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.
Curriculum
KS3 Overview
Year 7
Autumn Term 1
Topic 1 Basic Number
Topic 2 Rounding
Topic 3 Factors and Multiples
Topic 4 Basic Algebra and Substitution
Topic 5 Expanding and Factorising
Autumn Term 2
Topic 6 Angles
Topic 7 Angles in Polygons
Topic 8Fractions
Topic 9 Probability
Spring Term 1
Topic 10 Ratio
Topic 11 Equations
Topic 12 Area and Perimeter
Spring Term 2
Topic 13 Percentages
Topic 14 Sequences
Summer Term 1
Topic 15 Measure
Topic 16 Volume and Surface Area
Topic 17 Statistical Measures and Averages
Year 8 Foundation
Autumn Term 1
Topic 1 Rounding
Topic 2 Factors and Multiples
Topic 2b Bearings and Scale drawing
Topic 4 Pythagoras
Autumn Term 2
Topic 5 Standard Form
Topic 6 Ratio and Proportion
Spring Term 1
Topic 7 Algebra recap and extension
Topic 8 Perimeter and Area
Topic 9 Percentages
Spring Term 2
Topic 10 Circles
Topic 11 Linear graphs Recap and Extension
Topic 12 Real Life Graphs
Topic 13 Statistical Measures
Summer Term 1
Topic 14 3D shapes
Topic 15 Scatter graphs
Topic 16 Collecting and Representing data
Topic 17 Vectors
Summer Term 2
Topic 18 Polygons
Topic 19 Constructions and Loci
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
A-level maths is split into 3 components; pure, mechanics and statistics. Pure will be studied from one text book, and mechanics and statistics from another. Both text books are available from the shared L drive, and they provide notes, worked examples, exercises and answers. Students will be expected to use this resource 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
| Pure 2 Chapter | Assessed | Statistics/ Mechanics 2 Chapter | Assessed |
| Chapter1 - Algebraic methods | Penultimate week of Autumn Term 1 | Chapter1 - Regression, correlation and hypothesis testing | Penultimate week of Autumn Term 1 |
| Chapter2 - Functions and graphs | Chapter2 - Conditional probability | ||
| Chapter3 - Sequences and series | |||
| Chapter4 - Binomial expansion | Penultimate week of Autumn Term 2 | Chapter3 - The normal distribution | Penultimate week of Autumn Term 2 |
| Chapter5 - Radians | Chapter4 - Moments | ||
| Chapter6 - Trigonometric functions | Chapter5 - Forces and friction | ||
| Chapter7 - Trigonometry and modelling | Penultimate week of Spring Term 1 | Chapter6 - Projectiles | Penultimate week of Spring Term 1 |
| Chapter8 - Parametric equations | Chapter7 - Applications of forces | ||
| Chapter9 - Differentiation | Chapter8 - Further kinematics | ||
| Chapter10 - Numerical methods | Penultimate week of Spring Term 2 | ||
| Chapter11 - Integration | |||
| Chapter12 - Vectors | |||
| A level exam | Midway through Summer Term 2 | A level exam | Midway through Summer Term 2 |
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
Assessment is split into 2 types;
Low Stakes Test DIRT Tasks (directed improvement and reflection time). There are 14 of these both in Year 7 and 8 based on the topics that are covered. They are designed to help fill any gaps in student’s knowledge and support long term retention.
Medium Stakes Testing
In both Year 7 and 8 the are 2 medium stakes assessments (Autumn Term 2 and Summer Term 1). These are designed to check the understanding of the curriculum in Year 7 and 8.
All Year 7 and 8 content can be found on the courses section of Dr Frost Maths. Each topic has examples, video instructions and solutions to support independent learning. Please use the link below for more details.
Ks4
Assessment is split into 2 types;
Low Stakes Topic tests. These are at the end of each topic. The type of questions that students get in their Dr Frost homework, is the same to the feedback sheets that complete, which is the same as the topic test they do in lesson. They are designed to help fill any gaps in student’s knowledge and support long term retention.
Medium Stakes Testing
Year 9 complete 2 medium stakes tests in Autumn term 2 and Summer Term 1. These are based on everything they have learnt up to that point of the year.
Year 10 complete 2 medium stakes tests in Autumn 2 and Summer Term 2. The Autumn term test is based on everything they have learnt up to that point from Year 9 and the Summer Term 2 test is a full set of OCR GCSE Mathematics papers.
Year 11 complete 2 full sets of OCR GCSE Mathematics papers in Autumn Term 2 and Spring Term 2 with there final GCSE with OCR in the Summer.
All Year 9, 10 and 11 content can be found on the courses section of Dr Frost Maths. Each topic has examples, video instructions and solutions to support independent learning. For Year 11 there is a revision by grade course to support students of every ability. Please use the link below for more details.
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?
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