectangle and Triangle
- Properties of Solids and Nets

**Summer term 1:**

- Integers; Adding, Subtracting, Multiplying and Dividing
- Decimals; Ordering, Adding, Subtracting, Multiplying and Dividing
- Money Questions
- Four Rules of Negatives
- BIDMAS and Inverse Operations
- Factors, Multiples, Product of Primes, HCF and LCM
- Rounding to the nearest 10, 100, given Decimal Place and Significant Figures for Estimating Answers
- Working with Indices and Standard Form

**Summer term 2:**

- Fractions; Equivalent, Simplifying, Comparing, Adding, Subtracting and Finding a Fraction of an Amount
- Algebraic Manipulation - Addition, Subtraction, Multiplication and Division
- Forming Expressions
- Angles; Names, Measuring, Drawing, Angles on a Given Line and at a Point
- Tally Charts, Bar Charts, Pictograms, Vertical Line Charts and Frequency Tables and Diagrams
- Perimeter and Area of a Rectangle and a Triangle

### Year 8 Topics

**Autumn term 1:**

- Integers; Adding, Subtracting, Multiplying and Dividing
- Four Rules of Negatives
- Estimating Answers and using Place Value
- Fractions; Adding, Subtracting, Multiplying and Dividing
- Reciprocals
- Standard Form
- Factors, Multiples and Product of Primes
- Highest Common Factor
- Lowest Common Multiple
- Working with Indices

**Autumn term 2:**

- Fractions, Decimals and Percentages
- Calculate Percentage of an Amount (without a calculator), Increase/Decrease by a Percentage Amount
- Value for Money
- Introduction to Proportion
- Area and Perimeter; Parallelogram, Trapezium and Circle
- Algebraic Manipulation; Simplifying and Factorising Expressions
- Substitution
- Solving Equations
- Sequences; Generate Special Sequences

**Spring term 1:**

- Introduction to Proportion
- Money Questions
- Exchanging Money
- Ratio; using Ratio for Recipe Questions and Sharing Amounts using Ratio
- Data - Discrete and Continuous
- Two-way Tables
- Frequency Trees
- Averages and the Range

**Spring term 2:**

- Reflections
- Rotations
- Translations
- Angles at a Point and between Parallel Lines
- Angles in a Triangle
- Properties of Special Triangles
- Probability; Listing Outcomes, Calculating Probabilities and Mutually Exclusive Probabilities
- Increase/Decrease by a Percentage Amount

**Summer term 1:**

- Integers; Adding, Subtracting, Multiplying and Dividing
- Four Rules of Negatives
- Estimating Answers and using Place Value
- Fractions; Adding, Subtracting, Multiplying and Dividing
- Reciprocals, Indices and Standard Form
- Factors, Multiples, Product of Primes, HCF and LCM
- Percentages; Calculate an Amount (without a calculator) and Increase/Decrease by a Percentage
- Value for Money and Proportion
- Area and Perimeter; Parallelogram, Trapezium and Circle
- Algebra; Simplifying, Factorising Expressions and Solving Equations

**Summer term 2:**

- Ratio; using Ratio for Recipe Questions and Sharing Amounts using Ratio
- Data - Representation and Interpretation
- Transformations; Reflections, Rotations and Translations
- Angles; at a Point, between Parallel Lines and in a Triangle
- Probability; Listing Outcomes, Calculating Probabilities and Mutually Exclusive Probabilities

### Year 9 Topics

**Autumn term 1:**

- Integers; Adding, Subtracting, Multiplying and Dividing
- Estimating Answers and using Place Value
- Fractions; Adding, Subtracting, Multiplying, Dividing and Finding a Fraction of an Amount
- Percentages; Calculate Increase/Decrease, Change to a Percentage, Percentage Change and Reverse Percentages
- Simple Interest Calculations
- Index Notation
- Introduction to Bounds

