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Mathematics

Mathematics

Curriculum Intent

Intended curriculum outcomes:

At Holcombe Grammar School, we aim to deliver the following ambitious outcomes for our students through our curriculum. Students will:

  • Be aspirational and ready for the next step in life
  • Achieve high quality academic outcomes
  • Develop as effective, efficient, resilient learners who can work independently towards ambitious goals
  • Develop an awareness of their own strengths and acquire effective habits to be successful at school and beyond
  • Develop long term knowledge and skills which can be effectively deployed in new circumstances.
  • Develop the cultural capital to be able to successfully engage with a wide variety of social situations
  • Develop an awareness of their place as a citizen in the school, wider community and the world beyond

Mathematics is a creative and interconnected subject that has developed, over time, to provide solutions to exciting challenges. Mathematical reasoning is applied in everyday life and is important to science, technology and engineering. Mathematical fluency is essential for financial literacy and employment. An appreciation of the beauty and power of Mathematics supports our understanding the world. Students will be encouraged and enabled to:

  • Develop a sense of enjoyment and curiosity about Mathematics
  • Become fluent in the fundamentals of Mathematics
  • Develop conceptual understanding
  • Develop ability to recall and apply knowledge quickly and accurately
  • Reason mathematically by following a line of enquiry
  • Notice relationships and generalisations
  • Develop an argument, justification or proof using mathematical language
  • Solve problems by applying Mathematics
  • Sequence problems into a series of simpler steps
  • Persevere to search for and find solutions
  • Develop strong subject knowledge and skills in Mathematics
  • Give clear and effective explanation to convey understanding of new ideas
  • Model mathematical processes to show effective application of knowledge and skills
  • Ask questions to support, challenge and develop the depth and accuracy of their understanding
  • Action feedback, to show evidence of progress in their student response
  • Develop strong meta-cognition techniques to self-monitor, apply skills and attain goals
  • Develop strong meta-memory techniques to retain knowledge and skills
  • Create resources for effective retrieval with understanding and speed of processing in Mathematics.

In Mathematics, students will be provided with high quality, effective feedback, which enables them to make excellent progress and achieve high standards, through assessment and student response.

Accurate assessment analysis will be applied to track and monitor progress, inform intervention and provide measures of attainment and progress. Assessment will enable students to demonstrate what they know, can do and remember. Personal learning checklists (P.L.Cs) and feedback will enable students to know how to make the most effective progress in Mathematics.

Assessment in Mathematics will be challenging to allow students to exceed expectations; detailed to provide a range of outcomes; cyclical, to assess deep learning.

There will be a focus on mathematics mastery techniques and thinking skills. Online learning resources will provide opportunities for real world practical applications of mathematics, in financial planning, in the home and in career aspirations. Students will be enabled to make informed choices about destinations in further education, higher education, or employment.

MASTERY

ENDEAVOUR AND ENTERPRISE

THINKING

AWARENESS OF ONESELF AND OTHERS

Key Stage 3

At Holcombe Grammar School, we follow the National Curriculum for key stage 3. Pupils are taught in their form groups in year 7 and then split into five equal sized sets in year 8 and 9. A wide variety of teaching and learning styles are used with extension work available for the most able students, in order to provide them with a higher level of challenge.

As students progress through the curriculum they begin to develop their mathematical reasoning through problem solving activities and mathematical enrichment lessons. Students compete in the UKMT Junior Mathematics Challenge, which is a long standing national competition that provides a further opportunity to inspire the love of problem solving in mathematics. Students can achieve Gold, Silver and Bronze level certificates, with the top achievers progressing to further rounds to compete with other pupils from across the UK.

Students are assessed through regular standard tests, which are both calculator and non-calculator papers. In addition, all students are set extensive home learning tasks on drfrostmaths.com, which allows retrieval practice of all topics covered during time spent at Holcombe Grammar School.

A wide variety of careers are available with qualifications in mathematics. Opportunities exist in areas such as banking, pharmaceuticals, oil, retailing, accountancy, management consultancy or in the utilities. A qualification in mathematics is essential for careers in different branches of science, technology and engineering, and will support courses in many areas such as economics, business and finance.

