Maths

**Aims of the Department**

At FBS we aim to develop confident mathematicians who use their enterprising skills to become critical thinkers. We do this by continuing to grow their conceptual understanding by providing opportunities to encourage mathematical reasoning and problem solving. We take time to develop the boy’s reflection skills and engage in dialogue with their teachers to support their critical thinking and improve upon their mistakes.

During KS4 we start to prepare boys for the world of work and onward study. Boys continue to study the five strands of Mathematics; Number, Algebra, Geometry and Measure, Ratio and Proportion and Statistics and Probability, but in greater depth than covered at KS3 and with a focus on seeing how these skills and concepts are interlinked and can be used to solve problems.

Boys learn why it is important to manipulate and solve equations, which may include solving problems with speed, distance and time. We investigate more sophisticated methods of analysis and presentation of numerical data. All boys learn how to work with percentage and proportional change fluently, and solve problems which are relevant to all members of society; how interest on loans and savings accounts work, or how to know whether you are getting a fair deal on pricing and costing.

The maths department has a range of resources to support and stretch the boys which includes online learnings tools, hands on experiences and termly projects.

Department staff

- Chris McCormack - Head of Maths - c.mccormack@fulhamboysschool.org.uk
- Aimi Plant - Deputy Head of Maths
- Joshua Parkin - Maths Teacher
- Julia Fitzgerald - Maths Teacher
- Sarah Delas - Maths Teacher
- Jonathan Brophy - Head of Dickens and Maths Teacher

Our approach to lessons

In Maths our lessons are geared towards boys through engaging with ‘real life’ application and exploring different mathematical scenarios which challenge and draws on the boys’ experience.At KS4 we build on the core skills mastered in Year 7, 8 and 9 and extend these concepts to prepare boys for GCSE and onward study. We focus on mathematical rigour, communication and problem solving, and we see how various concepts are interlinked and multiple approaches can be used to solve problems. We ensure concepts are revisited regularly to reinforce learning, retention and understanding.

Year 7 Curriculum

Unit 1 - Number

- Place Value
- Powers of 10
- Ordering numbers
- Rounding
- Mental Calculation
- Negative Numbers

**Unit 3 - Algebra**

- Introduction to Algebra
- Collecting Like terms
- Simplifying expressions
- Solving one and two step equations
- Creating sequences
- Nth term of linear sequences

**Unit 4 - Ratio and Proportion **

- Fractions, Decimals and Percentage
- Fractions of Amounts
- Simplifying Ratios
- Dividing ratios
- Introduction to Proportion

**Unit 5 - Geometry, Angles and Graphs**

- Types of Angles
- Drawing Angles
- Angles in Parallel lines
- Constructions
- Intro to Pythagoras

**How the boys will be assessed in Year 7**

- 4 x half termly topic tests
- 2 x whole curriculum tests

Year 8 curriculum

**Unit 1 - Number **

- Indices and Roots
- Prime Factor Decomposition
- Estimation
- Negative numbers

**Unit 2 - Geometry And Measure**

- Reflections
- Rotations
- Enlargements
- Perimeter and Area
- Circles
- Volume

**Unit 3 - Algebra**

- Solving equations
- Special sequences (Fibonacci etc)
- Simplifying expressions
- Expanding and Factorising
- Substitution into Equations

**Unit 4 - Ratio and Proportion**

- Problem solving with fractions
- Working with ratios
- Fractions of amounts
- Percentage problems
- Direct and inverse proportion

**Unit 5 - Geometry, Angles and Graphs**

- Angles in Polygons
- Scale drawings and Bearings
- Nets, Plans and Elevations
- Combinations of Transformations
- Similarity
- Real life graphs.

**How the boys will be assessed in Year 8 **

4 x half termly topic tests

2 x whole curriculum tests

Year 9 curriculum

**Year 9 curriculum**

- Unit 1 - Number
- Calculations including Standard Form
- Solving Inequalities
- Rounding to significant figures
- Calculations with decimals
- Financial mathematics

**Unit 2 - Geometry And Measure**

- Transformations
- Area of Compound Shapes
- Area of Segments, Sectors.
- Volume of All 3D shapes
- Surface Area

**Unit 3 - Algebra**

- Quadratic Sequences
- Simultaneous Equations
- Rearranging Formula
- Solving harder equations (with Quadratics)
- Expanding and Factorising

**Unit 4 - Ratio and Proportion**

- Compound interest
- Reverse Percentages
- Problem solving with Ratio and Proportion
- Inverse Proportion to the square
- Representing proportionality graphically.

**Unit 5 - Geometry, Angles and Graphs**

- Introduction to Trigonometry
- Problem solving with Pythagoras
- Pythagoras and Trigonometry in 3D
- Isometric Drawings
- Speed, Density and Pressure
- Congruence and Similarity

**How the boys will be assessed in Year 9**

- 4 x half termly topic tests
- 2 x whole curriculum tests

Year 10 curriculum

We ensure all boys have a secure grasp on everything covered in KS3, with the following additions:

**Number **

- Surds
- Indices with Fractions and Negatives
- Bounds of calculations

**Algebra **

- Simultaneous equations (including a quadratic)
- Inequalities

**Ratio, proportion and rates of change **

- Speed, Density and Pressure
- Direct and Inverse Proportion

**Geometry and measures **

- Pythagoras and Trigonometry in 3D
- Bearings
- Constructions with compass and a straight edge

**Probability **

- Theoretical and Experimental Probability
- Tree Diagrams
- 6 Statistics
- Histograms and Cumulative Frequency

**How the boys will be assessed in Year 10**

Boys will sit regular, informal topic tests, and will be assessed formally three times in the year. These assessments are summative and assess boys understanding of all concepts covered in lessons prior to the assessments. Boys are given an outline of what topics to expect, and should undertake independent revision and study in preparation.

Year 11 curriculum

We ensure all boys have a secure grasp on everything covered in KS3 and Year 10, and ensure enough time is left for adequate revision and intervention where necessary in preparation for the examinations. Concepts from KS3 and Year 10 are revisited where necessary, to enable the conceptual leap to higher-level topics when they are ready.

**Algebra**

- Algebraic proof
- Iteration
- Functions and Transformations of Graphs

**Geometry and measures **

- Trigonometry for non right-angled triangles
- Vectors and Geometric proof

**Probability **

- Conditional Probability
- Sets and Venn Diagrams

## GCSE

Summary of the course, including exam board and nature of exams

The GCSE qualification covers the following content headings, which we build on from preparation in KS3:

- Number
- Algebra
- Ratio, proportion and rates of change
- Geometry and measures
- Probability
- Statistics

At the end of Year 11 all boys are entered into the GCSE Examination. Two tiers are available: Foundation (which covers up to a Grade 5) and Higher (which covers up to Grade 9). The qualification consists of three equally-weighted written examination papers at either tier. Paper 1 is a non-calculator exam and Paper 2 and 3 are calculator exams, and each paper contains a range of material from the curriculum.

**How the boys will be assessed in Year 11**

Boys are formally assessed three times in Year 11: Academic Fitness Tests in September, Mock Exams in January and a second Mock Exam in March/April. These assessments are summative and assess boys understanding of all concepts covered in lessons prior to the assessments. Boys are expected to undertake independent revision and study in preparation, and are given careful guidance from class teachers about which areas and concepts need work.

Year 12 and Year 13 curriculum

A Level

Mathematics - Edexcel

The course contains a mixture of pure maths, statistics and mechanics. All exam boards follow exactly the same specification.

Further Mathematics - Edexcel

The course contains a mixture of pure maths and optional modules in statistics, mechanics, discrete maths and additional pure maths. 50% of the course is compulsory and the remaining 50% will be made up of two optional modules. We will choose the modules based on staffing and the needs of the students on the course.

**A - Level Mathematics
Year 12 Curriculum**

**Pure Mathematics**

- Algebra and functions
- Coordinate geometry in the(x, y) plane
- Further algebra
- Trigonometry
- Vectors (2D)
- Differentiation
- Integration
- Exponentials and logarithms

**Statistics**

- Statistical sampling
- Data presentation and interpretation
- Probability
- Statistical distributions
- Statistical hypothesis testing

**Mechanics**

- Quantities and units in mechanics
- Kinematics 1 (constant acceleration)
- Forces & Newton’s laws
- Kinematics 2 (variable acceleration)

**How the boys will be assessed in Year 12 **

Boys will sit an internal Mock AS examination at the end of Year 12 to assess their progress and suitability for continuing to the full A-level in Mathematics.

For some boys it may be appropriate to sit the AS Mathematics exam only at the end of Year 13.

- AS level Mathematics

Paper 1: Pure Mathematics

62.5%, 2 hours, 100 marks

- AS pure mathematics content assessed

Paper 2: Statistics and Mechanics

37.5%, 1 hour 15 minutes, 60 marks

- AS applied content assessed

Section A: Statistics (30 marks)

Section B: Mechanics (30 marks)

Further Mathematics

**Year 12 and 13 Curriculum**

**Core Content (compulsory) **

Learners will extend their knowledge of proof, algebra, functions, calculus and vectors. They will also broaden their knowledge by exploring complex numbers, matrices, polar coordinates and hyperbolic functions.

**Statistics (optional) **

Students will explore the theory which underlies the content in A Level maths by studying combinatorics, probability distributions and hypothesis tests, chi-squared tests, correlation and regression.

**Mechanics (optional) **

Students will look at more complex physical systems such as those involving work, energy and power, impulse and momentum, centres of mass and circular motion.

**Discrete Maths (optional) **

Here students explore real life problems involving optimisation working with graphs and networks to aid them. We look at critical path analysis, linear programming and game theory.

**Additional Pure Maths (optional) **

Students will study topics which often form the foundation of undergraduate mathematics. This covers recurrence relations, number theory, group theory and partial differentiation.

**How the boys will be assessed in Year 12**

Boys will sit a Mock AS examination at the end of Year 12 to assess their progress and suitability for continuing to the full A-level in Further Mathematics. For some boys it may be appropriate to sit the AS Further Mathematics only at the end of Year 13.

*AS-level Further Mathematics*

Paper 1: Core Pure Mathematics 1

50%, 1 hour 40 minutes, 80 marks

Papers may contain any content from Pure Mathematics

Paper 2: Further Mathematics Options

50%, 1 hour 40 minutes, 80 marks

**Students take one of the following ten options: **

- 2A: Further Pure Mathematics 1 and Further Pure Mathematics 2
- 2B: Further Pure Mathematics 1 and Further Statistics 1
- 2C: Further Pure Mathematics 1 and Further Mechanics 1
- 2D: Further Pure Mathematics 1 and Decision Mathematics 1
- 2E: Further Statistics 1 and Further Mechanics 1
- 2F: Further Statistics 1 and Decision Mathematics 1
- 2G: Further Statistics 1 and Further Statistics 2
- 2H: Further Mechanics 1 and Decision Mathematics 1
- 2J: Further Mechanics 1 and Further Mechanics 2
- 2K: Decision Mathematics 1 and Decision Mathematics 2

What do students say about learning in Maths?

**Max Wilson Y10**

In Maths this term the Year 10’s have been preparing for their GCSEs. We are currently learning about the topic of Statistics and have been working hard towards it. We have been making the most out of our time in Maths out of lessons also. A Maths help club is up and running at lunch times and a lot of Year 10’s go to this club if they feel like they are struggling with certain topics leading up to the exam, or if they want to build on their knowledge. This club is run by students but teachers are available when extra help is needed.

**Zac Fenton Y8**

Maths has been the same as usual: smashing objectives and filling pages like it’s no big deal. Maths is always engaging and interactive with the best teachers in the world. Some people would say maths is boring and useless but that’s until they go to FBS. The ownwork can be pretty long though – that’s if you don’t put 100% into all your school work in maths.

In maths this term we have been focusing on algebra specifically. Algebra has the reputation of being boring, complicated and but I think the boys in our class have embraced algebra and given it their all. We have even moved on to the really complex Level 7 questions.

We give students opportunities to be enterprising through taking risks, becoming daring, developing resilience, being team players, and building tenacity.