## Mathematics

### Curriculum Leader: Mr E Hargreaves

Mr E Hargreaves (hargreavese@saintgeorgescofe.kent.sch.uk)

Mrs. E Lowe (lowee@saintgeorgescofe.kent.sch.uk)

Lessons and homework:
Year 7 & 8
– Fortnightly students have 7 lessons. Students receive a paper homework once a week. This contains a mixture of topics taught during the previous week, as well as a selection of questions on topics encountered in the past to aid students in retrieval practice. Homework support is available after school every day in rooms 3 & 8.

Year 9 – Fortnightly students have 9 lessons. Students receive homework in much the same way as years 7 & 8.

Lesson style:

All lessons have an embedded collaborative approach using Kagan structures, particularly when developing and embedding knowledge of a new skill or technique. Lessons also feature plenty of opportunity for pupils to practice, as well as develop their problem-solving ability by applying existing knowledge to unfamiliar contexts.

Assessment:

All students are assessed at least once a term on the topics that have been covered during that term’s work. There also are two allocated dates for summative assessment for each year group, these assessments will draw from all content encountered throughout the year of study and form the basis of our judgements when recording pupil grades and progress.

Curriculum

Year 7 Topics:

• Term 1 – Basic Number: Addition, subtraction, multiplication, and division, all including decimals. Factors, multiples, including Highest Common Factor (HCF) and Lowest Common Multiple (LCM). Perimeter and area of basic 2D shapes.
• Term 2 – Geometry: Draw, measure and name angles. Find unknown angles using angles rules, find unknown angles using rules within parallel lines. Understand properties of triangles and quadrilaterals.
• Term 3 – Fractions: Equivalent fractions, fractions and decimals, mixed and improper, fraction of a quantity. Add, subtract, multiply and divide with fractions and mixed numbers.
• Term 4 – Algebra: Completing and understanding how to apply the correct order of operations. Introduce the basics of algebra including substitution and simplifying algebraic expressions. Continuing sequences and calculating nth term.
• Term 5 – Percentages: Convert between fractions, decimals and percentages. Calculations with percentages, percentage of a quantity and percentage increase and decrease.
• Term 6 – Statistics: Collect and organise data. Read and draw bar charts, pie charts and pictograms. Understand averages by calculating mean, median and mode.

Year 8 Topics:

• Term 1 – Number: Exploring factors, multiples and primes including writing a number as a product of its primes. Highest Common Factor (HCF) and Lowest Common Multiple (LCM) and calculating these with Venn diagrams. Add, subtract, multiply and divide with fractions and mixed numbers.
• Term 2 – Equations and Inequalities: Calculating with negative numbers and understanding inequality statements, solving linear equations and inequalities and continuing sequences and calculating nth term.
• Term 3 – 2D Geometry: Construct triangles and quadrilaterals. Convert between units of length and area. Perimeter and area of 2D shapes including triangles, parallelograms and trapezia. Use compound measures for speed, density and pressure.
• Term 4 – Ratio and Proportion: Represent ratios, share parts into given ratios and write ratios as fractions. Direct and inverse proportion. Calculations with percentages, percentage increase and decrease, compound interest and reverse percentages.
• Term 5 – Circles and 3D Geometry: Rounding, significant figures and estimating. Circumference and area of a circle. Understand the properties of 3D shapes and draw nets. Calculate the volume of prisms.
• Term 6 – Linear Graphs: Plot coordinates and draw linear graphs. Paying attention to horizontal and vertical lines, calculating gradients, both positive and negative and calculating midpoints of lines.

Year 9 Topics:

• Term 1 – Algebraic Expressions: Understanding arithmetic and geometric sequences. Changing the subject of a formula. Expanding binomials and factorising quadratic expressions. Using rules of indices and writing and reading standard form.
• Term 2 – Constructions and shapes: Accurately completing constructions and understanding loci. Begin to prove congruency and similarity. Calculate missing angles in regular and irregular polygons.
• Term 3 – Equations and inequalities: Construct and solve equations and solve quadratic equations. Solve simultaneous equations graphically and algebraically. Drawing quadratic, cubic and reciprocal graphs.
• Term 4 – 2D Geometry: Pythagoras Theorem and Trigonometry in right angled triangles. Accurately complete and describe all transformations, including, translations, rotations, reflections and enlargements.
• Term 5 – Statistics: Understand averages by calculating mean, median and mode and from a grouped frequency table. Comparing data sets and sampling methods. Reading and drawing scatter graphs and using them to make predictions.
• Term 6 – 3D Geometry: Compare units of volume and area. Calculate the volume and surface area of prisms, cylinders, cones, spheres and pyramids.

