## Maths

All students at St. Anthony’s study Mathematics at Key Stages 3 and 4, and we also offer a range of A Level courses in Sixth Form. The Maths Department consists of a team of professionals who are dedicated to ensuring that all teaching and learning is of a high quality, and that all students enjoy studying this important subject.

**Key Stage 3 Maths Overview**

We are currently using the Mathematics for Key Stage Three CGP textbooks to support our Schemes of Learning that are differentiated to the ability of each class:

Book 1 Support

Book 2 Core

Book 3 Extension

**Book 1 Topic Order:**

- Numbers and Arithmetic
- Approximations
- Powers
- Multiples, Factors and Primes
- Fractions and Percentages
- Statistics
- Probability
- Perimeter, Area and Volume
- Algebraic Expressions
- Equations
- Formulas
- Sequences
- Ratio and Proportion
- Units and Scales
- Graphs and Equations
- Angles and Shapes
- Constructions
- Transformations

**Book 2 Topic Order:**

- Numbers and Arithmetic
- Approximations
- Powers
- Multiples, Factors and Primes
- Fractions and Percentages
- Statistics
- Probability
- Perimeter, Area, Volume and Pythagoras
- Algebraic Expressions
- Equations
- Formulas
- Sequences
- Ratio and Proportion
- Units and Scales
- Graphs and Equations
- Angles and Shapes
- Constructions
- Transformations

**Book 3 Topic Order:**

- Numbers and Arithmetic
- Approximations
- Powers
- Multiples, Factors and Primes
- Fractions and Percentages
- Geometric Relationships
- Statistics
- Probability
- Perimeter, Area and Volume
- Algebraic Expressions
- Equations and Inequalities
- Formulas
- Ratio, Proportion and Rates of Change
- Units and Scales
- Sequences
- Graphs and Equations
- Angles and Shapes
- Constructions
- Transformations

**Key Stage 3 Maths – Development of Skills**

Throughout Key Stage 3 students must try to:

- Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- Solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Through the mathematical content they should be taught to develop fluency, reason mathematically and solve problems.

The mathematical categories of Number & Calculation, Algebra, Shape Space & Measure and Handling Data have been replaced by

- Number

2. Algebra

3. Ratio, proportion & rates of change

4. Geometry & measures

5. Probability

6. Statistics

**Formal Assessment**

Every child is formally assessed 3 times a year (once each term) to monitor their progress. These assessments are created in line with the exam board we use at GCSE in order to establish continuity throughout the pupils’ time at the Academy. Furthermore, the pupils complete 12 assessed homework tasks that are used to monitor their understanding of particular topics.

**Extension Activities**

Differentiated lessons by a specialised team mean that extension activities are built into each lesson.

We also offer our most able pupils to opportunity to sit the Junior Maths Challenge which is organised by the Further Maths Support Programme.

Team challenges are attended at different venues to compete against other schools.

**Online Resources**

Every child has a login allowing textbook access at home via the internet. They can also access MyMaths for homework and revision. There are also a number of resources, including past papers on the Academy website.

**Equipment**

All pupils are expected to bring to every Maths lesson:

- Pen
- Pencil
- Ruler
- Green Pen (Peer and Self Assessment)
- Pair of Compasses
- Protractor
- Scientific Calculator

**Key Stage 4 Maths Overview**

Sets 1-5 follow the Higher GCSE syllabus.

Sets 6 – 10 follow the Foundation syllabus

Final assessment is currently with the Edexcel board. The course is linear, which means all papers are sat at the end of the course in Year 11.

We use CGP Higher and Foundation Text Books, designed in line with the new GCSE specification.

