**Head of Department**

Mrs C Herlihy

**Subject Overview**

Welcome to the Mathematics Department at Cornwallis Academy. We are a large and dynamic department whose aim is for students to enjoy and excel in mathematics at all levels. We believe that all students, irrespective of ability, should be given the opportunity to achieve their full potential in mathematics.

We continuously strive to provide opportunities for all students to develop independently and solve problems logically, in a way that is suited to their learning style, so that they gain the confidence to share their ideas with their teachers and peers.

As a department, we believe that there is true value in understanding mathematics conceptually and being able to apply mathematics as opposed to simply learning how to answer exam questions. This is why you will not only find mathematics solely in mathematics lessons, but in all subjects and aspects of school life.

We encourage students to have a Casio fx-83GTX calculator in every lesson from Years 7-11. Students will also be expected to arrive to all lessons with a full set of equipment: pen, pencil, ruler, protractor, a pair of compasses and a scientific calculator.

Each week, all students will be set at least one piece of homework on the Hegarty Maths website.

There are plenty of resources online to help with independent study and revision. Some of our favourites include:

- www.hegartymaths.com
- www.mathsgenie.co.uk
- www.vle.mathswatch.co.uk
- www.bbc.co.uk/bitesize
- www.corbettmaths.com

**Key Stage 3**

**Key Stage 3 Overview:**

The Key Stage 3 course is covered over a period of 2 years and covers the main content domains;

- Number
- Algebra
- Ratio and Proportion
- Geometry and Measures
- Probability
- Statistics

We follow the White Rose Maths schemes of learning in Years 7 and 8. There is a termly plan for both year groups. Every half term is split into blocks that ensure students spend enough time mastering a deep understanding of the topic being covered.

Our scheme of learning is designed with interleaving (revisiting topics within new contexts) as a key element. For example, Year 7 starts with developing algebraic thinking and further development of algebraic skills is then woven throughout the year so students reinforce and extend their knowledge and understanding.

We firmly believe that students who are successful with number are much more confident mathematicians, so we have continued to emphasise number work throughout. We also recognise, however, that arithmetic can be barrier to some students accessing other areas of the curriculum, so we have also incorporated the teaching and learning of calculator skills throughout the curriculum.

#### Year 7:

##### Terms 1&2:

- Sequences – sequences are explored in detail using both diagrams and lists of numbers. Technology is used to produce graphs so students can appreciate and use the words “linear” and “non-linear” linking to the patterns they have spotted. Calculators are used throughout so number skills are not a barrier to finding the changes between terms or subsequent terms.
- Algebraic Notation – The focus of this topic is developing a deep understanding of the basic algebraic forms, with more complex expressions being dealt with later. Function machines are used alongside bar models and letter notation, with time invested in single function machines and the links to inverse operations before moving on to series of two-step function machines and substitution into short abstract expressions.
- Equality and Equivalence – In this section students are introduced to forming and solving one-step linear equations, building on their study of inverse operations. The equations met will mainly require the use of a calculator, both to develop their skills and to ensure understanding of how to solve equations rather than spotting solutions. This work will be developed when two-step equations are met in the next place value unit and throughout the course. The unit finishes with consideration of equivalence and the difference between this and equality, illustrated through collecting like terms.
- Place Value and Ordering – In this unit, students will explore integers up to one billion and decimals to hundredths. Using and understanding number lines is a key strategy explored in depth, and will be useful for later work on scales for axes. After being taught how to put numbers in order, this is a suitable point to introduce both the median and the range, separating them from other measures to avoid getting them mixed up. Rounding to the nearest given positive power of ten is developed, alongside rounding to one significant figure. Decimal places will come later, again to avoid too similar concepts being covered at the same time.
- Fractions, Decimals and Percentages – Building on the recent work on decimals, the key focus for this topic is for students to gain a deep understanding of the links between fractions, decimals and percentages so that they can convert fluently between those most commonly seen in real-life. Whilst looking at percentages, pie charts will be introduced. In addition, various forms of representation of any fraction will be studied, focusing on equivalence. The focus is very much on a secure understanding of the most common fractions under one, but fractions above one will be touched upon.