Useful Resources:

https://www.bbc.co.uk/bitesize/subjects/zqhs34j

www.corbettmaths.co.uk

www.drfrostmaths.co.uk

Mr E Hargreaves (hargreavese@saintgeorgescofe.kent.sch.uk)

Mr L Smith-Shepherd (smith-shepherdl@saintgeorgescofe.kent.sch.uk)

Examinations

Students study towards the GCSE Mathematics exam to be taken at the end of Year 11. There are two tiers, Higher (Grades 4-9) and Foundation (Grade 1-5), students will be selected for appropriate tiers depending on work ethic and ability. Currently we use OCR for Foundation and Edexcel for Higher.

Lessons and homework:

Year 10 & 11 – Fortnightly students have 9 lessons. Students receive a paper homework once a week. This contains a mixture of topics taught during the previous week, as well as a selection of questions on topics encountered in the past to aid students in retrieval practice. Homework support is available after school every day in rooms 3 & 8.

Lesson style:

Year 10 – All lessons have embedded a collaborative (Kagan) approach to learning mathematics. Topics have a combination of mastery techniques, concrete pictorial and abstract (CPA), discovery and structured consolidation of topics. More emphasis is placed on exam technique and preparation for GCSEs.

Year 11 – Lessons are based around structured consolidation to ensure preparation for GCSEs. All topics from previous years are covered, exam papers are systematically used to support revision.

Assessment:

Year 10 – All students are assessed on all topics they have covered in a single half term. Students are expected to complete independent study to prepare for an assessment. SIT (Strengths, Improvements and Targets) marking will be given and an opportunity to reflect and improve on results is given after in the form of DIRT (Dedicated, Improvement and Reflection Time).

In the final term of the year students will take part in a PPE (Mock Exam) in the tier that has been chosen for them. Exams will take place in the hall.

Year 11 – Students are assessed through the whole school PPE schedule and are given full mock exams at two stages throughout the year. From year 11 we provide one-hour compulsory revision per week after school on a Wednesday between 3:15 and 4:15. This however will only support the independent revision that needs to take place to reach their full potential.

Year 10 Topics:

Foundation tier:

• Term 1 – Number: Estimating square roots and using rules of indices. Percentages including increase and decrease, profit and loss and compound interest. Calculating nth term of a sequence and calculating with standard form.
• Term 2 – Geometry: Solve problems with similar shapes. Read and draw bearings accurately and prove angle rules algebraically. Solve problems with Pythagoras theorem and trigonometry.
• Term 3 – Algebra and Graphs: Understand linear graphs including parallel and perpendicular lines. Using and manipulating constant acceleration formulae. Solve problems with basic vectors.
• Term 4 – Probability: Theoretical and experimental probability. Using two-way tables and listing outcomes of events. Understanding Venn diagrams and probability trees.
• Term 5 – Applications of Algebra: Expand and factorise quadratic expressions. Draw and read quadratic, cubic and reciprocal graphs. Solve simultaneous equations graphically and algebraically.
• Term 6 – Geometry and Algebra: Circumference and area of circles, arcs and sectors of circles. Solve problems with direct and inverse proportion.

Higher tier (In addition to all covered in Foundation):

• Term 1 – Number: Calculating with fractional powers, surds including rationalising the denominator. Calculating the nth term of quadratic sequences. Recurrence relations and solving equations by iterative methods.
• Term 2 – Geometry: Solving problems in 3D using Pythagoras theorem and trigonometry. Understanding exact values and trigonometric graphs.
• Term 3 – Algebra and Graphs: Solve complex vector problems. Calculate equations of parallel and perpendicular lines and shade regions of inequalities on graphs.
• Term 4 – Probability: Topics for probability and using probability trees and using conditional probability.
• Term 5 – Applications of Algebra: Drawing and reading exponential graphs. Solving quadratic with coefficients greater than 1 and by completing the square and using the formula. Calculating with algebraic fractions.
• Term 6 – Geometry and Algebra: Apply and prove circle theorems. Calculate the equation of a circle and tangent to a circle. Direct and inverse proportion with powers and roots.

