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Old Grammar

At this early stage the course is designed to promote understanding, enjoyment and good practice in Mathematics; we want the subject to be perceived as a puzzle to be unravelled rather than merely the collection of ticks. Building on topics pupils have met previously, the course consolidates the Mathematics of Key Stage 2 of the National Curriculum, extends pupils’ knowledge of grids, co-ordinates, factors, fractions, multiples, number systems, units, geometry and statistics, and introduces algebra. Some investigative work is also undertaken.

The basic use of calculators is introduced, but the importance of mental arithmetic is strongly emphasised. Homework is set twice a week, each session lasting about half an hour. We use the textbook Formula One Mathematics Book A.

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First Form

Curriculum

Pupils are taught the arithmetic skills needed for mental and written calculations using whole numbers, decimals, and fractions. Directed numbers, prime numbers, LCMs, HCFs, square roots, and the use of indices are all introduced. Geometrical instruments are used in work on scale drawings of various sorts, including constructing nets of solids. The metric system of units is emphasised with occasional reference to Imperial units where these are in everyday use. Pupils are introduced to algebra, enabling them to write formulae, solve simple (linear) equations and simplify expressions. Sequences, co-ordinates and simple graphs are dealt with, and probability is introduced.

Classes

There are four maths lessons per week. Boys are taught in their form groups.

Equipment and Books

All boys will be issued the same textbook: “Essential Mathematics Book 7” by David Rayner.
They will need the following equipment as a minimum requirement:

Homework

There are two homework tasks per week. Each task should last up to 30 minutes. Depending on the teacher’s guidance it will either be due in the next lesson, or the next day. Ideally it should be done at home, at a desk, without interruptions.

Assessment

The half-term grades during the year will be based on teachers’ class tests and homework assessments. The end of year exam will consist of two 45 minute papers; the first being a non-calculator paper and the second requiring a calculator. Results will be given as a percentage.

Extra-curricular

All pupils take part in the UK Junior Mathematical Challenge in April. See www.ukmt.org.uk for more details.

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Second Form

Curriculum

The Second Form curriculum introduces boys to some of the most ancient and powerful mathematical concepts. Here are some of the topics covered:

Number and Algebra: Prime factor decomposition, cubes and higher powers. Sequences. Fractions, Negative numbers. Percentages,

Shape and Space: Ruler and compass construction. Area of parallelograms and trapeziums. Pythagoras’s Theorem. Area and circumference of circles. Transformations. Volume of prisms.

Handling Data: Averages. Range. Probability.

Classes

There are four maths lessons per week. Boys are taught in sets, although all classes follow the same curriculum. Boys in the top set will generally have done very well in the 1st Form end of year exam, be a medal winner in the Junior Maths Challenge and have achieved excellent half term grades. Set allocation will be done at the end of the 1st Form.

Assessment

The half-term grades during the year will be based on teachers’ class tests and homework assessments. The end of year exam will consist of two 45 minute papers; the first being a non-calculator paper and the second requiring a calculator. Results will be given as a percentage.

Equipment and Books

All boys will be issued the same textbook: “Essential Mathematics Book 8” by David Rayner.
They will need the following equipment as a minimum requirement:

Homework

There are two homework tasks per week. Each task should last up to 30 minutes. Depending on the teacher’s guidance it will either be due in the next lesson, or the next day. Ideally it should be done at home, at a desk, without interruptions.

Extra-curricular

All pupils take part in the UK Junior Mathematical Challenge in April. Two boys will be selected to represent the school in the UK Team Maths Challenge. Boys who are interested in enrichment work could attend the weekly Maths Circle Society.

 

3rd Form Curriculum

Trigonometry is probably the most important topic introduced during the Third Form. Geometry includes work on similar triangles and transformations. Algebraic skills are developed, including the solution of simultaneous equations, how to multiply expressions in brackets, and then factorising quadratics. Pupils find the equations of straight line graphs and change the subject of formulae. Numerical work includes indices, standard form, errors and limits of accuracy.

Classes

There are four maths lessons per week. Depending on a his Form, boys will be allocated to one half of the year group; one half is Abbott, Hale and Seeley; the other is Beaufoy, Carpenter and Mortimer. In each half of the year group there are four mathematics sets. The more mathematically able will be placed in larger sets and the less able in smaller sets; it is not a strict ranking. All classes follow the same curriculum. We use either a boy’s previous exam results, or his entrance exam result, along with teacher recommendation, to allocate a boy to the most appropriate set. The final decision on allocation is made by the Head of Department.

Assessment

Boys will receive achievement grades in October, February and March. These grades will be based upon common tests which take place in lessons. The end of year exam will be two 1 hour papers, the first being a non-calculator paper and the second requiring a calculator. Results will be given as a percentage.

All this assessment data will be used at the end of the year to decide whether a boy should study for both Additional Mathematics and IGCSE Mathematics in the 4th and 5th Form, or only IGCSE Mathematics. This is an important decision which requires serious consideration from all parties concerned. For further information on these courses boys should speak to their mathematics teacher.

