# Mathematics

Curriculum Subjects

## Mathematics

See our Mathematics Curriculum below at Bentley Wood for KS3, KS4 and KS5

KS3 | Mathematics

Course Aims:

In Key Stage 3 we encourage students to master core skills and confidence in mathematics. Our scheme of learning develops not only our students’ understanding of Mathematics but also its importance in their own lives and in society.  It prepares students to make informed decisions about the use of technology, the management of money, further learning opportunities and career choices.  Students gain experience of mathematical activities and develop their appreciation and enjoyment of mathematics.

Course Content: There is a focus on fluency and mastery of key skills that will hold students in good stead for the next phase of their learning. In year 8 students build on prior knowledge and extend learning into the next level.

 Year 7 Year 8 Term 1 Number: Types of number, rounding, calculating, order of operations, fractions, decimals and percentages.    Algebra: manipulating/forming expressions and substitution.    Statistics: Data handling, averages, spread, graphs and charts.    Geometry: Describing, measuring and constructing angles. Properties and classifications of shapes. Number: Factors, multiples, negatives, powers, roots, standard form, rounding estimating, fractions, decimals and percentages.    Algebra: Expanding, factorising, manipulating expressions, forming/solving equations    Statistics: Graphs, charts, averages, range and frequency tables. Term 2 Algebra: Forming and solving equations.    Ratio and Proportion: Recipes, direct proportion, sharing and simplifying ratio.    Geometry: Converting units, area, perimeter, plans, elevations, 3D drawings, 2D shapes and angles.    Probability: Probability scale, two-way tables, sample space, experimental probability and relative frequency. Algebra: Rearranging, substitution, linear graphs.    Geometry: Area, perimeter, 3D shapes, volume, , Pythagoras.    Probability: Venn diagrams, theoretical and experimental probability.    Ratio and Proportion: Direct/ inverse proportion and comparing ratio, rates of change. Term 3 Algebra: Picture sequences, linear sequences, generating sequences, position to term rules, term-to-term rules.    Geometry: Rotation, reflection, translation, enlargement, constructing triangles and bisectors.    Consolidation and revision for EOY assessment Geometry: Angles, Loci and Construction        Consolidation & Preparation for GCSE course

Trips and visits:High achievers are able to attend co-curricular competitions and represent the school in regional and state events, including competing in the UKMT junior mathematical challenge.

Enrichment:At the end of the academic year the Mathematics departments leads on a Science, Technology, Engineering and Maths (STEM) based activity day, which requires students to apply Maths and Science concepts on different projects. Students have the opportunity to engage in weekly parallel challenges to gain an insight into interesting maths outside the national curriculum.

Key Stage 4 & 5 / Career Progression: Students will go on to study GCSE mathematics at either higher or foundation level. Bentley Wood also offers an excellent A-level Mathematics & Further Mathematics course which includes pure maths, statistics and mechanics. Maths degrees are often regarded as stimulating, highly rated, well-paid and valued by employers and maths graduates can go on to work in a variety of fields including but not limited to banking and finance, aeronautics, engineering, accounting, science research, investment banking and actuarial studies.

Recommended Reading:All students can access resources and revision materials remotely via the internet, especially use of Hegarty Maths which has the facility for monitoring students’ progress and providing teacher feedback and support. Students are encouraged to complete weekly challenges on parallel.org.uk.

KS4 | Mathematics

GCSE Mathematics

Exam board: Pearson/Edexcel

Continuing with the delivery of the National Curriculum, this qualification encourages students to develop confidence in, and a positive attitude towards, mathematics and to recognise its importance in their own lives and society.  It prepares students to make informed decisions about the use of technology, the management of money, further learning opportunities and career choices.  Student’s gain experience of mathematical activities and develop their appreciation and enjoyment of mathematics.

 Content Number: Calculations, Rounding & Accuracy Bounds Fractions, Decimal, Percentages Ratio, Proportion Indices & surds Standard Form Algebra: Expressions, Formulae, Equations Solving equations & inequalities Graphical methods Transformation of graphs Sequences Functions Iteration Geometry & Measures: Properties of 2D & 3D shapes Units of measure Loci & construction Pythagoras Trigonometry Bearings Transformations Area, Perimeter, Volume Geometrical reasoning Vectors Congruence & Similarity Circle theorems Compound measures Statistics & Probability: Collecting & representing data Interpreting statistical graphs Averages & range Spread Data analysis & comparison Theoretical & experimental probability Product rule for counting Frequency trees Probability trees Dependent & independent events

Method of assessment:

Assessment takes place in every lesson with student being given oral feedback throughout the lesson. Teachers use a variety of tools to assess students in the lesson, e.g. mini white boards, cold calling, targeted questioning, etc.