**Autumn term 2:**

- Algebra; Simplifying Expressions, Expanding Brackets, Forming and Solving Formulae/Equations
- Factorise Quadratics
- Generate a Sequence from the nth Term and Finding the nth Term
- Straight Line Graphs; Sketching and Finding the Gradient of a Line
- Drawing Quadratic Graphs
- Surface Area of a Prism
- Volume of a Prism

**Spring term 1:**

- Metric Conversions
- Properties of Special Triangles
- Angles; Angles in a Triangle and between Parallel Lines
- Angles of Polygons; Interior and Exterior of Regular and Irregular Polygons
- Bearings
- Probability; Listing Outcomes, Calculating Probabilities and Mutually Exclusive Events

**Spring term 2:**

- Data - Discrete and Continuous, Two-way Tables, Frequency Trees, Pie Charts and Scatter Graphs
- Averages and the Range
- Transformations; Reflections, Translations, Rotations and Enlargements
- Pythagoras’ Theorem
- Ratio; Sharing Amounts using Ratio, using Ratio in Recipe Style Questions
- Proportion

**Summer term 1:**

- Integers, Fractions and Decimals
- Percentages; Increase/Decrease, Change to a Percentage, Percentage Change, Reverse Percentages and Simple Interest Calculations
- Index Notation
- Bounds
- Algebra; Simplifying Expressions, Expanding Brackets, Forming and Solving Formulae/Equations
- Factorise Quadratics
- Generate a Sequence from the nth Term and Finding the nth Term
- Drawing Straight Line Graphs and Quadratic Graphs
- Surface Area and Volume of a Prism
- Angles; between Parallel Lines, Polygons and Bearings

**Summer term 2:**

- Probability; Listing Outcomes, Calculating Probabilities and Mutually Exclusive Events
- Data - Discrete and Continuous, Two-way Tables, Frequency Trees, Pie Charts and Scatter Graphs
- Averages and the Range
- Transformations; Reflections, Translations, Rotations and Enlargements
- Pythagoras’ Theorem
- Ratio; Sharing using Ratio, using Ratio in Recipe Style Questions and Proportion

#### Key Stage 4

GCSE Mathematics is perhaps the most important qualification that your child will receive.

It not only gives pupils the knowledge to deal with practical problems in the real world, it is also an important subject when applying for Further Education and employment.

The aim at Key Stage 4 is to enable students to master and enhance the knowledge acquired from Key Stage 3 whilst linking the various concepts in the mathematics curriculum. Students are taught to draw on alternative methods to solve such complex problems keeping in line with the demands of the GCSE curriculum.

At Key Stage 4 we empower our students to build their confidence within the key concepts; Numbers, Algebra, Geometry and Measures, Statistics and Ratio and Proportion through a range of activities to complement their knowledge and skills developed in Key Stage 2 and 3. Every lesson, teachers aim to link the concepts covered to GCSE exam style questioning.

Students have five contact hours per week in year 10 and year 11. Homework is set three to four times per week to provide students with an opportunity to practise the skills taught in lessons and to consolidate their understanding.

End of topic assessments (approximately every two weeks) will be given by class teachers. For these assessments pupils will receive a percentage only. End of term assessments will be completed at the end of each half term. All of the above assessments will be in their exercise books with parents’ signatures and feedback.

Our exam board is Edexcel.

Useful links for homework and revision:

Commencing Year 11; students are given a CGP Knowledge Organiser which has all the essential formulae and facts to aid in their revision.

There are two mock examinations in year 11: November/December and March. At the end of year 11 students will sit their GCSE Mathematics papers; one non-calculator and two calculator papers. There are two tiers of papers Foundation Tier with grades 1-5 and Higher Tier with grades 4-9.