Equipment and Books

All boys will be issued the same text: “Essential Mathematics Book 9” by David Rayner.

As well as standard school equipment, boys will need:

Homework

There are two homework tasks per week. Each task should last between 30 to 40 minutes. Depending on the teacher’s guidance it will either be due in the next lesson, or the next day. Ideally it should be done at home, at a desk, without interruptions.

Extra-curricular

All boys will be entered for the UK Intermediate Maths Challenge on the first Thursday in February. The best entrants will be invited to the follow up competitions; European Kangaroo or Olympiad. See www.ukmt.org.uk for more details.

One 3rd form boy will be selected to represent the school in the London Hans Woyda mathematics competition.

For more information visit www.clsmaths.org.uk.

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Fourth and Fifth Form

Mathematics is a compulsory and popular subject at City of London School, in which boys achieve excellent results.

Classes

In both the Fourth and Fifth Form the year group is split between seven maths sets. We allocate boys to a set depending on his projected 5th Form qualification plans, i.e. whether he hopes to take both IGCSE Mathematics and Additional Mathematics, or IGCSE Mathematics only, at the end of the 5th Form.

This set allocation is an important decision. We assess both the boys’ mathematical potential, and his aspirations, towards the end of the 3rd Form. We base our assessment of his mathematical potential on his 3rd Form Common Test results, end of year exam result, and application in class. His classroom teacher will discuss his mathematical aspirations with him in lesson time in order to gauge his interest in the Additional Mathematics qualification. If there is doubt we will start the boy on the Additional Maths route in the Fourth Form.

Equipment and Books

Boys will be issued with the following books:

And for boys taking Additional Maths:

Boys should have the following mathematical equipment:

Homework

Homework is set twice per week; boys should spend approximately 45 minutes on each task. It will either be due in the next day or the next lesson depending on the teacher.

Assessment

The IGCSE will be assessed by two 2 hour exams in the summer of the 5th Form. The exam board is Edexcel International. See:

http://www.edexcel.com/quals/igcse/igcse09/maths/mathsA/Pages/default.aspx

Additional Maths will be assessed by one 2 hour exam in the summer of the 5th Form. The exam board is OCR. See:

http://www.ocr.org.uk/qualifications/type/fsmq/maths/add_maths/index.html

 

In the Fourth Form there will be a March Common Test, and an end of year school exam.

Extra-curricular

We enter the Additional Maths sets in the Fourth and Fifth Form for the UK Mathematics Challenge in February. The top boys in the year will then be invited onto the Mathematical Olympiad competitions.

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Sixth Form

Junior 6th

Why study mathematics? First of all you must enjoy the subject. Secondly you have the opportunity to study a long-standing academic discipline, in which you will learn to demonstrate clear analytical thought, develop the idea of proof, and solve difficult problems. The generality of mathematics makes it an ideal complement to a wide range of subjects, and many university tutors will be looking for a good grade in A level Mathematics.

Mathematics is the most popular Sixth Form choice at CLS. Boys regularly achieve excellent results and enjoy the flexibility that our modular course has to offer. We offer the specification written by Mathematics in Education and Industry (www.mei.org.uk). This specification is designed to help students fulfil their potential by taking and enjoying mathematics courses that are relevant to their needs post-16.

Nearly half of the Junior Sixth maths students will be on our Further Mathematics course which is appropriate either for those considering a degree course for which Further Mathematics A Level would be an advantage (Mathematics, Physics, Engineering, Economics.) or for those who wish to enhance their sixth form studies with a full A level as their fourth course rather than an AS.

Senior 6th

Senior Sixth Form Mathematics students will be either continuing with Single or Further Mathematics.

Single Mathematics

Classes: You will have 5 periods per week of Pure Mathematics (C3 and C4) with one teacher, and 3 periods of Applied Mathematics (either M2 or S2) with another.

Exams and Curriculum.In January you will take C3 for the first time and have the opportunity to retake your exams from the J6 if needs be. The C3 module has a coursework component which will be covered by the applied teacher over the October half term. Your pure teacher will be able to give you past papers over the Christmas holidays to prepare for C3 and retakes. In June you will take C4 for the first time and your new applied module, plus any retakes you wish to. It is the best mark from all your retakes which goes forward for accreditation.

Grades: A*, total 480 and average 90 in C3 and C4, including retakes. A 480, B 420, C 360.

Further Mathematics

Classes: You will have 5 periods per week of Pure Mathematics (FP1, FP2, FP3) with one teacher, and 4 periods of Applied Mathematics (either M2, M3, DE, or S2 S3 DE) with another.

Exams and Curriculum.In January you will take FP1 for the 1st time, one or two of your applied modules and have the opportunity to retake your exams from the J6 if needs be.

Grades: Mathematics A*, total 480 and average 90 in C3 and C4, including retakes. A 480, B 420, C 360.

Further Mathematics: A* total 480 plus average 90 in any three A2 modules, A 480, B 420, C360

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