**Year 10**

**Topic Order – Foundation**

- Integers and Place Value
- Decimals
- Indices, Powers and Roots
- Factors, Multiples and Primes
- Algebra: the basics
- Expressions and substitution
- Tables, Charts and Graphs
- Statistics, Sampling and the Averages
- Pie Charts
- Scatter Graphs
- Fractions, Decimals and Percentages
- Percentages
- Equations and Inequalities
- Sequences
- Properties of Shapes, Parallel Lines and Angle Facts
- Interior and Exterior Angles
- Perimeter, Area and Volume
- Real-life Graphs
- Straight Line Graphs
- Transformations
- Ratio and Proportion
- Pythagoras and Trigonometry
- Probability
- Multiplicative Reasoning
- Plans and Elevations
- Constructions, Loci and Bearings

**Topic Order – Higher**

- Calculations, Checking and Rounding
- Indices, Roots, Reciprocals and Hierarchy of Operations
- Factors, Multiples and Primes
- Standard Form and Surds
- Algebra: Setting Up, Rearranging and Solving Equations
- Sequences
- Averages and Range
- Representing and Interpreting Data
- Scatter Graphs
- Collecting Data
- Cumulative Frequency, Box Plots and Histograms
- Fractions and Percentages
- Ratio and Proportion
- Polygons, Angles and Parallel Lines
- Pythagoras and Trigonometry
- Real Life Graphs
- Linear Graphs and Co-Ordinate Geometry
- Quadratic, Cubic and Other Graphs
- Perimeter, Area and Circles
- Volume
- Accuracy and Bounds
- Transformations
- Constructions, Loci and Bearings
- Solving Quadratic and Simultaneous Equations
- Inequalities
- Probability
- Multiplicative Reasoning
- Similarity and Congruence
- Graphs of Trigonometric Functions
- Sine and Cosine Rule

**Year 11**

**Topic Order – Foundation**

- Quadratic Equations: Expanding and Factorising
- Quadratic Equations: Graphs
- Circles, Cylinders, Cones and Spheres
- Fractions and Reciprocals
- Indices and Standard Form
- Similarity and Congruence
- Vectors
- Rearranging Equations
- Graphs of Cubic and Reciprocal Functions
- Simultaneous Equations

**Topic Order – Higher**

- Quadratics: Expanding More Than 2 Brackets
- Sketching Graphs
- Graphs of Circles, Cubes and Quadratics
- Circle Theorems
- Circle Geometry
- Changing the Subject of a Formula
- Algebraic Fractions
- Rationalising Surds
- Algebraic Proof
- Vectors
- Geometric Proof
- Reciprocal and Exponential Graphs
- Gradient and Area Under Graphs
- Direct and Inverse Proportion

Please note that these are the time frames in which we hope to cover the topics in order to give ample time for revision in Year 11. However, depending on the nature of each class, topics may be covered quicker or slower to give each pupil the best chance of success.

**Key Stage 4 Maths – Development of Skills**

Throughout Key Stage 4, we aim for our students to:

- Develop fluent knowledge, skills and understanding of mathematical methods and concepts
- Acquire, select and apply mathematical techniques to solve problems
- Reason mathematically, make deductions and inferences and draw conclusions
- Comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.

**Formal Assessment**

**Year 10**

Every child is formally assessed 4 times a year to monitor their progress. These assessments are created using past exam paper questions from the same exam board we use. Furthermore, the pupils complete 15 assessed homework tasks each year that are used to monitor their understanding of particular topics.

**Year 11**

Every child sits a formal Mock Exam before Christmas in Year 11, along with a further 3 to 4 Key Assessments throughout the year. The pupils are required to complete 5 assessed homework tasks and are given a course of Past Papers in the run up to their final exams.

We currently use the linear course set out by Edexcel. All papers are sat at the end of Year 11. For more details on the course specification, please search for Edexcel Maths Linear (1MA1).

**Extension Activities**

Differentiated lessons by a specialised team mean that extension activities are built into each lesson.

Sets 1 and 2 will sit the Intermediate Maths Challenge, run by the Further Maths Support Programme.

Team challenges are attended at different venues to compete against other schools.

**Online Resources**

Every child has a login allowing textbook access at home via the internet. They can also access MyMaths for homework and revision. There are also a number of resources, including past papers on the Academy website. We also give the pupils the opportunity to purchase a revision guide to supplement their learning.

