# Mathematics

## Head of Faculty - Mr Mark Adams

**Mathematics**

*‘Mathematics is the language with which God has written the universe.’* Galileo Galilei. Maths is a fundamental part of everyday life, often in ways that are not obvious. An in-depth knowledge of Maths provides the key to understanding why and how things work and the ability to predict how they might change over time and under different conditions. As importantly, Maths increases confidence with numbers so that aspects of everyday life such as personal finance, DIY, shopping, planning a holiday and cooking or baking are more easily understood.

We are passionate about our subject and we believe our curriculum provides students the opportunities to become confident in their understanding and application of mathematics. To achieve this, students need to become fluent in the fundamentals of mathematics, so that they develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. They need to be able to reason mathematically by following a line of enquiry or developing an argument or proof using mathematical language. They should also be able to solve problems by applying their mathematics in a range of contexts.

Through this, students develop resilience, logical and analytical thinking, the ability to work independently and to solve problems. These skills are useful whatever path students should take, although obviously we would expect that path to include more maths!

At St Thomas Aquinas we have a double spiral curriculum, Year 7 to 8 (KS3) then Year 9 to 11 (KS4). Year 7 is mixed ability teaching with strong assessment for learning and differentiation to ensure that all students are able to make outstanding progress. In Year 8 classes are in sets, which continues through to Year 11. Each topic that is taught has the same flow structure to reduce cognitive load and support long term learning.

Click to view actual image

All of the curriculum for St Thomas Aquinas Mathematics from Year 7 through to Year 13 can be found on the Dr Frost Maths Course that we have created. Here you can see the order that topics are taught along with over 1000 examples and videos for each individual topic, and the opportunity to practice with feedback to support independent learning. Dr Frost Maths tracks the amount of work each student is doing, so their strengths and areas to work on are highlighted. Please use the link below for more details.

**Curriculum**

**KS3 Overview**

**Year 7**

__ Autumn Term 1__Topic 1 Place Value

Topic 2 Rounding

Topic 3 The four operations and BIDMAS

Topic 4 Decimals

Topic 5 Negative Numbers

Topic 6 Factors, Multiples and Primes

__Topic 7 Introduction to Algebra__

**Autumn Term 2**Topic 8 Substitution

Topic 9 Brackets and Equations

Topic 9 Sequences

__Topic 10 Units and Conversions__

**Spring Term 1**Topic 11 Shapes and Perimeter

Topic 12 Area

Topic 13 Angles

__Topic 14 Unitary Methods and Recipes__

**Spring Term 2**Topic 15 Simplifying and equivalent Fractions

Topic 16 FDP Conversions

Topic 17 Percentages Non-Calculator

__Topic 18 Percentages with a Calculator__

**Summer Term 1**Topic 19 Fraction essentials

Topic 20 Multiplying and dividing Fractions

Topic 21 Adding and subtracting fractions

**Summer Term 2**

Topic 22 Collecting and representing data

Topic 23 Averages from a list

Topic 24 Frequency Table

**Year 8 Foundation**

__Autumn Term 1__

Topic 1 Extending Rounding

Topic 2 Indices

Topic 3 Equations extension

Topic 4 Changing the subject

Topic 5 Product of Primes (HCF/LCM)