### Year 10 Topics

**Autumn term 1:**

- Negative Indices
- Bounds
- Error Intervals
- Estimating Answers and using Place Value
- Mathematical Reasoning
- Percentages; Percentage Change, Reverse Percentages, Simple Interest, Compound Interest and Depreciation problems
- Growth and Decay Problems
- Algebra; Simplifying Expressions, Forming and Solving Equations
- Factorise Quadratics
- Inequalities on a Number Line and Solving Linear Inequalities

**Autumn term 2:**

- Fibonacci Sequences
- Geometric Progressions
- Straight Line Graphs; the Gradient of a Line and the Midpoint of a Line
- Finding the Equation of a Straight Line
- Simultaneous Equations; Algebraically and Graphically
- Factorising and Solving Quadratics
- The Difference of Two Squares
- Roots and Turning Points of Quadratics

**Spring term 1:**

- Tangents, Arcs, Sectors and Segments
- Area and Perimeter of a Sector of a Circle
- Surface Area and Volume; Spheres, Pyramids, Cones and Frustums
- Compound Units
- Distance-Time Graphs
- Constructions; Bisecting an Angle, Perpendiculars and Drawing Triangles using a Compass
- Loci

**Spring term 2:**

- Pythagoras’ Theorem
- Trigonometric Ratios to Find Missing Sides and Angles in Right-Angled Triangles
- Exact Trigonometric Values
- Probability; Venn Diagrams and Tree Diagrams
- Data - Sampling Populations, Stratified Sampling and Time Series Graphs
- Similar Shapes
- Congruent Triangles
- Scale Drawings
- Introduction to Vectors

**Summer term 1:**

- Negative Indices
- Bounds and Error Intervals
- Mathematical Reasoning
- Percentages; Percentage Change, Reverse Percentages, Simple Interest, Compound Interest, Depreciation, Growth and Decay Problems
- Inequalities on a Number Line and Solving Linear Inequalities
- Fibonacci and Geometric Progressions
- Straight Line Graphs; the Gradient of a Line, Midpoint of a Line and Finding the Equation of a Straight Line
- Simultaneous Equations; Algebraically and Graphically
- Quadratics; Factorising, Solving, Roots and Turning Points

**Summer term 2:**

- Tangent, Arcs, Sectors and Segments
- Surface Area and Volume; Spheres, Pyramids, Cones and Frustums
- Compound Units and Distance-Time Graphs
- Constructions and Loci
- Trigonometry; Pythagoras’ Theorem and Trigonometric Ratios
- Probability; Venn Diagrams and Tree Diagrams
- Data - Sampling Populations, Stratified Sampling and Time Series
- Similar Shapes and Congruent Triangles
- Introduction to Vectors

### Year 11 Foundation Topics

**Autumn term 1:**

- Negative Indices
- Bounds
- Error Intervals
- Estimating Answers and using Place Value
- Mathematical Reasoning
- Percentages; Percentage Change, Reverse Percentages, Simple Interest, Compound Interest and Depreciation problems
- Growth and Decay Problems
- Algebra; Simplifying Expressions, Forming and Solving Equations
- Inequalities on a Number Line and Solving Linear Inequalities

**Autumn term 2:**

- Fibonacci Sequences
- Geometric Progressions
- Straight Line Graphs; the Gradient of a Line and the Midpoint of a Line
- Finding the Equation of a Straight Line
- Simultaneous Equations; Algebraically and Graphically
- Factorising and Solving Quadratics
- The Difference of Two Squares
- Roots and Turning Points of Quadratics

**Spring term 1:**

- Tangents, Arcs, Sectors and Segments
- Area and Perimeter of a Sector of a Circle
- Surface Area and Volume; Spheres, Pyramids, Cones and Frustums
- Compound Units
- Distance-Time Graphs
- Constructions; Bisecting an Angle, Perpendiculars and Drawing Triangles using a Compass
- Loci

**Spring term 2:**

- Pythagoras’ Theorem
- Trigonometric Ratios to Find Missing Sides and Angles in Right-Angled Triangles
- Exact Trigonometric Values
- Probability; Venn Diagrams and Tree Diagrams
- Data - Sampling Populations, Stratified Sampling and Time Series Graphs
- Similar Shapes
- Congruent Triangles
- Scale Drawings
- Introduction to Vectors