Year 7

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Apply directed numbers, sequences, perimeter and volume. Decimal numbers, square numbers, square roots, rounding, order of operations and statistics. Algebra, fractions and angles. Coordinates, graphs and percentages. Probability, symmetry and equations. Interpreting data, 3D shapes and ratio.

Year 8

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Equations and formulae, perimeter and volume, 3D shapes and ratio. Surface area and volume of prisms, proportion, sequences, algebra, percentages and fractions. Coordinates and graphs, application of graphs, solving equations graphically, standard form and decimal numbers. Circles, Pythagoras’ theorem and trigonometry. Surface area and volume of cylinders, symmetry, geometry, shape, ratio and probability. Congruent shapes, polygons, using data, compound units and interpreting data.

Year 9

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Number skills, fractions, ratio and proportion, statistical diagrams and averages, number and sequences. Ratio, proportion and angles. Transformations, constructions, loci and algebraic manipulation. Length, area and volume, right angled triangles and trigonometry. Similarity, exploring and applying probability, powers and standard form. Equations and inequalities, counting, accuracy, powers and surds.

Key Stage 4

In Key Stage 4, all students study Edexcel GCSE (9-1) Mathematics (1MA1). Students are challenged to do their best. Concepts learned in Key Stage 3 will be applied, to increasingly more complex problems. We support students to apply a very secure understanding of the fundamental ideas in mathematics. We provide motivating learning assignments in mathematics. There is a strong emphasis on the functional applications of Mathematics and examinations will include problem solving in a real-life context. We are a team of enthusiastic teachers and we inspire students to be independent and confident learners. Students are encouraged to ask questions, to strengthen their understanding and to develop strong communication skills. Students compete in the Intermediate Mathematics Challenge, a national competition, to achieve Bronze, Silver and Gold certificates. The most successful students progress to further rounds in the competition. In addition, all students are set extensive home learning tasks on drfrostmaths.com, which allows retrieval practice of all topics covered during time spent at Holcombe Grammar School. Additional courses are available:

Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Statistics (1ST0)

AQA Level 2 Certificate in Further Mathematics (8365)

Pearson Edexcel Level 1/Level 2 GCSE (9–1) in Mathematics (1MA1)

Students are enabled to:

  • Develop fluent knowledge, skills and understanding of mathematical methods and concepts
  • Acquire, select and apply mathematical techniques to solve problems
  • Reason mathematically, make deductions and inferences, and draw conclusions
  • Comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.

Students acquire knowledge and understanding of

Number

Algebra

Ratio, proportion and rates of change

Geometry and measures

Probability and statistics

Assessment Objectives

AO1 Use and apply standard techniques

Students are enabled to: Accurately recall facts, terminology and definitions; use and interpret notation correctly; accurately carry out routine procedures or set tasks requiring multi-step solutions.

AO2 Reason, interpret and communicate mathematically

Students are enabled to: Make deductions, inferences and draw conclusions from mathematical information; construct chains of reasoning to achieve a given result; interpret and communicate information accurately; present arguments and proofs; assess the validity of an argument and critically evaluate a given way of presenting information.

AO3 Solve problems within mathematics and in other contexts

Students are enabled to: Translate problems in mathematical or non mathematical contexts into a process or a series of mathematical processes; make and use connections between different parts of mathematics; interpret results in the context of the given problem; evaluate methods used and results obtained; evaluate solutions to identify how they may have been affected by assumptions made.

Pearson Edexcel GCSE (9-1) Mathematics, 1MA1 is assessed in three equally-weighted written examination papers at either Foundation tier or Higher tier.

Paper 1 is a non-calculator assessment and a calculator is allowed for Paper 2 and Paper 3.

Each paper is 1 hour and 30 minutes long.

Each paper has 80 marks.

Foundation tier: grades 1 to 5;

Higher tier: grades 4 to 9 (grade 3 allowed).

Year 10

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Counting, accuracy, powers, surds and quadratic equations. Sampling, more complex diagrams and combined events. Properties of circles and variation. Triangles and graphs. Algebraic fractions and functions. Vector geometry.

Year 11

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Retrieval practice to apply fractions, ratio, percentages, angles and trigonometry, graphs, area, volume, transformations, equations, inequalities, probability and multiplicative reasoning. Retrieval practice to apply similarity, congruence, trigonometry, statistics, equations and graphs. Retrieval practice to apply circle theorems, algebra, vectors, proof, proportion and graphs. Examination preparation. GCSE examinations. GCSE examinations.

