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.

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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.

Dr Frost Maths

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
Autumn Term 2
Topic 7 Introduction to Algebra
Topic 8 Substitution
Topic 9 Brackets and Equations
Topic 9 Sequences
Spring Term 1
Topic 10 Units and Conversions
Topic 11 Shapes and Perimeter
Topic 12 Area
Topic 13 Angles
Spring Term 2
Topic 14 Unitary Methods and Recipes
Topic 15 Simplifying and equivalent Fractions
Topic 16 FDP Conversions
Topic 17 Percentages Non-Calculator
Summer Term 1
Topic 18 Percentages with a Calculator
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.

https://qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-mathematics-specification-issue4.pdf

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)

Statistics (Year 1)

Mechanics (Year 1)

Pure (Year 2)

Statistics (Year 2)

Mechanics (Year 2)

Further Mathematics A level

Core Pure (Year 1)

Core Pure (Year 2)

Further Stats 1 (** A-level only)

Further Mechanics 1 (** A-level only)

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.

Dr Frost Maths

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

Hello World

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

A Brief History Of Time

Brief History of Infinity: The Quest to Think the Unthinkable

Brief History of Infinity

Does God Play Dice?: The Mathematics of Chaos

Does God Play Dice?

Flatland: A Romance of Many Dimensions

Flatland

Big Data: Does Size Matter?

Big Data