Maths Department
Introduction
At Yavneh College, we believe that our pupils can achieve a high level of success in Mathematics, whilst developing the arithmetical and problem solving skills needed for their everyday lives. Pupils are expected to achieve their full potential and encouraged to enjoy the subject and the mental exercise it provides. The mathematics programme is structured to allow for differences in ability and allows pupils and to take part in nationally recognised accreditation schemes and competitions.
Aims
- To teach pupils the necessary mathematical skills to cope with everyday life.
- To teach pupils that mathematics provides a powerful means of communication.
- To teach pupils that mathematics can be used to present information in many ways.
- To teach pupils the importance and usefulness of mathematics in many other fields.
- To help pupils develop powers of problem solving, logical thinking, accuracy and spatial awareness.
Lessons and Homework
Mathematics is allocated 3 x 60 minute lessons per week at Key Stages 3 and 4. A variety of teaching strategies and materials are used in an effort to accommodate the learning styles of all pupils.
Homework is set twice a week in Key Stage 3 and 4. The time spent on homework should be:
Year 7 up to 30 minutes
Years 8/9 up to 40 minutes
Years 10/11 up to 60 minutes.
It is expected that homework will be completed on time and according to the teacher’s instructions. It will be marked by the class teacher every week.
Assessment
AfL (Assessment for Learning) is used throughout the school. In Mathematics AfL is an integrated part of the learning experience:
- Through oral/written starters.
- Through questions and answers in the main part of the lesson.
- Through appropriate classwork which tests pupil’s understanding (as well as allowing time to practice fundamental skills and routines).
- Through appropriate plenaries which test pupil understanding.
- Through appropriate homework which is marked according to AfL principles.
- Through peer assessment and sharing good work.
Calculator Policy
Pupils are encouraged to use calculators only where it is appropriate to the task. They are taught a range of mental and paper-and-pencil methods of calculation.
Curriculum
The curriculum includes all the learning objectives from the National Numeracy Strategy, but is extended to achieve a high level of arithmetical and problem solving skills. The top set in Year 8 and the top two sets in Year 7 follow a very challenging programme aiming at Level 8 in the Key Stage 3 SATs.
Topics taught in Year 7 include:
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Spring Term |
Summer Term |
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Topics taught in Year 8 include:
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Additional topics taught in Year 9 include:
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Spring Term |
Summer Term |
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All the ability groups are taught the same topics at different levels to allow ease of movement between groups. Although the same topics are repeated every year, they are taught to a higher level each time.
GCSE
Syllabus: Edexcel 1MA0.
There is no coursework in mathematics.
TIERS
There are two tiers of entry:
Tier |
Grades |
Foundation |
C to G |
Higher |
A* to D |
ASSESSMENT
The GCSE is examined by two written examinations which pupils will sit in May/June of Year 11.
Paper |
Weighting |
Time |
Calculator |
Paper 1 |
50% |
1 h 45 min |
No |
Paper 2 |
50% |
1 h 45 min |
Yes |
A SAMPLE OF THE TOPICS
NUMBER AND ALGEBRA |
SHAPE, SPACE AND MEASURES |
HANDLING DATA |
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DISTRIBUTION OF MARKS
Assessment objective |
Weighting |
Recall and use knowledge of the prescribed content |
45-55% |
Select and apply mathematical methods in a range of contexts |
25-35% |
Interpret and analyse problems and generate strategies to solve them |
15-25% |
Note: 20-30% of each higher tier paper and 30-40% of each foundation tier paper will assess the functional elements of mathematics
ADDITIONAL LESSONS
Many pupils will have an extra lesson a week in Mathematics; they will do either Functional mathematics or GCSE Statistics.
FUNCTIONAL MATHEMATICS
- One lesson per week throughout years 10 and 11
- Year 10 and first term of year 11 will be used to enhance understanding of how mathematics is used in a variety of real life problem solving situations e.g. Disaster relief (see below).
- The rest of year 11 will be used for extra revision and exam practice
STATISTICS
SYLLABUS: Edexcel 1ST0
Higher Tier – Grades A* to D
2 hr examination – 75%
Controlled conditions task – 25%
Foundation Tier – Grades C to G
1 ½ hr examination – 75%
Controlled conditions task – 25%
Key subject aims
This specification:
- actively engages students in an accessible and relevant discipline
- helps students acquire knowledge and understanding of statistical techniques and concepts
- encourages statistical problem solving
- develops student understanding of the importance and limitations of statistics
- supports students in their progression through statistics and other related disciplines
Knowledge and understanding
The Edexcel GCSE in Statistics requires students to develop knowledge and understanding in the following areas –
Planning and data collection: planning a line of enquiry or investigation; types of data; census and sample data; sampling techniques collecting or obtaining data.
Processing, representing and analysing data: methods of tabulation; diagrams and similar forms of representation; measures of central tendency; measure of dispersion; summary statistics; scatter diagrams, correlation and regression; time series; quality assurance; estimation.
Reasoning, interpreting and discussing results: inference and other reasoning; predictions; interpretation and conclusion.
Probability: definitions and calculations; discrete probability distributions.