__Autumn Term 2__

Topic 6 Pythagoras Theorem

Topic 7 Coordinates and the lines of x=a/y=a

Topic 8 Straight Line graphs

Topic 9 Angles in Parallel Lines

__Spring Term 1__

Topic 10 Scatter Graphs

Topic 11 Expanding Brackets and Factorising

Topic 12 Expanding Double Brackets

__Spring Term 2__

Topic 13 Standard Form

Topic 14 Probability Extension

__Summer Term 1__

Topic 15 Circles

Topic 16 Ratio

Topic 17 Extending Area of shapes

Topic 18 Volume of 3D shapes

__Summer Term 2__

Topic 19 Sequences

Topic 20 Factorise Quadratics

**Year 8 Higher**

__Autumn Term 1__

Topic 1 Indices

Topic 2 Standard Form

Topic 3 Solving Equations Building to Quadratics

__Autumn Term 2__

Topic 4 Ratio and Proportion

Topic 5 Forming and Solving Equations

Topic 6 Rearranging Formulae and Identities

__Spring Term 1__

Topic 7 Rounding and Bounds

Topic 8 Right Angled Triangles

Topic 9 Straight Line Graphs

__Spring Term 2__

Topic 10 Surds

Topic 11 Scale Diagrams

Topic 12 Representing Data

__Summer Term 1__

Topic 13 Equations and Simultaneous Equations

Topic 14 Vectors

__Summer Term 2__

Topic 15 Displaying Data

Topic 16 Constructions and Loci

**Ks4 Overview**

**Year 9 Foundation GCSE**

__Autumn Term 1__

Topic 1 Number

Topic 2 Factors, Multiples and Primes

Topic 3 Algebra and Substitution

Topic 4 Expanding and Factorising

__Autumn Term 2__

Topic 5 Coordinates and Linear Graphs

Topic 6 Fractions

Topic 7 Equations

__Spring Term 1__

Topic 8 Percentages

Topic 9 Angles

Topic 10 Changing the subject

Topic 11 Real-life graphs and Measures

Topic 12 Perimeter and Area

__Spring Term 2__

Topic 13 Circumference and Area

Topic 14 Probability

__Summer Term 1__

Topic 15 Volume and Surface area

Topic 16 Ratio and Proportion

Topic 17 Speed, Distance and Time

__Summer Term 2__

Topic 18 Transformations

Topic 19 Analysing data

**Year 9 Higher GCSE**

__Autumn Term 1__

Topic 1 Number

Topic 2 Factors, Multiples and Primes

Topic 3 Algebra and Substitution

Topic 4 Expanding and Factorising

__Autumn Term 2__

Topic 5 Coordinates and Graphs

Topic 6 Fractions

Topic 7 Equations

__Spring Term 1__

Topic 8 Percentages

Topic 9 Angles and Polygons

Topic 10 Changing the subject

__Spring Term 2__

Topic 11 Measures

Topic 12a Perimeter and Area

Topic 12b Circumference and Area

__Summer Term 1__

Topic 13 Probability

Topic 14 Ratio & Proportion

__Summer Term 2__

Topic 15 Transformations

Topic 16 Analysing data

**Year 10 Foundation GCSE**

__Autumn Term 1__

Topic 1 Indices & Standard form

Topic 2 Pythagoras

Topic 3 Bearings and Scale drawing

__Autumn Term 2__

Topic 4 Sequences

Topic 5 Inequalities

Topic 6 Volume and Surface area

Topic 7 Vectors

__Spring Term 1__

Topic 8 Scatter graphs

Topic 9 Equations of straight lines

Topic 10 Trigonometry

Topic 11 Simultaneous equations

__Spring Term 2__

Topic 12 Polygons

Topic 13 Direct and Inverse proportion

__Summer Term 1__

Topic 14 Probability

Topic 15 Collecting and Representing data

__Summer Term 2__

Topic 16 Quadratics

**Year 10 Higher GCSE**

__Autumn Term 1__

Topic 1 Indices

Topic 2 Standard Form

Topic 3 Pythagoras and Trigonometry

Topic 4 Bearings and Scale drawing

__Autumn Term 2__

Topic 5 Surds

Topic 6 Solving quadratics

__Spring Term 1__

Topic 7 Error intervals and Bounds

Topic 8 Simultaneous equations

Topic 9 Volume and Surface area

__Spring Term 2__

Topic 10 Sequences

Topic 11 – Collecting and Representing data

__Summer Term 1__

Topic 12 Parallel and Perpendicular lines

Topic 13 Sine and Cosine rules

Topic 14 Inequalities

__Summer Term 2__

Topic 15 Real life graphs

Topic 16 - Gradient and Area under a curve

**Year 11 Foundation GCSE**

__Autumn Term 1__

Topic 1 - Congruence and Similarity

Topic 2 - Constructions and Loci

__Autumn Term 2__

Topic 3 - Fractions recap

Topic 4 - Percentages recap

__Spring Term 1 to GCSE Exams__

Tailored scheme of work based on the class gaps. Data security direct teaching.

**Year 11 Higher GCSE**

__Autumn Term 1__

Topic 1 - Algebraic Fractions

Topic 2 - Algebraic Proof

Topic 3 - Graph Transformations

__Autumn Term 2__

Topic 4 – Vectors

__Spring Term 1__

Topic 5 - Equations of Circles and Tangents

Topic 6 - Congruence and Similarity

Topic 7 - Iteration

Topic 8 - Circle Theorems

__Spring Term 2 to GCSE Exams__

Tailored scheme of work based on the class gaps. Data security direct teaching.