### Year 11 Higher Topics

**Autumn term 1:**

- Mathematical Reasoning, Negative Indices, Error Intervals and Standard Form
- Recurring Decimals to Fractions
- Upper and Lower Bounds
- Surds
- Direct and Inverse Proportion
- Product of Three Binomials
- Factorising Quadratics with a coefficient >1
- Iterative Processes
- Algebraic Proof
- Transformations - Negative Scale Factor

**Autumn term 2:**

- Proof and Application of Circle Theorems
- Similarity - Area and Volume and Congruency
- Trigonometry - The Sine and Cosine Rule, Pythagoras’ Theorem and Trigonometric Ratios in 3D Shapes
- Data - Cumulative Frequency Tables, Boxplots and Histograms
- Finding the Equation of Perpendicular Lines

**Spring term 1:**

- Algebraic Fractions
- Roots and Turning Points of Quadratics
- Completing the Square
- Simultaneous Equations with a Quadratic Equation
- Functions; Inverse and Composite
- Finding the Equation of a Line given Two Points and the Equation of Perpendicular Lines
- Equation of a Circle
- Pythagoras on a Line
- Distance-Time Graphs and Velocity-Time Graphs
- Quadratic Sequences
- Regions

**Spring term 2:**

- Finding the Equation of a Line given Two Points and the Equation of Perpendicular Lines
- Quadratic Inequalities
- Vectors
- Trigonometric Graphs
- Transformation of Functions
- Surface Area and Volume; Spheres, Cones, Pyramids and Frustums

#### Key Stage 5

Many universities consider mathematics to be one of the most valuable A-levels.

You will have the opportunity to develop decision making and problem solving skills, transferable to any career path you choose.

The aim at Key Stage 5 is to enable students to develop into mathematical scholars through an enquiring and investigative approach to their mathematical studies. We actively encourage independent research and study outside of the curriculum in preparation for their higher educational studies.

Having mastered a secure mathematical background at grade 7 or above in their GCSE, we aim for our students to explore the many fields that surround mathematics.

The key areas we focus on are Pure and Applied Mathematics, including Statistics and Mechanics. Teachers aim to consistently link the applied content to other Key Stage 5 curriculums within the school so students broaden their background of what they can do with a solid mathematical education.

We also offer our highly able students the opportunity to study the Further Mathematics syllabus including Core and Further Pure Mathematics. Teachers at Key Stage 5 challenge student’s analytical problem solving skills through targeted questioning which allows the students to mature into highly sought after mathematicians.

Our exam board is Edexcel.

**A-Level Mathematics: **

Paper 1 and Paper 2 Pure Mathematics

Topics include: Proof, Algebra and Functions, Co-ordinate Geometry in the (x,y) Plane, Sequences and Series, Trigonometry, Exponentials and Logarithms, Vectors, Binomial Expansion, Differentiation, Integration and Numerical Methods.

Paper 3 Statistics and Mechanics

Topics include: Data Presentation and Interpretation, Correlation and Regression, Statistical Distributions, Normal Distribution and Statistical Hypothesis Testing, Probability, Kinematics, Forces and Newton's Laws, Moments, Projectiles, Application of Forces and Further Kinematics.

**A-Level Further Mathematics: **

Paper 1 and 2 Core Mathematics

Topics include: Complex Numbers, Series, Roots of Polynomials, Volumes of Revolution, Matrices, Linear Transformations, Proof by Induction, Vectors, Methods in Calculus, Polar Coordinates, Hyperbolic Functions, Methods in Differential Equations and Modelling with Differential Equations.

Paper 3 and 4 Further Pure Mathematics

Topics include: Inequalities, Vectors, Conic Sections, Taylor Series, Methods in Calculus, Numerical Methods, Reducible Differential Equations, Number Theory, Groups, Recurrence Relations, Matrix Algebra and Integration Techniques.

#### Careers

Mathematics is a pre-requisite for some degree courses: Physics, Accountancy, Mathematics and Statistics, Engineering and Economics. With a mathematics degree graduates can seek employment in the business, science, or technology sectors.