##### Terms 3&4:

- Addition and subtraction – The focus for this topic is building on the formal methods of addition and subtraction students have developed at Key Stage 2. All students will look at this in the context of interpreting and solving problems. For those for whom these skills are secure, there will be even more emphasis on this. Problems will be drawn from the contexts of perimeter, money, interpreting bar charts and tables and looking at frequency trees. We believe all these are better studied alongside addition and subtraction rather than separately. Calculators should be used to check and/or support calculations, with significant figures and equations explicitly revisited.
- Multiplication and division – This topic is dedicated to the study of multiplication and division, so allowing for the study of forming and solving two-step equations both with and without a calculator. Unit conversions will be the main context as multiplication by 10, 100 and 1000 are explored. As well as distinguishing between multiples and factors, substitution and simplification are also revisited and extended. Again, the emphasis will be on solving problems, particularly involving area of common shapes and the mean. Choosing the correct operation to solve a problem will also be a focus. There will also be some exploration of the order of operations, which will be reinforced alongside much of the content next term when studying directed number.
- Fractions and percentages of amounts – This topic focuses on the key concept of working out fractions and percentages of quantities and the links between the two. This is studied in depth in Year 8.
- Directed numbers – This block is designed to extend and deepen their understanding of directed number. Multiple representations and contexts will be used to enable students to appreciate the meaning behind operations with negative integers rather than relying on a series of potentially confusing “rules”. As well as exploring directed number in its own right, this block provides valuable opportunities for revising and extending earlier topics, notably algebraic areas such as substitution and the solution of two-step equations.
- Arithmetic with fractions – This block builds on the Autumn term study of “key” fractions, decimals and percentages. It will provide more experience of equivalence of fractions with any denominators, and to introduce the addition and subtraction of fractions. Bar models and concrete representations will be used extensively to support this. Adding fractions with the same denominators will lead to further exploration of fractions greater than one.

##### Terms 5&6:

- Constructing, measuring and using geometric notation – Students will build on their skills using rulers, protractors and other measuring equipment to construct and measure increasingly complex diagrams using correct mathematical notation. This will include three letter notation for angles, the use of hatch marks to indicate equality and the use of arrows to indicate parallel lines. Pie charts will be studied here to gain further practice at drawing and measuring angles.
- Developing geometric reasoning – This block covers basic geometric language, names and properties of types of triangles and quadrilaterals, and the names of other polygons. Angles rules will be introduced and used to form short chains of reasoning.
- Developing number sense – Students will review and extend their mental strategies with a focus on using a known fact to find other facts. Strategies for simplifying complex calculations will also be explored. The skills gained in working with number facts will be extended to known algebraic facts.
- Sets and probability – Fraction, decimal and percentage equivalence will be revisited in the study of probability, where students will also learn about sets, set notation and systematic listing strategies.
- Prime numbers and proof – Factors and multiples will be revisited to introduce the concept of prime numbers. Venn diagrams will be used to solve more complex HCF and LCM problems. Odd, even, prime, square and triangular numbers will be used as the basis of forming and testing conjectures. The use of counterexamples will be addressed.

#### Year 8:

##### Terms 1&2:

- Ratio and scale – This unit focuses initially on the meaning of ratio and the various models that can be used to represent ratios. Based on this understanding, it moves on to sharing in a ratio given the whole or one of the parts, and how to use e.g. bar models to ensure the correct approach to solving a problem. After this we look at simplifying ratios, using previous answers to deepen the understanding of equivalent ratio rather than ‘cancelling’ purely as a procedure. We also explore the links between ratio and fractions and understand and use pi as the ratio of the circumference of a circle to its diameter.
- Multiplicative change – Students now work with the link between ratio and scaling, including the idea of direct proportion, linking various forms including graphs and using context such as conversion of currencies which provides rich opportunities for problem solving. Conversion graphs will be looked at in this block and could be revisited in the more formal graphical work later in the term. Links are also made with maps and scales, and with the use of scale factors to find missing lengths in pairs of similar shapes.
- Multiplying and dividing fractions – Students will have had a little experience of multiplying and dividing fractions in Year 6; here we seek to deepen understanding by looking at multiple representations to see what underpins the (often confusing) algorithms. Multiplication and division by both integers and fractions are covered, with an emphasis on the understanding of the reciprocal and its uses. Links between fractions and decimals are also revisited.
- Working in the Cartesian plane – Building on their knowledge of coordinates from KS2, students will look formally at algebraic rules for straight lines, starting with lines parallel to the axes and moving on to the more general form. They can explore the notions of gradient and intercepts, but the focus at this stage is using the equations to produce lines rather than interpretation of m and c from a given equation; this will be covered in Year 9. Use of technology to illustrate graphs should be embedded. Appreciating the similarities and differences between sequences, lists of coordinates and lines is another key point.
- Representing data – Students are introduced formally to bivariate data and the idea of linear correlation. They extend their knowledge of graphs and charts from KS2 to deal with both discrete and continuous data.
- Tables and probability – Building from the Year 7 unit, this short block reminds students of the ideas of probability, in particular looking at sample spaces and the use of tables to represent these.