Year 11 Topics:

Year 11 will complete a program of study which will cover each of the following topics given in various forms and with exam technique highlighted throughout.

Foundation Tier

1. Basic Number
1. Multiples, Factors and Primes – HCF and LCM
2. Place Value – Square and Cube numbers
3. Prime Factors
4. Long Multiplication and Division – Negative numbers
5. Order of Operations
2. Fractions, Decimals and Percentages
1. Equivalent and simplifying
2. Ordering Fractions – Mixed and Improper numbers
4. Problems
5. Order fractions, decimals and percentages
6. Percentage of an amount
7. Percentage increase/decrease – Percentage profit/loss
8. Percentage problems
9. Compound Interest
3. Angles
1. Straight line, vertically opposite and round a point
2. Parallel lines, Perpendicular lines
3. Triangles – Special triangles
4. Polygons – interior/exterior angles
5. Bearings
4. Algebra
1. Collecting like terms
2. Expanding Brackets – Double brackets
4. Solve equations – 1 step/2 step/brackets/variables on both sides
5. Graphs
1. Linear – Coordinates, y=n, x=n, y=mx+c
3. Cubic and reciprocal
6. Inequalities
1. Number line
2. Solving inequalities
7. Change the subject of a formula
2. Recognise parallel lines
9. Area and Perimeter
1. Rectangle, Triangle, Parallelogram, Trapezium, Circle.
2. Circle – Area sectors and Arc Length
3. Compound shapes
4. Problem solving
10. 3D Shapes
1. Plans, Elevations and Nets
2. Volume of Cuboids
3. Volume of Prisms
4. Surface Area – Cubes, Cuboids, Prisms
5. Volume/Surface Area – Cylinder
11. Pythagoras and Trigonometry
1. Simple Pythagoras
2. Trigonometric ratios and how to use them
3. Problem solving
12. Data Handling
1. Pictograms – Bar Charts – Pie Charts – Scatter Graphs
2. Types of data
3. Frequency Polygon – Venn diagram
4. Averages – Mean, median, mode and range – advantages and disadvantages
5. Grouped frequency tables
13. Transformations
1. Rotational symmetry
2. Translation, rotation, reflection and enlargement
14. Construction and Loci
1. Construct triangles, angle bisector, perpendicular bisector
2. Problem solving
15. Ratio
1. Simplifying and writing
2. Writing as fractions
3. Calculating amounts from a ratio
4. Worded problems
5. Direct and Inverse proportion problems
16. Probability
1. Of an event
2. Two-way tables, sample space diagrams
3. Mutually exclusive and independent events
4. Probability trees – AND/OR – Dependant events
17. Vectors
1. Basic vectors –column vectors
2. Problem solving
18. Measures
1. Convert unit lengths, area and volume
2. Imperial/ Metric
3. Speed, distance and time – calculations and graphs – problem solving
4. Density, mass and volume – problem
19. Sequences
1. Complete a sequence
2. Nth term
3. Is a number part of a sequence?
20. Standard Form
1. Write numbers in standard form – large/small
2. Calculating with standard form
21. Congruent Shapes
1. Conditions for congruency
2. Problems and proof
22. Simultaneous equations
1. Solving
2. Forming and solving

Higher Tier

All foundation topics are deemed assumed knowledge, therefore any gaps in knowledge would also need to be revised from the foundation tier list.