**Equipment**

All pupils are expected to bring to every Maths lesson:

- Pen
- Pencil
- Ruler
- Green Pen (Peer and Self Assessment)
- Pair of Compasses
- Protractor
- Scientific Calculator

__Key Stage 5 Maths Overview__

__Course: A-Level Mathematics__

__Year 12__

**Topics Covered**

Core 1 Module:

- Indices and Surds
- Polynomials
- Coordinate Geometry and Graphs
- Differentiation

Core 2 Module

- Trigonometry
- Algebra – Factor Theorem
- Integration
- Algebra – Exponentials and Logarithms
- Numerical Integration
- Sequences and Series

Decision 1 Module:

- Algorithms
- Graph Theory
- Networks
- Minimum Connectors
- Shortest Path
- Route Inspection
- Travelling Salesperson
- Linear Programming
- Simplex Algorithm

**Development of Skills**

In undertaking the course pupils will:

- 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 more difficult, 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;
- read and comprehend mathematical arguments and articles concerning applications of mathematics;
- 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.

**Formal Assessment**

Every student is formally assessed 6 times a year (once each half term) to monitor their progress. These assessments are created in line with the exam board in order to establish continuity throughout the pupils’ time at the Academy. Furthermore, the pupils complete end of unit assessed homework tasks that are used to monitor their understanding of particular topics.

**Exam Information**

The A level in Mathematics (OCR Specification A) is taught across six modules. Three are studied at AS level in the first year of the course and three at A2 level in the second year of the course. AS Mathematics includes the study of the Core 1, Core 2 and Decision 1 modules and A2 Mathematics includes the study of the Core 3, Core 4 and Statistics 1 modules.

**Extended Tasks**

All year 12 Mathematics pupils sit the Senior Maths Challenge set by the UK Mathematics Trust and a small group of talented pupils will represent the school in the Team Challenge event.

**Equipment **

It is expected that all pupils provide their own stationery and bring a pen, pencil, ruler and a scientific calculator to all lessons.

__Year 13__

**Topics Covered**

Core 3 Module:

- Differentiation and Integration
- Algebra and Functions
- Trigonometry
- Numerical Methods

Core 4 Module

- Differentiation and Integration
- Differential Equations
- Algebra and Graphs
- Vectors

Probability and Statistics 1 Module:

- Representation of Data
- Measures of Location
- Measures of Spread
- Correlation
- Regression
- Probability
- Permutations and Combinations
- Probability Distributions
- Binomial and Geometric Probabilities
- Expectation and Variance of random variables.

**Development of Skills**

In undertaking the course pupils will:

- 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 more difficult, 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;
- read and comprehend mathematical arguments and articles concerning applications of mathematics;
- 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.

**Formal Assessment**

Every student is formally assessed 6 times a year (once each half term) to monitor their progress. These assessments are created in line with the exam board in order to establish continuity throughout the pupils’ time at the Academy. Furthermore, the pupils complete end of unit assessed homework tasks that are used to monitor their understanding of particular topics.

**Exam Information**

The A level in Mathematics (OCR Specification A) is taught across six modules. Three are studied at AS level in the first year of the course and three at A2 level in the second year of the course. AS Mathematics includes the study of the Core 1, Core 2 and Decision 1 modules and A2 Mathematics includes the study of the Core 3, Core 4 and Statistics 1 modules.

**Extended Tasks**

All year 12 Mathematics pupils sit the Senior Maths Challenge set by the UK Mathematics Trust and a small group of talented pupils will represent the school in the Team Challenge event.

**Equipment **

It is expected that all pupils provide their own stationery and bring a pen, pencil, ruler and scientific calculator to all lessons.

__Course: A-Level Further Mathematics__

__Year 12 & 13__

In the Further Mathematics course there is slightly more room for flexibility, we are able to adapt some of the modules studied to meet the needs and abilities of the pupils. Six modules are required with Further Pure 1 being compulsory alongside one or both of Further Pure 2/3 and a selection from Probability and Statistics 2 & 3, Decision 2 and Mechanics 2/3.