##### Terms 3&4:

- Brackets, equations and inequalities – Building on their understanding of equivalence from Year 7, students will explore expanding over a single bracket and factorising by taking out common factors. The higher strand will also explore expanding two binomials. All students will revisit and extend their knowledge of solving equations, now to include those with brackets and with unknowns on both sides. Bar models will be recommended as a tool to help students make sense of the maths. Students will also learn to solve formal inequalities for the first time, learning the meaning of a solution set and exploring the similarities and differences compared to solving equations. Emphasis is placed on both forming and solving equations rather than just looking a procedural methods of finding solutions.
- Sequences – This short block reinforces students’ learning from the start of Year 7, extending this to look at sequences with more complex algebraic rules now that students are more familiar with a wider range of notation.
- Indices – Before exploring the ideas behind the addition and subtraction laws of indices (which will be revisited when standard form is studied next term), the groundwork is laid by making sure students are comfortable with expressions involving powers, simplifying e.g. 3x
^{2}y x 5xy^{3}. - Fractions and percentages – This block focuses on the relationships between fractions and percentages, including decimal equivalents, and using these to work out percentage increase and decrease. Students also explore expressing one number as a fraction and percentage of another. Both calculator and non-calculator methods are developed throughout to support students to choose efficient methods. Financial maths is developed through the contexts of e.g. profit, loss and interest.
- Standard index form – Standard index form is introduced to all students building from their earlier work on indices last term. The use of context is important to help students make sense of the need for the notation and its uses.
- Number sense – This block provides a timely opportunity to revisit a lot of basic skills in a wide variety of contexts. Estimation is a key focus and the use of mental strategies will therefore be embedded throughout. We will also use conversion of metric units to revisit multiplying and dividing by 10, 100 and 1000 in context. We also look explicitly at solving problems using the time and calendar as this area is sometimes neglected leaving gaps in student knowledge.

##### Terms 5&6:

- Angles in parallel lines – This block builds on KS2 and Year 7 understanding of angle notation and relationships, extending all students to explore angles in parallel lines and thus solve increasingly complex missing angle problems. Links are then made to the closely connected properties of polygons and quadrilaterals. Students will also start to explore constructions with rulers and pairs of compasses.
- Area of trapezia and circles – The formulae for the area of a trapezium and for the area of a circle is taught to all students. A key aspect of the unit is choosing and using the correct formula for the correct shape, reinforcing recognising the shapes, their properties and names, and looking explicitly at compound shapes.
- Line symmetry and reflection – The teaching of reflection is split from that of rotation and translation to try and ensure students attain a deeper understanding and avoid mixing up the different concepts. Students will revisit and enhance their knowledge of special triangles and quadrilaterals and focus on key vocabulary such as object, image, congruent etc. Rotation and translations will be explored in Year 9.
- The data handling cycle – Much of the statistics content in Key Stage 3 is a continuation of that studied at primary school, and many of the charts and graphs in this block have been used in Year 7 and earlier in Year 8. A particular focus is using charts to compare different distributions. We also explore when graphs may be misleading, an important real-life consideration.
- Measures of location – Students have already met the median and the mean earlier in KS3. This block introduces the mode and also looks at when and why each average should be used. The previous block is built on as students have the opportunity to compare distributions, use these averages and the range. We also consider outliers, considering what effect these have on all the measures studied, and whether they should be included or excluded in our calculations.