1. Indices
1. Basic indices multiplying and dividing
2. Negative indices
3. Fractional indices
2. Standard Form
1. Writing small and large numbers
2. Calculating with standard form
3. Percentages
1. Percentage increase/decrease – Percentage profit/loss
2. Percentage problems
3. Compound Interest and depreciation
4. Sequences
1. Complete a sequence
2. Nth term
3. Is a number part of a sequence?
5. Transformations
1. Rotational symmetry
2. Translation, rotation, reflection and enlargement
3. Enlargement with negative scale factor
4. Combining transformations
6. Similar shapes
1. Using scale factor to calculate lengths
2. Proving similarity and congruence in triangles
7. Surds
1. Simple rules of surds
2. Rationalising the denominator
8. Angles
1. Straight line, vertically opposite and round a point
2. Parallel lines, Perpendicular lines
3. Triangles – Special triangles
4. Polygons – interior/exterior angles
5. Bearings
9. Pythagoras and Trigonometry
1. Simple Pythagoras
2. Trigonometric ratios and how to use them
3. Problem solving
4. Sine and cosine rule
5. Using trigonometry to calculate area of a triangle
10. Graphs
1. Linear – Coordinates, y=n, x=n, y=mx+c
2. Understanding y = mx + c
4. Cubic
5. Reciprocal
6. Exponential
11. Vectors
1. Basic vectors –column vectors
2. Problem solving
12. 3D Shapes
1. Plans, Elevations and Nets
2. Volume of Cuboids
3. Volume of Prisms
4. Surface Area – Cubes, Cuboids, Prisms, Spheres
5. Volume – Cubes, Cuboids, Prisms, Spheres
13. Probability
1. Of an event
2. Two-way tables, sample space diagrams
3. Mutually exclusive and independent events
4. Probability trees – AND/OR – Dependant events
5. Venn Diagrams and data set
14. Algebra
1. Collecting like terms
2. Expanding Brackets – Double brackets
4. Solve equations – 1 step/2 step/brackets/variables on both sides
1. By factorising
2. Using the formula
3. Completing the square
4. Solving simultaneous equations
6. Algebraic fractions – All functions
7. Area and Perimeter
1. Rectangle, Triangle, Parallelogram, Trapezium, Circle.
2. Circle – Area sectors and Arc Length
3. Compound shapes
4. Problem solving
8. Variation
1. Direct proportion
2. Inverse proportion
9. Circle theorems
10. Equation of a circle
1. Recognising
2. Calculating the equation of a line perpendicular to a circle
11. Cumulative Frequency
1. Plotting and drawing the graph
2. Using quartiles and inter quartile range
12. Histograms
1. Drawing and using histograms
2. Calculating frequency density
13. Compound measure
1. Speed
2. Density
3. Pressure

Useful Resources:

www.corbettmaths.co.uk

www.mathsbox.org.uk

Exam Specifications and past papers

 Contact : Mr E Hargreaves Examination Board : Edexcel.

What is Maths A level about?

Mathematics at AS and A2 level is comprised of three main areas:

Pure Mathematics, Statistics and Mechanics.  Pure Mathematics is the study of the basic principles of Mathematics that underpin many real life processes.  During this part of the course you will extend your knowledge of such topics as algebra, trigonometry and sequences.  You will also learn new concepts such as calculus.  Statistics is the study of data.  This part of the course will teach you how to critically analyse data and how probability theory can be used to model real life situations. Mechanics is a practical application of Mathematics. It considers how we can use Mathematics to model real-life situations and how best to solve physical problems.

Course Requirements

Prospective students must have at least a grade B at GCSE Mathematics, though an A grade is desirable.  There is a significant difference in the expected outcome of students who achieved an A grade at GCSE compared with those who achieved a B grade due to the difficult nature of the subject.

Since the course is very algebra based you must also have good skills in manipulating algebra and you will be tested on this during the first week of the course.

Between Year 11 and Year 12, students are required to complete a summer work booklet.  This is a unit of work designed to bridge the gap between GCSE and A level.  It should take students around two hours to complete and mainly focuses on the B, A and A* topics of GCSE which are fundamental in A level Maths.

Three weeks after commencing the A level Maths course, students will be given an induction assessment to complete.  This allows us to accurately assess whether or not Mathematics A level is the correct course.  We carry out this testing very early in the course, as it is extremely important that students who will struggle to cope with the nature and demands of Mathematics A level are identified.

Mathematics is a highly employable A level to have.  Most students who study Mathematics go on to careers in Engineering, Computer Science, Finance, Investment Analyst, Science and Research, Medicine, Economics, Statistician, Chartered Accountant, Systems Developer.

Expectations

• The department expects all ‘A’ level students to approach their studies in a mature fashion and to complete all tasks to the best of their ability both in class and for homework tasks.
• Students are expected to complete at least 4 hours of additional work outside of lessons per week. This is particularly important in Maths as the techniques learnt cannot be simply learnt and then recalled in a test.  They need to be practiced.
• Each student will need to bring their Module textbook and a lever arched folder to each lesson together with a stationary supply and scientific calculator.
• Students carry out an assessment after each unit of work (around every two weeks).  Students are expected to remain on target and complete each assessment to a satisfactory standard.  Students who do not perform as expected will be required to retake the assessment/s (times will be announced).
• Most importantly, students must arrive with enthusiasm and a willingness to learn.