SYLLABUS: EDEXCEL 8371/9371/8372/9372
Mathematics is an essential qualification for a wide number of careers and university courses (e.g. maths, economics/business, science and social sciences) and is highly valued by employees because of the problem solving nature of the discipline.
Students study three units at AS-Level and three units at A-Level. There are a variety of combinations of these units which lead to a full A-Level in Mathematics some of which are compulsory. Each unit is assessed by a 1½ hour written paper, all of which are equally weighted.
Students studying for AS or A Level mathematics at Yavneh College study units C1, C2 and S1 in Year 12, and C3, C4 and S2 in Year 13. C1 is one of the compulsory papers and is the only non-calculator paper.
Students studying for AS or A Level Further mathematics study units FP1, D1 and M1 in Year 12 and units FP2, and M2 in Year 13.
C1: Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series;
differentiation; integration.
C2: Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series;
trigonometry; exponentials and logarithms; differentiation; integration.
C3: Algebra and functions; trigonometry; exponentials and logarithms; differentiation;
numerical methods.
C4: Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series;
differentiation; integration; vectors.
FP1: Complex number; numerical solutions of equations, coordinate systems, matrix algebra, series, proof by mathematical induction.
FP2: Inequalities; series, further complex numbers; first order differential equations; second order differential equations; Maclaurin and Taylor series; polar coordinates.
FP3: Hyperbolic functions; further coordinate systems; differentiation; integration; vectors; further matrix algebra.
S1: Mathematical models in probability and statistics; representation and summary of data; probability; correlation and regression; discrete random variables; discrete distributions; the Normal distribution.
S2: Binomial distribution; Poisson distribution; continuoiuso random variable; continuous uniform distribution; normal approoximations; populations and smaples; sampling; hypothesis testing.
M1: Mathematical models in mechanics; vectors in mechanics; kinematics of a particle moving in a straight line; dynamics of a particle moving in a straight line or plane; statics of a particle; moments.
M2: Kinematics of a particle; centres of mass; work, energy and power; collisions; statics of rigid bodies.
D1: Algorithms; graphs and networks; algorithms on netowrks; route inspection; critical path analysis; linear programming; matchings.
Note: C = Core (pure) mathematics, FP = Further pure, M = Mechanics, S = Statistics, D = Decision
ICT
Teaching and learning are enhanced by the use of ICT. Each classroom has a data projector linked to a computer and a visualiser. This enables the class teacher to easily display information from the computer and to demonstrate in detail how to use a protractor and compass and share and discuss the pupil’s work. Examination classes are able to access past papers and mark schemes at home via the VLE.
Enrichment
There are a variety of activities in Maths enrichment
- Games
- Problem solving
- Mathematical pattern
- Catch up arithmetic
- Gifted and talented maths
- Jigsaw puzzles
Maths Challenge
Every year pupils participate in the UK Maths Challenge, which is a problem solving competition for able mathematicians. This leads to bronze, silver and gold certificates and the possibility of taking part in the European competition or the International Olympiad.
Business and Enterprise Status
As a Business & Enterprise College, the additional funding that we receive is used for promoting teaching and learning in
- Business and Enterprise
- Mathematics
- ICT
The mathematics department runs or contributes to activities related to the specialist status of the school:
- Maths masterclasses for able year 6 pupils from local primary schools
- Year 6 financial awareness workshops for local primary schools
- A cross curricular day of mathematics, enterprise and ICT for year 9 pupils
- Problem solving workshops for Year 8 pupils
The LRC
The department is continually extending the range of mathematics related books available in the LRC. These books are intended to stimulate a wider interest in mathematics. Below is a very small sample of the books available:
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Lewis Carroll was a mathematician with a special interest in logic. The Annotated Alice contains the full text of Alice’s Adventures in Wonderland and Through the Looking-Glass and What Alice Found There, Tenniel’s original sketches and annotations about the language, riddles and mathematical logic contained in this masterpiece. |
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The Man who Counted is the creation of a celebrated Brazilian mathematician who wanted to bring some of the mysteries and delights of mathematics to a wider public. The adventures of Beremiz Samir take the reader on an exotic journey in which he summons his extraordinary powers to settle disputes and give wise advice. |
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Mathematicians have been very influential in the development of strategies for international economic cooperation and conflict resolution. John Nash and Robert Aumann are two mathematicians who have won the Nobel prize for economics for their work on game theory, and its applications to various aspects of international relations, such as arms races, crisis bargaining, wars of attrition, terrorism, interstate cooperation, conflict resolution, and peacemaking. Game Theory A Very Short Introduction would be a useful read for anyone applying to study mathematics or international relations at university. |
Example Problems
An example of a gifted talented and talented activity:
- These additions are all correct, can you explain why?
Some problems from the school newsletter.
- A very fast growing sun-flower grows to a height of 12 feet in 12 weeks by doubling its height every week. If you only want your sun-flower to be 6 feet tall, after how many weeks should you stop it growing?
- Find the smallest possible number that leaves a remainder of 1 when divided by 2, 3, 4 or 6, but which can be divided by 5 exactly.
- Find the smallest possible number that leaves a remainder of 1 when divided by 2, 3, 4, 5 or 6, but which can be divided by 7 exactly.