**Assessment at Key Stage 3:**

Students will be graded in line with the GCSE grades (Grades 9-1 with the addition of Entry Level and Novice Level) to allow students to see their progress across all five years of their secondary education.

During the first term of Year 7, all students will take a baseline assessment to assess their current strengths and weaknesses and determine which set we feel will suit each student best.

All students in Years 7 and 8 will be expected to take an assessment at the end of each unit taught. There will also be regular assessments at the end of terms 2, 4 and 6 that consist of both non-calculator and calculator papers.

**Key Stage 4**

**Key Stage 4 Overview:**

All students follow the Edexcel GCSE (9–1) in Mathematics (1MA1) course. There are six content domains covered within the specification:

- Number

- Algebra
- Ratio and Proportion
- Geometry and Measures
- Probability
- Statistics

**Years 9 and 10:**

The GCSE Mathematics course allows students to further their understanding of the core basics covered in Key Stage 3. This is achieved with an exciting and engaging course which is designed to incorporate real life scenarios and situations which allow students to apply their mathematical knowledge and understanding to everyday problems.

#### Year 9 – Foundation

##### Terms 1&2

Number (Chapters 1 and 18)

- Calculations
- Decimal numbers
- Place value
- Factors and multiples
- Squares, cubes and roots
- Index notation
- Prime Factors
- Standard Form

Algebra (Chapters 2 and 5)

- Simplifying Algebraic expressions
- Substitution and Formulae
- Expanding brackets
- Factorising
- Solving equations
- Inequalities
- Sequences

##### Terms 3&4

Geometry and Angles (Chapters 6 and 12)

- Properties of shapes
- Angles in parallel lines
- Angles in triangles
- Angles in polygons
- Pythagoras’ theorem
- Trigonometry

Fractions, Decimals and Percentages (Chapter 4)

- Working with fractions
- Operations with fractions
- Multiplying and dividing fractions
- Fractions, decimals and percentage equivalences
- Calculating percentages

##### Terms 5&6

Graphs (Chapter 9)

- Coordinates
- Linear graphs
- Real-life graphs
- Distance-time graphs

Perimeter, Area and Volume (Chapters 8 and 17)

- Area of rectangles, parallelograms and triangles
- Area of trapezia
- Changing units
- Area of compound shapes
- Surface area of 3D solids
- Volume of prisms
- Area and circumference of a circle

#### Year 9 – Higher

##### Terms 1&2

Number (Chapter 1)

- Number problems and reasoning
- Place value and estimating
- HCF and LCM
- Counting with powers (indices)
- Zero, negative and fractional indices
- Powers of 10 and standard form
- Surds

Algebra (Chapter 2)

- Algebraic indices
- Expanding and factorising
- Equations
- Formulae
- Linear sequences
- Non-linear sequences

##### Terms 3&4

Geometry (Chapter 5)

- Angle properties of triangles and quadrilaterals
- Angles in polygons
- Pythagoras’ theorem
- Trigonometry

Fractions, Ratio and Percentages (Chapter 4)

- Fractions
- Ratio and proportion
- Percentages
- Fractions, decimals and percentage equivalences

##### Terms 5&6

Graphs (Chapter 6)

- Linear graphs
- Real-life graphs
- Line segments
- Quadratic graphs
- Cubic and reciprocal graphs

Perimeter, Area and Volume (Chapters 7 and 8)

- Perimeter and area
- Units and accuracy
- Volume and surface area of prisms
- Area and circumference of circles
- Sector area and arc length
- Volume and surface area of cylinders
- Volume and surface area of spheres
- Pyramids and Cones

#### Year 10 – Foundation

##### Terms 1&2

Quadratic Equations and Graphs (Chapters 16 and 20)

- Expanding double brackets
- Plotting quadratic graphs
- Factorising quadratic expressions
- Solving quadratic equations algebraically
- Cubic and reciprocal graphs
- Simultaneous equations
- Rearranging formulae