**Topics Covered:**

Further Pure 1 Module:

- Summation of series
- Mathematical induction
- Roots of polynomial equations
- Complex numbers
- Matrices

Further Pure 2

- Rational functions and graphs
- Polar coordinates
- Hyperbolic functions
- Differentiation and integration
- Numerical methods.

Further Pure 3

- Differential equations
- Vectors
- Complex numbers
- Groups

Probability and Statistics 2 Module:

- Continuous random variables
- The normal distribution
- The Poisson distribution
- Sampling and hypothesis tests.

Probability and Statistics 3 Module:

- Continuous random variables
- Linear combinations of random variables
- Confidence intervals and the t distribution
- Difference of population means and proportions
- 2 χ tests

Mechanics 1

- Force as a vector
- Equilibrium of a particle
- Kinematics of motion in a straight line
- Newton’s laws of motion
- Linear momentum

Mechanics 2

- Centre of mass
- Equilibrium of a rigid body
- Motion of a projectile
- Uniform motion in a circle
- Coefficient of restitution and impulse
- Energy, work and power

Mechanics 3

- Equilibrium of rigid bodies in contact
- Elastic strings and springs
- Impulse and momentum in two dimensions
- Motion in a vertical circle
- Linear motion under a variable force
- Simple harmonic motion.

Decision Mathematics 2

- Game theory
- Flows in a network
- Matching and allocation problems
- Critical path analysis
- Dynamic programming.

**Development of Skills**

In undertaking the course pupils will:

- 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 more difficult, 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;
- read and comprehend mathematical arguments and articles concerning applications of mathematics;
- 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.

**Formal Assessment**

Every student is formally assessed 6 times a year (once each half term) to monitor their progress. These assessments are created in line with the exam board in order to establish continuity throughout the pupils’ time at the Academy. Furthermore, the pupils complete end of unit assessed homework tasks that are used to monitor their understanding of particular topics.

**Exam Information**

The A level in Mathematics/Further Mathematics follows OCR Specification A

http://www.ocr.org.uk/Images/67746-specification.pdf

**Extended Tasks**

All year 12 Mathematics pupils, and any year 13s who wish to participate, sit the Senior Maths Challenge set by the UK Mathematics Trust and a small group of talented pupils will represent the school in the Team Challenge event.

**Equipment **

It is expected that all pupils provide their own stationery and bring a pen, pencil, ruler and scientific calculator to all lessons.

__Course: Level 3 Mathematical Studies (Core Maths)__

__Y12 &13__

__Topics Covered__

- Analysis of data
- Maths for personal finance
- Estimation
- Critical analysis of given data and models (including spreadsheets and tabular)

- The normal distribution

- Probabilities and estimation

- Correlation and regression

**Development of Skills**

Students will develop and demonstrate confidence and competence in the understanding and application of statistical techniques, interpreting data and drawing conclusions in the solution of problems. They will develop confidence and competence in the understanding and application of calculations in the solution of problems relating to personal finance and should become familiar with and gain confidence in ideas concerning the formulation of mathematical models.

**Formal Assessment**

Every student is formally assessed 6 times a year (once each half term) to monitor their progress. These assessments are created in line with the exam board in order to establish continuity throughout the pupils’ time at the Academy.

**Exam Information**

We follow the AQA Level 3 Mathematical studies specification, also known as Core Maths. This is a new level 3 Maths qualification roughly equivalent to an AS Level. The content of this course is 80% GCSE Higher Mathematics and 20% of A-Level Mathematics with a focus on finance, estimation, critical thinking and statistics.

The Core Maths qualification is for students with a grade C or above in GCSE. It develops mathematical skills and thinking appropriate for a Level 3 qualification.

Assessment is through two equally weighted examinations taken at the end of the course.

**Equipment **

It is expected that all pupils provide their own stationery and bring a pen, pencil, ruler and scientific calculator to all lessons.