Formal assessments take place at the end of every half term. Results are used to clear any misconceptions in subsequent lessons. Students are given feedback and work to complete following every assessment as well as an improvement task. At the end of year 9 and year 10 there is a longer End of Year assessment consisting of two papers, one non calculator and one calculator. At the end of year 11 students are externally assessed by sitting their GCSE in Maths.

Maths is a tiered subject, Foundation & Higher. The GCSE exam consists of three written papers, one non calculator and two calculator papers. Each paper is worth 33.3 % of the final GCSE grade. Each papers covers a range of different topics and consists of a range of question styles, from single mark questions to multi-step problem solving.

Other qualifications:

Level 2 Certificate in Further Mathematics (AQA)

This course is offered to our most able mathematicians in year 10 & 11 and is assessed at the end of year 11. Students embarking on this course have to be fully committed, as it requires discipline and independent studying. It is most suitable for those students wanting to continue studying Mathematics at A level.

Entry Level 1, 2 or 3 in Mathematics (Edexcel)

The course is designed for students who find Mathematics challenging. It covers the basic numeracy skills and is assessed by the class teacher. There are two components in the assessment: one exam paper and a task. The study of topics complements their GCSE topics and students can sit this at any point during Year 11.

• “The hidden Maths of everyday life” by Jordan Ellenberg
• “Humble pi” by Matt Parker
• “The art of Statistics” by David Spiegelhalter
• “Do dice play God?: The Mathematics of uncertainty” by Ian Stewart
• “The Simpsons and their Mathematical secrets” by Simon Singh
• “Reaching for the moon: the autobiography of NASA mathematician
Katherine Johnson” by Katherine Johnson

Enrichment

• Chess Club
• UKMT intermediate & senior Maths challenge (years 9 to 11)
• Level 2 Further Maths (A level bridging course for Year 10 and 11 top end students)

Revision Guides

Pearson

Higher

Pearson Edexcel GCSE (9-1) Mathematics Higher tier Revision Guide

Foundation

Pearson Edexcel GCSE (9-1) Mathematics Foundation tier Revision Guide

CGP

Higher Bundle

https://www.cgpbooks.co.uk/secondary-books/gcse/maths/mxhcub42-gcse-maths-edexcel-revision

Foundation Bundle

https://www.cgpbooks.co.uk/secondary-books/gcse/maths/mxfcub42-gcse-maths-edexcel-revision

KS5 | Mathematics

Is Mathematics the subject for you?

Do you enjoy analysing and solving problems? Do you enjoy the challenge of finding a solution involving many logical applications and steps? Do you have a love of algebra? If the answer is yes, then mathematics is definitely the subject for you.

 Pure Applied A series of Pure Mathematics concepts covered over 2 years along with Applied concepts composed of Statistics and Mechanics. When studying Mathematics at A2 and AS level you will be extending your knowledge of topics such as algebra and trigonometry as well as learning some brand new ideas such as calculus. You will learn to appreciate how these concepts serve as the foundation for other branches of mathematics. In statistics lessons, you will learn to analyse and summarise data in order to draw out statements that describe what the data is all about. In today’s society we are bombarded with information from a variety of sources. The Statistics content will give you the tools to look at this information critically and efficiently. In Mechanics, you will learn to apply mathematical calculations to the movement of objects and understand the forces that control movement and shape the world around us. Year 1: Index laws, manipulating expressions, equations & inequalities, quadratic equations & inequalities, graphs & transformations, coordinate geometry, equation of circles & tangents, dividing polynomials, factor theorem, proof, binomial expansion, trigonometry & trig graphs, trig identities & equations, vector geometry & proof, integration, differentiation, exponentials & logarithms. Year 1: Statistics: Data collection, sampling, Measures of location and spread, variance and standard deviation, coding, representations of data, outliers, comparing data, correlation, linear regression, calculating probabilities, mutually exclusive and independent events, statistical distributions, cumulative probabilities, hypothesis testing and finding critical values. Mechanics: Modelling in mechanics, working with vectors, constant acceleration, velocity-time graphs, vertical motion under gravity, forces and motion, forces as vectors, motion in 2 dimensions, connected particles, pulleys, variable acceleration, functions of time, maxima and minima problems, constant acceleration formula. Year 2: Algebraic methods, proof by contradiction, algebraic division, functions and graphs, composite functions, combining transformations, solving modulus problems, sequences and series, (arithmetic, geometric), sum to infinity, recurrence relations, binomial expansion, using partial fractions, radians, areas of sectors and segments, small angle approximations, trigonometric functions, trig identities, inverse trigonometric functions, double angle formulae, proving trig identities, parametric equations, curve sketching, points of intersection, differentiating (sin x, cos x, exponentials and logarithms), chain rule, product and quotient rules, parametric differentiation, rates of change, numerical methods, iteration, Newton-Raphson method, integration of standard functions, by substitution and by parts, finding areas, trapezium rule, solving differential equations, vectors in 3D, solving geometric problems, application to mechanics. Year 2: Statistics: Regression, correlation and hypothesis testing, measuring correlation, hypothesis testing for zero correlation, conditional probability, set notation, conditional probability in Venn diagrams, tree diagrams, normal distribution, approximating the binomial distribution, hypothesis testing with the binomial distribution. Mechanics: Moments, resultant moments, centres of mass, tilting, forces and friction, resolving forces, inclined planes, projectiles, horizontal and vertical components or projection, projectile motion formulae, application of forces, static particles, friction and static particles, dynamics and inclined planes, kinematics, vectors in kinematics, variable acceleration in one dimension, differentiating vectors, integrating vectors.