Congruence, Similarity and Vectors (Chapters 12 and 19)

- Congruence
- Geometric proof
- Similarity and enlargement
- Vectors

##### Terms 3&4

Ratio and Proportion (Chapters 11 and 14)

- Writing ratios
- Ratios and measures
- Using ratio and proportion
- Proportion and graphs
- Percentages
- Growth and decay
- Distance, speed and time
- Compound measures

Transformations, Constructions and Bearings (Chapters 10 and 15)

- Translation
- Reflection
- Rotation
- Enlargement
- Plans and elevations
- Scale drawings and maps
- Constructions
- Loci and regions
- Bearings

##### Terms 5&6

Probability (Chapter 13)

- Calculating probability
- Two events
- Experimental probability
- Venn diagrams
- Tree diagrams

Statistics (Chapters 3 and 7)

- Frequency tables
- Two-way tables
- Bar charts, line charts and pictograms
- Time series
- Stem and leaf diagrams
- Pie charts
- Scatter graphs
- Averages and range

#### Year 10 – Higher

##### Terms 1&2

Equations and Inequalities (Chapters 9 and 15)

- Solving quadratic equations by factorising
- The quadratic formula
- Completing the square
- Solving quadratic equations graphically
- Solving simultaneous linear equations
- Solving linear and quadratic simultaneous equations
- Solving linear inequalities
- Representing inequalities graphically
- Solving quadratic inequalities

Similarity, Congruence and More Trigonometry (Chapters 12 and 13)

- Congruence
- Geometric proof
- Similarity
- Trigonometric functions
- Area of a triangle
- The sine and cosine rule
- 3D pythagoras’ theorem and trigonometry problems

##### Terms 3&4

Algebra (Chapters 17 and 19)

- Rearranging formulae
- Algebraic fractions
- Surds
- Inverse and composite functions
- Iteration
- Algebraic proof
- Direct and inverse proportion
- Exponential functions
- Transformations of functions

Transformations, Constructions and Circle Theorems (Chapters 8 and 16)

- 3D solids
- Reflection, translation and rotation
- Enlargement
- Bearings and scale drawings
- Constructions
- Loci
- Circle Theorems

##### Terms 5&6

Probability (Chapter 10)

- Combined events
- Mutually exclusive events
- Experimental probability
- Independent events and tree diagrams
- Conditional probability
- Venn diagrams and set notation

Statistics (Chapters 3 and 14)

- Statistical diagrams
- Time series
- Scatter graphs
- Averages and range
- Cumulative frequency
- Box plots
- Histograms

**Year 11:**

This is the final year of the GCSE Mathematics course, which will draw together all content learnt over the last two years and focus heavily on the application of this to different problems and exam style questions. Following each assessment sat by Year 11, the class teacher will choose topics that students did not perform well on and revisit these in class. The main focus of these lessons will be on answering past exam questions so students can develop their exam technique as well as consolidating their knowledge, skills and understanding.

**Assessment at Key Stage 4:**

This qualification consists of three equally-weighted written examination papers. Paper 1 is a non-calculator assessment and both Paper 2 and 3 are calculator assessments. Each paper is 1 hour and 30 minutes in duration and each paper contains a total of 80 marks. Each paper has a range of question types; some questions will be set in both mathematical and non-mathematical contexts.

There are two overlapping tiers of entry (Foundation and Higher), with students being entered for the most appropriate tier. Movement between tiers is possible – however, students generally follow the same tier that they begin in Year 9. The final level of entry will be decided at the time of entry for GCSE, which is normally in January of Year 11.

The qualification will be graded and certificated on a nine-grade scale from 9 to 1 using the total mark across all three papers, where 9 is the highest grade. The available grades are as follows:

- Foundation tier: grades 1 to 5
- Higher tier: grades 3 to 9

Key stage 4 students follow the same assessment pattern as Key Stage 3 students in that they will have an end of topic assessment after every unit of work. In addition, all students in Years 9 and 10 will sit a GCSE paper at the end of terms 2, 4 and 6. At the end of Year 9 and 10, students will take an end of year assessment, which will be a set of all three GCSE papers to ensure that students are entered for the correct tier and to assess how well they have achieved during this year. In Year 11, students sit PPE examinations in Terms 2 and 4.

