  # Maths

## Intent

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.

Throughout Key Stage 3,4 & 5 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The mathematical categories of Number & Calculation, Algebra, Shape Space & Measure and Handling Data have been replaced by

1. Number
2. 2. Algebra
3. 3. Ratio, proportion & rates of change
4. 4. Geometry & measures
5. 5. Probability
6. 6. Statistics

## Implementation at KS3

Year 7 Implementation in  Maths

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

1. Number2. Algebra3. Ratio, proportion & rates of change4. Geometry & measures5. Probability6. 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

## Implementation at KS4

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
• 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

## Implementation at KS5

Key Stage 5 Maths Overview

Course: A-Level Mathematics

Year 12

Topics Covered

Pure Maths:

• Indices and Surds
• Polynomials
• Coordinate Geometry and Graphs
• Differentiation
• Trigonometry
• Algebra – Factor Theorem
• Integration
• Algebra – Exponentials and Logarithms
• Vectors

Statistics:

• Displaying and Interpreting Data
• Probability
• Statistical Hypothesis Testing

Mechanics:

• Kinematics
• Motion with Constant Acceleration
• Force and Motion
• Objects in Contact

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 at least 3 times a year (once each 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 students 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 following the programme of study in Pure Maths, Statistics and Mechanics.  Students will sit 2 internal examinations at the end of Year 12, one covering Pure Maths and Statistics and one covering Pure Maths and Mechanics, each will be 90 minutes long.

All year 12 Mathematics pupils sit the Senior Maths Challenge set by the UK Mathematics Trust and a small group of talented pupils usually 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 suitable calculator to all lessons.

Year 13

Topics Covered

Pure Mathematics

• Differentiation and Integration
• Algebra and Functions
• Trigonometry
• Numerical Integration
• Sequences and Series
• Numerical Methods
• Differential Equations
• Algebra and Graphs

Statistics:

• Probability
• The Normal Distribution
• Further Statistical Hypothesis Testing

Mechanics:

• Vectors in Context
• Projectiles
• Forces in Context
• Moments

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 at least 3 times a year (once each 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 following the programme of study in Pure Maths, Statistics and Mechanics. Students will sit 3 external examinations at the end of Year 13, one covering Pure Maths, one covering Pure Maths and Statistics and one covering Pure Maths and Mechanics, each will be 2 hours long.

All Year 13 Mathematics pupils are given the option to sit the Senior Maths Challenge set by the UK Mathematics Trust and a small group of talented pupils usually 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 suitable calculator to all lessons.

Course: A-Level Further Mathematics

Year 12 & 13

In the Further Mathematics course students will cover topics from the Pure Core, Additional Pure and Statistics content.

Topics Covered:

Pure Core:

• Matrices
• Vectors
• Complex Numbers
• Polynomials
• Mathematical Induction
• Series and Induction
• Lines and Planes in Space
• Simultaneous Equations and Planes
• Hyperbolic Functions
• Further Calculus
• Polar Co-ordinates
• Differential Equations

• Sequences and Series
• Number Theory
• Groups
• Further Vectors
• Surfaces and Partial Differentiation
• Further Calculus

Statistics:

• Counting Principles and Probability
• Discrete Random Variables
• Poisson Distribution
• Non-Parametric Hypothesis Tests
• Correlation and Regression
• Chi-Squared Tests
• Continuous Distributions
• Combining Random Variables
• Further Hypothesis Tests and Confidence Intervals

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 3 times a year (once each 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.  Students will sit internal examinations at the end of Year 12, each will be 75 minutes long.

Students will sit 3 external examinations at the end of Year 13, each will be 90 minutes long.

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 usually 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 suitable 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 3 times a year (once each 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.