Mathematics

Curriculum Leader: Mr L Barker

Subject Leader(s):
Mr. L Barker (Barkerl@sgsce.co.uk)

Lessons and homework:
Year 7 & 8
– Fortnightly students have 7 lessons. Students receive homework on my maths every Monday and Friday during term time.

Milestones are given at set times throughout the year. For maths, students will need to be up to date with all my maths tasks given during that period. There is a maths teacher present in room 8 to support homework every Tuesday in room 8.

Year 9 – Fortnightly students have 9 lessons. Students receive homework on my maths every Monday and Friday during term time. There is a maths teacher present in room 8 to support homework every Tuesday in room 8.

Lesson style:

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.

 

Assessment:

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 sit a paper reviewing all topics taught during that year.

 

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:

Homework – www.mymaths.co.uk

 

School login: saintgeorges
School password: circle

All students have individual logins to access their online homework, these are given out at the start of the year and remain the same the whole way through school.

 

BBC Bitesize KS3 website

www.corbettmaths.co.uk

www.mathsbox.org.uk

 

All of our Key Stage 4 students follow their GCSE course based on the following textbooks:  Edexcel GCSE Maths A Linear Higher/ Foundation. We will advise students on revision books to help them reach their full potential when appropriate.

All students are given a minimum of one piece of homework per week. We use a website for students to access and complete their homework.

The link is www.mymaths.co.uk

School login: saintgeorges
School password: number

From year 11 we provide one hour compulsory revision per week after school on a Wednesday between 3:15 and 4:15 and the homework they receive is linked to their milestones.

We currently use the Edexcel examination board for the Higher tier GCSE. You can access via this link: http://www.edexcel.com/subjects/mathematics

We currently use the Edexcel and OCR examination board for the Foundation tier GCSE. The Edexcel link is the same as above and you can access the OCR details via this link:
http://www.ocr.org.uk/qualifications/by-subject/mathematics

We offer revision/homework club to all pupils with the help of a maths teacher during Friday lunchtime and Tuesday after school in room 10.

 

KS4 – Mathematics

Subject Leader(s):
Mr. L Barker (Barkerl@sgsce.co.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 homework on my maths every Monday and Friday during term time. There is a maths teacher present in room 8 to support homework every Tuesday in room 8.

Milestones are given at set times throughout the year. For maths, students will need to be up to date with all my maths tasks given during that period.

 

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 Tuesday 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
    3. Add/Subtract/Multiply/Divide
    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
    3. Factorising – Factorising quadratics
    4. Solve equations – 1 step/2 step/brackets/variables on both sides
    5. Solve quadratics
  5. Graphs
    1. Linear – Coordinates, y=n, x=n, y=mx+c
    2. Quadratic
    3. Cubic and reciprocal
  6. Inequalities
    1. Number line
    2. Solving inequalities
  7. Change the subject of a formula
  8. Midpoints and gradients
    1. Calculate midpoint and gradient
    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?
    4. Quadratic nth term
  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
    3. Quadratic
    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
    3. Factorising – Factorising quadratics
    4. Solve equations – 1 step/2 step/brackets/variables on both sides
    5. Solve quadratics
      1. By factorising
      2. Using the formula
  • Completing the square
  1. Solving simultaneous equations
  1. Algebraic fractions – All functions
  2. Area and Perimeter
    1. Rectangle, Triangle, Parallelogram, Trapezium, Circle.
    2. Circle – Area sectors and Arc Length
    3. Compound shapes
    4. Problem solving
  3. Variation
    1. Direct proportion
    2. Inverse proportion
  4. Circle theorems
  5. Equation of a circle
    1. Recognising
    2. Calculating the equation of a line perpendicular to a circle
  6. Cumulative Frequency
    1. Plotting and drawing the graph
    2. Using quartiles and inter quartile range
  7. Histograms
    1. Drawing and using histograms
    2. Calculating frequency density
  8. Compound measure
    1. Speed
    2. Density
    3. Pressure

Useful Resources:

 

Homework – www.mymaths.co.uk

 

School login: saintgeorges
School password: circle

All students have individual logins to access their online homework, these are given out at the start of the year and remain the same the whole way through school.

 

www.corbettmaths.co.uk

www.mathsbox.org.uk

 

Exam Specifications and past papers

www.edexcel.com/subjects/mathematics
www.ocr.org.uk/qualifications/by-subject/mathematics

Contact : Ms C Boarer
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.

 

Where could it lead?

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.

 

Useful Links

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)
 

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