**Key Stage 5**

**Course Title:**

A-Level Mathematics

**Examining Body:**

Edexcel

**Overview of the course:**

A-Level Mathematics builds on GCSE Mathematics as well as introducing a number of new and exciting topics such as Statistics and Mechanics. This is a linear two year course with all final examinations taken at the end of the second year. Mathematics at this level, is a fantastic opportunity for students to gain a highly sought after qualification from future employers. Graduates of Mathematical based courses can go on to highly paid careers, often substantially higher than other disciplines.

**What Will You Study:**

Over the two year course you will study the following units:

**Pure Mathematics:**

- Topic 1 – Proof
- Topic 2 – Algebra and functions
- Topic 3 – Coordinate geometry in the (x, y) planet
- Topic 4 – Sequences and series
- Topic 5 – Trigonometry
- Topic 6 – Exponentials and logarithms
- Topic 7 – Differentiation
- Topic 8 – Integration
- Topic 9 – Numerical methods
- Topic 10 – Vectors

**Statistics:**

- Topic 1 – Statistical sampling
- Topic 2 – Data presentation and interpretation
- Topic 3 – Probability
- Topic 4 – Statistical distributions
- Topic 5 – Statistical hypothesis testing

**Mechanics**

- Topic 1 – Quantities and units in mechanics
- Topic 2 – Kinematics
- Topic 3 – Forces and Newton’s laws
- Topic 4 – Moments

**Assessment:**

At the end of the two-year course, students will sit three examination papers:

**Paper 1:**

- Pure Mathematics 1
- Worth 33.33% of the final grade
- Two-hour paper
- 100 marks available
- Calculator

**Paper 2:**

- Pure mathematics 2
- Worth 33.33 % of the final grade
- Two-hour paper
- 100 marks available
- Calculator

**Paper 3:**

- Statistics and Mechanics
- worth 33.33% of the final grade
- Two-hour paper
- 100 marks available
- Calculator

**Possible Career Paths: **

“Maths is the only A level proven to increase earnings in later life – by an average of 10%.” – Elizabeth Truss

There is a huge shortage of people with STEM skills needed to enter the workforce. **There are many new applications of Mathematics in technology as well as in engineering and science:**

- Games Design
- Internet Security
- Programming
- Communications
- Aircraft Modelling
- Fluid Flows
- Acoustic Engineering
- Electronics
- Civil Engineering
- Quantum Physics
- Astronomy
- Forensics
- DNA Sequencing

**Course Title:**

Level 3 Certificate in Mathematical Studies (Core Mathematics)

**Examining Body:**

AQA

**Overview of the course:**

Level 3 Mathematical Studies (Core Maths) is a new qualification designed for students who have achieved a grade 4 or above at GCSE. It helps to develop students’ mathematical skills and thinking and supports courses such as A-Level Psychology, Sciences, Geography, as well as technical and vocational qualifications. This qualification is a two year linear course with all final examinations taken at the end of the second year.

**What Will You Study:**

Over the two year course you will study the following units:

**Compulsory Content:**

- Topic 1 – Analysis of Data
- Topic 2 – Maths for Personal Finance
- Topic 3 – Estimation
- Topic 4 – Critical Analysis of Given Data and Models

**Optional Content:**

- Topic 1 – The Normal Distribution
- Topic 2 – Probabilities and Estimation
- Topic 3 – Correlation and Regression
- Topic 4 – Critical Path and Risk Analysis
- Topic 5 – Expectation
- Topic 6 – Cost-Benefit Analysis
- Topic 7 – Graphical Methods
- Topic 9 – Rates of Change
- Topic 9 – Exponential Functions

**Assessment:**

At the end of the two-year course, students will sit two examination papers:

**Paper 1:**

- Compulsory Content (Topics 1, 2 and 3)
- Worth 50% of the final grade
- 1 hour 30 minutes
- 60 marks available
- Calculator allowed

**Paper 2:**

- Compulsory Content (Topic 4) and Optional Content
- Worth 50% of the final grade
- 1 hour 30 minutes
- 60 marks available
- Calculator allowed