Complementary Subject Combinations
The main links between other subjects and Maths come from the choice of applied topic:

• Mechanics – fits well with Physics as there is a lot of overlap in the content of the courses
• Decision – there are many A levels and degrees that use the techniques learned in Decision Maths.  Computer Sciences and Programming, Business and Management and Electronics all have elements of Discrete Maths (another name for Decision Maths), in their university courses.
• Statistics – fits well with Psychology and Biology as they use statistical analysis in some of their coursework.

Video Tutorials. The most useful website in my opinion is www.examsolutions. It contains videos on all A level topics which are a useful start point for students who are reading ahead.
Past question papers are an essential part of the revision process for Mathematics, it is important to get plenty of practice of the type of questions you will be asked in exams. At the end of each chapter in the text book there is a mixed exercise made up of past exam questions and we always leave plenty of time after completing the learning for the module to do past paper practice, both under exam conditions and as an open book revision tool. The entire collection of Edexcel past Quest Papers for all modules is located via this link http://www.mathspapers.co.uk/edexcel.html.

Textbooks

Edexcel AS and A Level Modular Mathematics: Core Mathematics 1 (C1),  by Keith Pledger and Mr Dave Wilkins (13 May 2008).

Edexcel AS and A Level Modular Mathematics: Core Mathematics 2 C2),  by Keith Pledger and Mr Dave Wilkins (13 May 2008).

Edexcel AS and A Level Modular Mathematics: Core Mathematics 3 (C3), by Keith Pledger and Mr Dave Wilkins (13 May 2008).

Edexcel AS and A Level Modular Mathematics: Core Mathematics 4 (C4),  by Keith Pledger and Mr Dave Wilkins (13 May 2008).

Edexcel AS and A Level Modular Mathematics – Statistics 1, by Keith Pledger et al (Author), Alan Clegg (Author), Susan Gardner (Editor).

Edexcel AS and A Level Modular Mathematics – Mechanics 1 by Ms Susan Hooker, Mr Michael Jennings, Bronwen Moran and Mr Laurence Pateman (3 Oct 2008).

How is this course structured?

All units are equal weighting.

 Unit Content Unit Assessment AS Unit 1:  Core Maths 1  This extends your GCSE knowledge of Algebra.Indices and Co-ordinate systems.  It also teaches you how to express your Mathematics correctly.  This is the only non-calculator option. Module examination in May/June ofYear 12. AS Unit 2: Core Maths 2  This builds upon the work you did in Core 1. In this module you begin to look at such topics as Calculus and Trigonometry. Module examination in May/June ofYear 12. AS Unit 3:  Statistics 1  This module covers how to analyse data, the binomial distribution, probability theory and how to test whether a particular result is significant Module examination in June of Year 12. A2 Unit 4: Core Maths 3  This module extends the calculus techniques that you learnt in Core 2.  It also looks at functions and natural logarithms.  You will be required to produce a piece of coursework. Module examination in June of Year 13. A2 Unit 5: Core Maths 4 This module is called Applications of Advanced Mathematics.  The module extends all the topics you have learnt thus far and asks you to apply them in more complex situations. Module examination in June of Year 13. AS Unit 3: Mechanics 1 This looks at how to model situations involving velocity, distance and time.  It also considers the motion of projectiles. Module examination in June of Year 13.

Mathematics Course Pathways

 Course Modules Studied – AS AS Cash-in code Modules Studied  – A2 A2 Cash-in code Maths Mechanics C1 6663 C2 6664M1 6677 Maths 8371 C3 6665 C4 6666M2 6678 Maths 9371 Maths Statistics C1 6663 C2 6664S1 6683 Maths 8371 C3 6665 C4 6666D1 6689 Maths 9371 Pure Maths C1 6663 C2 6664C3 6665 Maths 8371 C4 6666FP1 6667FP2 6668 Pure Maths 9372 Further Maths M1 6677 S1 6683 D1 6689 Maths 8371and Further Maths 8372 M2 6678 S2 6684 S3 6685 M3 6679 Maths 9371and Further Maths 9372 Two A – Levels (Maths and Further Maths) Maths (using C1-2 and e.g. M1) and Further Maths (using FP1, and remaining two applied units)