Methods of study

Mathematics is a very practical subject; it is not about learning facts or writing essays. You will learn by problem solving, working both independently and in groups, to find the best route to a solution. The use of graphical calculators enhances the approaches to teaching and learning and the quality of students’ involvement, interaction, and appreciation for the subject. Communicating in writing and in discussion, using the unique language of mathematics is crucial.

How will it be examined?

AS qualification will not count towards the final grade of an A Level and will be a separate qualification in its own right (Linear). Your AS grade will be based on two exams (one Pure and one Applied). Grade at A2 will be based on 3 exams (2 Pure and one Applied). Your teachers will also be assessing your progress throughout the academic year with chapter tests and mock exams.

Career opportunities

A qualification in Mathematics is very valuable as a supporting subject at A Level and degree level, especially in the sciences and geography, psychology, sociology and medical courses. A full A level Mathematics is a much sought-after qualification for entry to a wide variety of full-time courses in higher education. Mathematics is a very powerful A level to have. The skills developed in mathematics are highly regarded by many universities and employers. Good Mathematics qualifications open the windows of opportunity for a much wider choice of very exciting careers. They could lead to a career in medicine, teaching, accountancy, finance, business, architecture, aeronautics, economics, computer science, engineering, meteorology and many more.

Useful websites:

General Information to student & parents from Pearson:
https://qualifications.pearson.com/en/support/support-for-you/students.html

Specifications:

KS5 | Further Mathematics

Is Further Mathematics the subject for you?

Further Mathematics is offered to those who achieve a grade 8 or 9 at GCSE and are also going to study A level Mathematics. This option would be beneficial for students wanting to study maths/science/computing based subjects at some of the top universities. If you wish to study Further Maths, you must choose Maths and Further Maths in two option blocks.

Course content

You can choose to complete the full Further Maths A level course consisting of 4 components: 2 Core Pure Maths components, which are compulsory and 2 additional components. At BW we offer Further Statistics & Further Mechanics as the additional options.

You will be taking the full A level Maths in Year 12 and completing all 4 components of the Further Maths in Year 13.

Methods of study

The study of Pure mathematics develops logical thinking and a systematic approach to problem solving.  Most problems will focus on how the methods learnt can be applied in the areas of engineering and computing. The use of graphical calculators will enhance students’ appreciation for the subject.

How will it be examined?

You will be taking the full A level Maths in Year 12 and completing all 4 components of the Further Maths in Year 13.

• End of Y12: 2 Pure papers and 1 Applied paper (stats & mech combined). All papers are 2 hours long.
• End of Y13: 2 Core pure papers, 1 Further Stats & 1 Further Mechanics. All papers are 90 mins long.

Your teachers will also be assessing your progress throughout the academic year with chapter tests and mock exams.

Career opportunities

Those students who have studied for an AS or A level in Further mathematics will have had the opportunity to study more applied mathematics modules than those with just the single A level mathematics. This highlights the worth of the Further Mathematics qualification for those students who wish to study for Mathematics, Physics and Engineering & Computing degrees at university. The study of Pure mathematics develops logical thinking and a systematic approach to problem solving – attributes which are highly valued in the workplace. It is desirable qualification for Oxbridge candidates.

Useful websites:

General Information to student & parents from Pearson:
https://qualifications.pearson.com/en/support/support-for-you/students.html

Specifications: