Curriculum – Mathematics

Curriculum – Mathematics

Mathematics

The Curriculum

Curriculum Intent

Mathematics is a hugely important subject which is woven in to every aspect of what we do; it is essential to everyday life, crucial to STEM and necessary for financial literacy and fluency. The Mathematics curriculum at SHSG interweaves all of these aspects into forming a coherent, relevant and stimulating programme of study for all. Our curriculum aims to empower all students to develop and apply mathematical processes and skills for use in academic pursuit as well as for the sheer love and appreciation of the beauty and the power of maths.  We adopt a mastery approach with one set of mathematical concepts and big ideas for all.  At all levels students are provided with opportunities to showcase their mathematical ability both to routine and non-routine problems of increasing difficulty. The emphasis is on empowering students to notice, make connections, explain, conjecture, prove and build on foundation knowledge and skills acquired at each stage of their education.  Challenge is provided through depth rather than acceleration – beliefs in line with the current ‘National Centre for Excellence in the Teaching Mathematics’ drive on ‘Mastery’ as well as the national curriculum’s philosophy that progression should always be based on the security of pupils’ understanding. Depth of understanding and retrieval of knowledge are always prioritised, and students will be engaged with more rich and sophisticated problems that require them to delve into their toolkit of mathematical techniques.

Opportunities to study GCSE Statistics and GCSE/A-Level Further Mathematics within the curriculum as well as participating in mathematical challenges enable pupils to push the boundaries of their abilities to a much greater level allowing them to experience success in maths early on.

Our ambition is that every student within the school can continue to the next phase of mathematical education should they wish and embrace the challenge, problem solving and rigour they encounter with gusto. SHSG students will leave school confident in their ability to apply their knowledge to unseen problems in further study, the workplace or everyday life, will have strong numerical literacy and share our love of Mathematics.

What does it feel like to be a student in the Maths Department?

At Southend High School for Girls we intend to develop not just academic mathematicians, but students who love the beauty and power of mathematics combined with an enjoyment and passion for the subject. When students leave the school, all will be confident in their ability and able to apply their knowledge to unseen problems that they encounter in continued study, the workplace, or everyday life. Mathematics is a hugely important subject woven into every aspect of what we do, it is essential to everyday life, crucial to STEM and necessary for financial fluency and most forms of employment.

At KS3 you will build on the fundamental skills you learnt in the Primary phase, further developing your competence in solving sophisticated problems whilst also being able to use maths commutatively across other subjects and not segregating it into its own remit. You will be encouraged to become perseverant and unwavering mathematicians, learning from your mistakes, mastering, and revisiting content you have been taught and becoming resilient to non-routine problems. Your journey through KS3 will ensure you are fully prepared to begin your adventure into GCSE content, and you will feel confident and empowered with the knowledge that you have. At KS3 you will have the opportunity to enter the UKMT Junior maths challenge, an opportunity to showcase your problem solving and reasoning skills.

At KS4 you will progressively and proactively build on skills taught throughout your experience in education to solve problems of increasing difficulty in a programme of study that consolidates and spirals through the national curriculum. In preparation for your future experiences, you will also study Financial Mathematics and commonly used Statistics having the option to sit this extra examination towards the end of year 10. Progression will always be based on your understanding of the subject, and this will be strengthened through our own philosophy of Mastery that is embedded within the course mapped out for you on your needs as an individual. For those who wish to continue to study mathematics at A-Level, opportunities to study GCSE Further Mathematics will be provided. The dream within the mathematics department is that everyone of you can finish your GCSE journey with three mathematics related qualifications that will enable you to compete for the world class opportunities you deserve. Like KS3, at KS4 you will have the chance to be entered into the UKMT Intermediate and even Senior maths challenge, competing against the best mathematicians in the country. At KS4 you will also work with the KS5 Mathematics Captains to support the younger years become confident with their maths.

KS5 allows you, as Mathematicians, to flourish, as you hone your skills from GCSE and embark on a challenging course which opens many doors to further education and is highly regarded within the workplace. Mathematics should ignite in you a sense of excitement as well as a hunger to purse perfection; methodically and meticulously working your way through problems until you reach your ‘Eureka’ moment arriving at the correct solution. Your maths teachers will support and guide you every step of the way in your quest for academic excellence, helping you to identify and develop your own areas of specialist interest, but you, too, have a role to play by deepening and reinforcing your learning beyond the classroom.

For those students that choose to study Further Mathematics, the course will be tailored to individual requirements and the knowledge that you wish to seek The SHSG Mathematics department is able to teach every optional module within the Further Mathematics specification, so should you wish to study Decision Mathematics to support Computer Science, Further Mechanics to support Engineering, Further Pure to support higher level mathematics or Further Statistics for actuarial and financial careers, you can pick and choose an option that is best suited to you. As Further Mathematicians you will also study the full A-Level Mathematics course in Year 12, allowing you to have a running start to the Further Mathematics material and letting you to focus on the respective A-Level in each year.

As KS5 students you will be entered into the Senior maths challenge; an early opportunity to be certificated in a rigorous assessment that will demonstrate your excellent problem-solving skills. You will also be able to compete within the school’s team at UKMT regional competitions, or the Girl’s Olympiad for an extra challenge. For those that wish to work with the department, opportunities to be a Mathematics Captain will allow you to raise the profile of mathematics and help support those in younger years as they begin their journey.

At Southend High School for Girls we appreciate the language and creativity of Mathematics, as Adler said ”Mathematics is pure language – the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. It is also an art – the most intellectual and classical of the arts”. As SHSG students, you will be exposed to a huge variety of language of the highest quality that develops your vocabulary and ability to justify, argue and prove. You will also be encouraged to explore mathematics and develop a curiosity for the subject that stimulates you to continue further in its academic pursuit.

Journey

Maths Curriculum

At Southend High School for Girls, we teach a curriculum that is ambitious and takes students on a learning journey beyond the National Curriculum for Mathematics. The SHSG Mathematics curriculum is what we believe will expose and challenge students to a cultural capital in Mathematics that is the best that has been thought and said in this subject.

The mathematics curriculum is planned and delivered using the intellectual framework of the classical education model, the Trivium:

  • Grammar (Knowledge and skills) knowledge, learning by heart, subject terminology, cultural capital
  • Dialectic (Enquiry and exploration) debate, question, challenge, analyse, evaluate
  • Rhetoric (Communication) proof, speeches, performances, presentations

Year 7 – 11

Pre-requisite or helpful knowledge from Year 6 mathematics ready to study in Year 7 if applicable

  • Students will continue to build and develop the skills learnt during KS2 and begin to apply their knowledge to less routine questions.

Adjustments from the Pandemic for years 7 – 9 if applicable?

  • Students in year 7 will have a baseline assessment on KS2 National Curriculum content so that intervention and support can be provided to help support pupils catch up with their most able peers.
  • Students in Years 8 and 9 have had their learning sequencing reordered during the pandemic so that more practical mathematics has been taught in person rather than through remote provision.

Adjustments from the Pandemic for years 10 – 11 if applicable?

  • Both years 10 and 11 will set baseline tests to assess their prior knowledge with a focus on lockdown content. Intervention strategies will be in place for students to bring them in line with their peers.
  • Content was changed during lockdowns so that more practical maths was done in school and more theoretical maths completed via remote provision.

The topics below have been chosen as they reflect the ambitions of the National Curriculum, and as a Grammar school, also challenge students beyond the National Curriculum. They have been carefully sequenced in this order to build a student’s learning journey to achieve the aims of our maths intent. Along the way students are assessed and topics will be revisited in assessments to keep each stage of this learning journey alive.

Year 7

Term 1

Units

  • Number and the Number System
  • Indices and Surds
  • Algebraic Manipulation
  • Area and Perimeter
  • Fractions
  • Solving Equations

Assessment

  • Applications and Mastery 1
  • Topic tests

Term 2

Units

  • Angles
  • Presenting Data
  • Estimation and Approximation
  • Standard Form

Assessment

  • Applications and Mastery 2
  • Topic tests

Term 3

Units

  • Probability
  • Substitution and Linear Graphs
  • Ratio and Proportion

Assessment

  • PUP examinations
  • Topic tests

Year 8

Term 1

Units

  • Compound Measures
  • Transformations
  • Percentages

Assessment

  • Applications and Mastery 3
  • Topic tests

Term 2

Units

  • Drawing More Complex Graphs
  • Inequalities
  • Simultaneous Equations
  • More Complex Algebra

Assessment

  • PUP Examination
  • Topic Tests

Term 3

Units

  • Sequences
  • Volume and Surface Area
  • Pythagoras and Trigonometry
  • Scale Drawing and Constructions

Assessment

  • Applications and Mastery 4
  • Applications and Mastery 5
  • Topic Tests

Year 9

Term 1

Units

  • Number and Bounds
  • Indices, Standard Form and Surds
  • Foundations of Algebra
  • Collecting and Recording Data
  • Angles
  • Fractions

Assessment

  • PUP examination
  • Topic Tests

Term 2

Units

  • Summarising Data 1
  • Linear and Quadratic Equations 1
  • Percentages
  • Representing Data 1
  • Area, Perimeter and Volume

Assessment

  • Applications and Mastery
  • Topic tests

Term 3

Units

  • Straight Line Graphs
  • Linear and Quadratic Equations 2
  • Probability
  • Scatter Graphs
  • Measure

Assessment

  • Topic tests

Year 10

Term 1

Units

  • Summarising Data 2
  • Rearranging
  • Financial Mathematics
  • Graphing
  • Time Series
  • Sequences

Assessment

  • Applications and Mastery
  • Topic Tests

Term 2

Units

  • Representing Data 2
  • Inequalities
  • Probability Distributions
  • Transformations

Assessment

  • GCSE Statistics Examination
  • Topic Tests

Term 3

Units

  • Simultaneous Equations
  • Ratio and Proportion
  • Trigonometry and Pythagoras

Assessment

  • Topic tests
  • PPE Examination

Year 11

Term 1

Units

  • Functions and Algebraic Fractions
  • Congruence and Similarity
  • Proof
  • Bounds
  • Vectors

Assessment

  • PPE Examinations
  • Topic Tests

Term 2

Units

  • Circle Theorems
  • Advanced Graphing
  • Constructions and Loci

Assessment

  • PPE Examinations
  • Topic tests

Term 3

Units

  • Matrices
  • Differentiation
  • Introduction to A-Level Algebra

Assessment

  • Topic tests
  • GCSE Mathematics Examination
  • GCSE Further Mathematics Examination

Achieving mastery in Mathematics – knowing and remembering even more than what is expected in a grammar school

Our assessment practice at SHSG reflects on how successful students have been in knowing, remembering and doing more through the above topics. They are either emerging, developing or proficient in this journey throughout the lower school.

To go beyond being proficient in what is expected of a mathematics student in lower school and achieve mastery in mathematics, students should read widely, engage in extracurricular pursuits, read recommended research, and learn key language and subject specific terminology. Students can also read ahead in the curriculum and are pushed to extend their knowledge through depth and interlinking of topics.

Students in the middle school are assessed on the 9-1 scale and will receive feedback in line with these grades. Students who are deemed to be behind the expected standard will have individualised targets set ensuring that they make the maximum progress they can.

Our aim is that all our students achieve the highest grade possible.

Recommended reading in Maths for Lower School (Years 7 – 9)

Teacher recommendations:

  • Mr Hollick – The Tiger That Isn’t: Seeing Through a World of Numbers – Andrew Dilnot
  • Mrs Coker – Things to Make and Do in the Fourth Dimension – Matt Parker
  • Mrs Law – How Not to be Wrong – Jordan Ellenberg
  • Mr Shaikh – Fermat’s Last Theorem – Simon Singh
  • Miss Elnaugh – Humble Pi – Matt Parker

Useful websites, TED Talks and research for Lower School (Years 7 – 9)

Mathematics-specific language to master in Lower School (Years 7 – 9)

Pre-requisite or helpful knowledge from Year 11 mathematics ready to study in Year 12 if applicable

  • Students will be provided with an induction pack available on the school’s padlet which will cover all the essential skills required for A-Level maths. Many of the skills focus on a competence and creativity with Algebra as well as other typical grade 8/9 topics from GCSE.

Adjustments from the Pandemic for years 12-13 if applicable?

  • Assessment has focused on lockdown topics with intervention provided on areas identified for development. The mathematics department provided live lessons for every lesson during lockdowns or isolation periods.

The topics below have been chosen as they reflect the ambitions of the exam board, and as a Grammar school, also challenge students beyond the exam board. They have been carefully sequenced in this order to build a student’s learning journey to achieve the aims of our maths intent. Along the way students are assessed and topics will be revisited in assessments to keep each stage of this learning journey alive.

Year 12

Term 1

Units

  • P1: Algebra Basics
  • P2: Graphs
  • P3: The basics of Trigonometry
  • P4: Radians and Reciprocal Trigonometry
  • P5: Exponentials
  • P6: Modelling with Trigonometry
  • P7: Algebraic Methods
  • P12: Circles
  • P13: Functions and Graphs
  • P15: Sequences and Series
  • A1: Data Collection and Measures of Location and Spread
  • A2: Representations of Data
  • A3: Probability
  • A4: Constant Acceleration
  • A5: Forces and Motion

Assessment

  • Topic tests

Term 2

Units

  • P8: Basic Differentiation
  • P9: Basic Integration
  • P10: Advanced Differentiation
  • P11: Integration
  • P16: Binomial Expansion
  • P17: Vectors
  • P19: Proof
  • A6: Statistical Distributions and Hypothesis Testing
  • A7: Correlation
  • A8: Normal Distribution
  • A9: Moments
  • A10: Variable Acceleration
  • CP1/1: Complex Numbers
  • CP1/2: Argand Diagrams

Assessment

  • Topic tests

Term 3

Units

  • P18: Numerical Methods
  • A11: Projectiles
  • A12: Application of Forces
  • A13: Further Kinematics
  • CP1/3: Series
  • CP1/4: Roots of Polynomials
  • CP1/5: Volumes of Revolution
  • CP1/6: Matrices
  • CP1/7: Linear Transformations
  • CP1/8: Proof by Induction
  • CP1/9 Vectors

Assessment

  • PPE Examination
  • Topic tests

Year 13

Term 1

Units

  • CP2/1: Complex Numbers
  • CP2/2: Series
  • CP2/3: Methods in Calculus
  • CP2/4: Volumes of Revolution
  • CP2/5: Polar Coordinates
  • CP2/6: Hyperbolic Functions
  • CP2/7: Methods in Differential Equations
  • CP2/8: Modelling with Differential Equations
  • FP1/1: Vectors
  • FP1/2: Conic Sections 1
  • FP1/3: Conic Sections 2
  • FP1/4: Inequalities
  • FP1/5: T-Formulae
  • FP1/6: Taylor Series
  • FP1/7: Methods in Calculus
  • FP1/8: Numerical Methods
  • FP1/9: Reducible Differential Equations
  • FM1/1 Momentum and Impulse
  • D1/1: Algorithms
  • D1/2: Graphs and Networks
  • D1/3: Algorithms on Graphs
  • D1/6: Linear Programming

Assessment

  • EB1
  • Topic tests

Term 2

Units

  • FM1/2: Work, Energy and Power
  • FM1/3: Elastic strings and springs
  • FM1/4: Elastic Collisions in one Dimension
  • FM1/5 Elastic Collisions in two dimensions
  • D1/4: Route Inspection
  • D1/5: Travelling Salesman Problem
  • D1/7: The Simplex Algorithm
  • D1/8: Critical Path Analysis

Assessment

  • PPE Examinations
  • Topic Tests

Term 3

Units

  • Pure 1 Revision and Consolidation
  • Pure 2 Revision and Consolidation
  • Applied 1 Revision and Consolidation
  • Applied 2 Revision and Consolidation
  • CP1 Revision and Consolidation
  • CP2 Revision and Consolidation
  • FP1/FM1 Revision and Consolidation
  • D1 Revision and Consolidation

Assessment

  • Topic Tests
  • A-Level Examinations

Achieving outstanding outcomes in Mathematics – knowing and remembering even more than what is expected in a grammar school

Students in the upper school are assessed on the A*-E scale and will receive feedback in line with these grades. Students who are deemed to be behind the expected standard will have individualised targets set ensuring that they make the maximum progress they can.

Our aim is that all our students achieve the highest grade possible.

Recommended reading in Mathematics for Upper School (Years 12 – 13)

Teacher recommendations:

  • Mr Hollick – The Tiger That Isn’t: Seeing Through a World of Numbers – Andrew Dilnot
  • Mrs Coker – Things to Make and Do in the Fourth Dimension – Matt Parker
  • Mrs Law – How Not to be Wrong – Jordan Ellenberg
  • Mr Shaikh – Fermat’s Last Theorem – Simon Singh
  • Miss Elnaugh – Humble Pi – Matt Parker

Useful websites, TED Talks and research for Upper School (Years 12 – 13)

Biology-specific language to master in Upper School (Years 12 – 13)