**KS5 Overview**

**Overview of KS5 course**

The Mathematics A-level and Further Mathematics A level are 2 separate A-levels that we offer which are split into 3 components; pure, mechanics and statistics. All text books are available from the shared L drive, and they provide notes, worked examples, exercises and answers. Students will be expected to use these resources to work independently to master the concepts taught in each lesson. Independent work should amount to 4-5 hours minimum per week.

This guide is designed to inform you of all the resources available to you in order to make the most of any available time you can devote to independent study.

**A level Resources**

Pearson A level mathematics text books (available on the L drive).

‘Madasmaths’ exam question practice materials (website address; https://madasmaths.com/archive_maths_booklets_advanced_topics.html).

This resource offers exam standard questions set in a hierarchy of difficulty, with many questions coming with written solutions.

**Support resources**

Support for the exercises offered in the Pearson text books can be found from the ‘physics and maths tutor’ website (web address; https://www.physicsandmathstutor.com/).

This website offers answers and some detailed method to all exercises in the Pearson text books.

Students will also be provided with an Excel spreadsheet linking each chapter of the text book to the relevant task on the Madasmaths website.

**A level Assessments/Course Outline**

**Mathematics A Level**

**Pure (Year 1)**

**Chp1 - Algebraic Expressions****Chp2 - Quadratics****Chp3 - Equations & Inequalities****Chp4 - Graphs & Transformations****Chp5 - Straight Line Graphs****Chp6 - Circles****Chp7 - Algebraic Methods****Chp8 - Binomial Expansion****Chp9 - Trigonometric Ratios****Chp10 - Trigonometric Identities & Equations****Chp11 - Vectors****Chp12 - Differentiation****Chp13 - Integration****Chp14 - Exponentials & Logarithms**

**Statistics (Year 1)**

**Chp1 - Data Collection****Chp2 - Measures of location and spread****Chp3 - Representations of data****Chp4 - Correlation****Chp5 - Probability****Chp6 - Statistical distributions****Chp7 - Hypothesis testing**

**Mechanics (Year 1)**

**Chp8 - Modelling in Mechanics****Chp9 - Constant acceleration****Chp10 - Forces and motion****Chp11 - Variable acceleration**

**Pure (Year 2)**

**Chp1 - Algebraic methods****Chp2 - Functions and graphs****Chp3 - Sequences and series****Chp4 - Binomial expansion****Chp5 - Radians****Chp6 - Trigonometric functions****Chp7 - Trigonometry and modelling****Chp8 - Parametric equations****Chp9 - Differentiation****Chp10 - Numerical methods****Chp11 - Integration****Chp12 - Vectors**

**Statistics (Year 2)**

**Chp1 - Regression, correlation and hypothesis testing****Chp2 - Conditional probability****Chp3 - The normal distribution**

**Mechanics (Year 2)**

**Chp4 - Moments****Chp5 - Forces and friction****Chp6 - Projectiles****Chp7 - Applications of forces****Chp8 - Further kinematics**

**Further Mathematics A level**

**Core Pure (Year 1)**

**Chp1 - Complex Numbers****Chp2 - Argand Diagrams****Chp3 - Series****Chp4 - Roots of Polynomials****Chp5 - Volumes of Revolution****Chp6 - Matrices****Chp6 - Matrices****Chp7 - Linear Transformations****Chp8 - Proof By Induction****Chp9 - Vectors**

**Core Pure (Year 2)**

**Chp1 - Complex Numbers****Chp2 - Series****Chp3 - Methods in Calculus****Chp4 - Volumes of Revolution****Chp5 - Polar Coordinates****Chp6 - Hyperbolic Functions****Chp7 - Methods in Differential Equations****Chp8 - Modelling with Differential Equations**

**Further Stats 1 (** A-level only)**

**Chp1 - Discrete Random Variables****Chp2 - Poisson Distributions****Chp3 - Geometric & Negative Binomial Distributions******Chp4 - Hypothesis Testing****Chp5 - Central Limit Theorem******Chp6 - Chi-Squared Tests****Chp7 - Probability Generating Functions******Chp8 - Quality of Tests****

**Further Mechanics 1 ****(** A-level only)**

**Chp1 - Momentum & Impulse****Chp2 - Work, Energy & Power****Chp3 - Elastic Strings & Springs******Chp4 - Elastic Collisions in One Dimension****Chp5 - Elastic Collissions in Two Dimensions****

The independent use of both of these resources offers instruction via notes and worked examples, practice using the exercises and answers, and exam practice using the mixed exercises and past exam questions using the Madasmaths materials.