Years 12 and 13

Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)

Students are enabled to:

  • Understand Mathematics and mathematical processes, in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study
  • Extend their range of mathematical skills and techniques
  • Understand coherence and progression and how different areas of Mathematics are connected
  • Apply Mathematics in other fields of study; be aware of the relevance of Mathematics to the world of work and to situations in society
  • Use their mathematical knowledge to make logical and reasoned decisions in solving problems and communicate the mathematical rationale for these decisions clearly
  • reason logically and recognise incorrect reasoning
  • Generalise mathematically; construct mathematical proofs
  • Use their mathematical skills and techniques to solve challenging problems that require them to decide on the solution strategy
  • Recognise when Mathematics can be used to analyse and solve a problem in context
  • Represent situations mathematically and understand the relationship between problems in context and mathematical models that may be applied to solve them
  • Draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions
  • Make deductions and inferences
  • Draw conclusions by using mathematical reasoning
  • Interpret solutions and communicate their interpretations effectively in the context of the problem
  • Read and comprehend mathematical arguments, justifications and applications and communicate their understanding
  • Use technology effectively
  • Take increasing responsibility for their own learning.

Students acquire knowledge and understanding in:

Pure Mathematics: Proof; algebra and functions; coordinate geometry in the (x,y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation; integration; numerical methods and vectors.

Statistics: Statistical sampling; data presentation and interpretation; probability; statistical distributions; statistical hypothesis testing.

Mechanics: Quantities and units in mechanics; kinematics; forces and Newton’s laws; moments.

Assessment objectives

AO1 Use and apply standard techniques

Students are enabled to: Select and correctly carry out routine procedures; accurately recall facts, terminology and definitions.

AO2 Reason, interpret and communicate mathematically

Students are enabled to: Construct rigorous mathematical arguments (including proofs); make deductions and inferences; assess the validity of mathematical arguments; explain their reasoning; use mathematical language and notation correctly.

AO3 Solve problems within mathematics and in other contexts

Students are enabled to: Translate problems in mathematical and non-mathematical contexts into mathematical processes; interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations; translate situations in context into mathematical models; use mathematical models; evaluate the outcomes of modelling in context, recognise the limitations of models and, where appropriate, explain how to refine them.

Overarching themes:

Mathematical argument, language and proof; Mathematical problem solving; Mathematical modelling.

Assessment consists of three externally examined papers:

Paper 1 Pure Mathematics 1; Paper 2 Pure Mathematics 2; Paper 3 Statistics and Mechanics.

Each paper is a two hour written examination, 33.33% and 100 marks.

Students must answer all questions and calculators can be used.

Pearson has provided a large data set, which will support the assessment of statistics in Paper 3: Statistics and Mechanics.

Additional Edexcel qualifications are available:

8FM0 AS Level Further Mathematics;

9FM0 Advanced Level Further Mathematics.

 

At Holcombe Grammar School, we provide engaging enrichment activities to consider real world applications of mathematics.

Potential OXBRIDGE and Russell group students practice STEP Papers and Advanced Extension Awards.

Students progress from Advanced Level Mathematics to courses at Oxford, Cambridge, Russell group universities, apprenticeships and employment.

Holcombe habits are encouraged in mathematics:

Applying past knowledge is developed through application and practice;

Persistence is developed through extended reasoning and problem solving contexts;

Questioning and problem solving are developed through cognitive processes and thinker’s key activities.

Year 12

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Algebraic expressions, quadratics, equations and inequalities, graphs and transformations, data collection, measures and location of spread, introduction to mechanics. Circles, algebraic methods, the binomial expansion, representations of data, correlation and constant acceleration. Apply trigonometric ratios, trigonometric identities and equations, vectors, forces and motion, probability and statistical distributions. Apply differentiation and integration, forces and motion, variable acceleration and hypothesis testing. Apply integration, exponentials and logarithms. Investigations on the large data set.

Year 13

Term 1 Term 2 Term 3 Term 4 Term 5 Term 6
Apply algebraic methods, functions and graphs, sequences and series, radians, mechanics moments, forces and friction. Trigonometric functions, trigonometry and modelling, parametric equations, differentiation and integration, projectiles and kinematics. Apply integration techniques, the binomial expansion, numerical methods and vectors, conditional probability and further kinematics. Examination practice. Advanced Level examinations. Advanced Level examinations.

Online Learning Support

Pearson Active Learn

https://www.pearsonactivelearn.com/app/Home

CollinsConnect

https://connect.collins.co.uk/school/portal.aspx

Dr.Frost Maths

https://www.drfrostmaths.com/

Exams solutions

https://www.examsolutions.net/

GCSEPod

https://www.gcsepod.com/

MyMaths

https://www.mymaths.co.uk/

Mathsaurus

https://mathsaurus.com/

Corbett Maths

https://corbettmaths.com/

Hegarty Maths

https://hegartymaths.com/

nrich

https://nrich.maths.org/

Careers

Mathematics offers potential for joint university courses, graduate prospects and transferable skills.

Links to other subjects: although many of our students take Mathematics with Sciences, some of our students study Mathematics with Further Mathematics, Computer Science, Economics, Business Studies, Geography, History, Psychology, Art or Design Technology; during the advanced level course, we study how Mathematics is applied in other fields of study, to the world of work and to situations in society.

Career pathways: students can progress from this qualification to a range of different, relevant academic or vocational higher education qualifications; employment in a relevant sector; further training; many students go on to study honours degrees in physics, engineering, actuarial science, economics and mathematics; mathematics is recommended for computer science, accounting, chemistry, biology and life sciences, medicine, nursing, dentistry, business studies, management studies, finance, architecture, geology, psychology, surveying, philosophy and some advanced apprenticeships.

Top ten universities for mathematics:

University of Oxford

University of Cambridge

University of St Andrews

Durham University

Imperial College London

University of Warwick

University of Edinburgh

UCL (University College London)

Lancaster University

University of Bath

Students will develop skills needed to succeed in mathematics:

Critical thinking;

Problem solving;

Analytical thinking;

Quantitative reasoning;

Ability to manipulate ideas;

Construct logical arguments;

Communication;

Time management;

Teamwork;

Independence.

Students will develop transferable skills:

Cognitive skills: Non-routine problem solving; systems thinking; critical thinking; ICT literacy.

Interpersonal skills: Communication; teamwork and collaborative problem solving.

Intrapersonal skills: Adaptability; motivation and independence.

British Values

British values are defined as including:

“Democracy, the rule of law, individual liberty and mutual respect and tolerance for those with different faiths and beliefs.”

The Law and Democracy

Maths provides many opportunities to explore democracy and the rule of law. This may take the form of studying general or local election results. This might include the relationship between the number of votes and the number of seats that parties win. There are also opportunities to study how local or national funding is spent. There are always opportunities to review government data and study how data can influence decision making and legislation. One particular example is the annual budget which through financial allocations show where government priorities lie.

Individual liberty

Students can explore individual liberty through a study of numerical constraints on behaviour such as paying tax once they earn a certain income, speed limits in cars and how these are arrived at, choices of progressing in education or future careers

Rule of Law

Within Maths there are opportunities to study areas where numerical data is part of the rule of law. Examples to teach different aspects of maths can come directly from statistics used in law. This might include taxation or calculations which need to be made to make sure that industry complies with Health and Safety legislation. Statistics can also be used to identify the impact of legislative change. The Office of National Statistics may be helpful. The level of analysis will vary according to the level of maths being taught. In A level maths there is the opportunity to understand how statistics are calculated and used.

Democracy

Maths and the use of data have a significant role in the democratic decision making and influencing change. Students will hear statistics quoted to justify and argue for particular positions. Within Maths, using varied levels of complexity, the validity of these statistics can be explored. The BBC Radio 4: More or Less programme helpful in this. Critical thinking skills will be developed in Maths.

Individual liberty

Students might explore the extent of individual liberty bearing in mind legal constraints which are numerical in nature e.g. taxation of income; levels of alcohol in the blood when driving. Students may discuss future education choices and careers in Mathematics.

Tolerance and mutual respect

Good working relationships in the classroom which promote effective learning in Mathematics.