**A level Revision**

Revision is continuous and not targeted at specific tests. There will be frequent tests and students are expected to be ready to tackle them at any time. Lesson time will not be set aside for revision.

‘Dr Frost Maths’ (website address; https://www.drfrostmaths.com/) will be used frequently to set work, but students are expected to use this as a resource for exam questions to help on-going revision.

Students are expected to have completed all tasks set for the given deadline. Difficulties and misconceptions should be dealt with before the due date. Problems with the work cannot be dealt with during the lesson – therefore students are expected to seek help from teachers before the due date.

Students are strongly advised to have found a routine and timetable that allows completion of homework, practice of new concepts and revision for exams – as well as allowing time to ask teachers for additional help, within the first 2 weeks of the course.

**A level Tips**

- Maths is mastered by doing maths – complete questions from start to finish thoroughly and on a regular basis.
- Aim to tackle questions at the most challenging level and be resilient. Once the question is understood, tackle the same question again in the near future and on a regular basis after that. This will build up long term memory. A level standard questions require more steps than GCSE and they therefore require more regular practice.
- Exam questions will not have the same obvious starting points as GCSE standard questions – students will therefore need to be willing to explore a variety of starting points before finding the correct technique.
- Thorough working out is always advisable, but students still only have a limited amount of time in an exam. It is therefore vital that students have some key techniques practiced so that they are intuitive and completed quickly. These techniques include;
- completing the square
- solving quadratic inequalities through sketching the graph
- substitution into formulae, simplifying and rearranging efficiently

using the formulae for straight line graphs, the distance between 2 points and the midpoint of 2 coordinates

**Assessment Details**

**KS3**

In Year 7 Students will sit a baseline test within the first few weeks to assess strengths and weaknesses in mathematics that they already have. This information will then be used to address these gaps. Students will sit through two main assessment windows that will be reported back to parents taking place in Autumn 2 and Summer 1. Students will sit additional low stakes assessments in Autumn 1, Spring 2 and Summer 2 set by the maths faculty to monitor their retention of what they have been learning and to assess any weaknesses.

In Year 8 Students will sit through two main assessment windows One in Spring 1 and the second in Summer 2. These are medium stake assessments that are designed to check the overall understanding of the curriculum that students have acquired. Students will also sit a low stakes assessment of maths in Autumn 1, Autumn 2, Spring 2 and Summer 1 set by the maths faculty to monitor their retention of what they have been learning and to assess any weaknesses.

**KS5**

For students at our school, A-Level Mathematics and Further Mathematics assessments are essential checkpoints in their academic journey. These assessments occur at the end of each half term over the two-year A-Level program. They play a crucial role in evaluating the understanding of the topics covered in these challenging courses.

A-Level Mathematics covers a wide range of topics, including calculus, algebra, geometry, and statistics. Further Mathematics takes your understanding to a deeper level, introducing complex concepts like differential equations and matrices. What makes these assessments unique is their cumulative nature – they link back to the very beginning of the course. This means that you'll revisit and reinforce fundamental concepts throughout your studies, which is crucial for mastering the more advanced material.

These assessments are not just about preparing for the final A-Level exams; they help you develop strong problem-solving skills that are invaluable for your future education and careers in various fields. So, remember that each assessment is an opportunity to show your growth and understanding of mathematics, ensuring that you're on the right track to excel in these subjects.

**Additional Resources**

It is helpful to be able to put the ideas you are learning into some real-life context. These books will help place the use and purpose of what students are learning into practical situations, and can lead to giving students a clearer choice of degree course or career path.

- Hello World: How to be Human in the Age of the Machine

- A Brief History Of Time: From Big Bang To Black Holes

- Brief History of Infinity: The Quest to Think the Unthinkable

- Does God Play Dice?: The Mathematics of Chaos

- Flatland: A Romance of Many Dimensions

- Big Data: Does Size Matter?

Close