Maths is a subject that opens the world to creativity and problem solving. It is a subject that creates moments of pleasure and wonder, enhancing the ability to reason logically, algebraically, and geometrically and to make sense of the world. An essential life skill, it is important as a stand-alone subject and for its impact in many other areas of study, particularly Geography, Science and Technology. Finally, it is also important in everyday life, in many forms of employment and in general decision-making.
Mathematics is a means of making knowledge useful, allowing students to build a secure framework of mathematical reasoning, which they can use and apply with confidence. The power of mathematical reasoning lies in its use of precise and concise forms of language, symbolism and representation to reveal and explore general relationships.
As typical maths enthusiasts, we want all our students to become fluent in the fundamentals of mathematics, to be able to reason mathematically and to solve problems by applying their mathematical understanding to a variety of problems. Mathematical Mastery for all is our over-riding aim.
A key department in the school, we aim to set challenging targets with high expectations for all students. We strongly believe in the importance of offering a variety of different approaches to teaching and learning to help motivate & engage our students and future mathematicians.
When students leave us at the end of sixth form, it is our aim that they will:
- Experience the satisfaction and enjoyment of their mathematical achievements.
- Think and act as independent learners.
- Identify patterns and understand the meaning behind these.
- Reason clearly and logically and set out logical and well thought-out arguments.
- Approach problems systematically choosing appropriate techniques for their solution..
- Communicate with a team; sharing and investigating problems.
- Perform basic numeracy skills.
- Understand the mathematics likely to be encountered in everyday life.
- Obtain their best possible results at all times, especially with the public examinations at KS4 and KS5.
Our Curriculum Learning Pathway
Transition & building on KS2
As a department, we have collaborated with our local Primary schools to identify what is taught at KS2 and through our transition work we are able to identify and support any gaps in students’ knowledge.
What do our students learn?
Maths is a content heavy subject covering a broad range of topics. Our curriculum is sequenced to develop, and consolidate students’ knowledge & understanding at every stage.
The main concepts covered are:
- Problem solving
- Place value and ordering
- Symmetry and reflection
- Three dimensional shapes
- Probability & algebraic representation
- Congruency, similarity & enlargement
Key Stage 3
The KS3 schemes of learning builds upon KS2 objectives and introduces those that will support progression into KS4. A full range of topics cover the 4 main attainment areas of Number, Algebra, Geometry and Data Handling.
Students engage in rich End Point Tasks that look for students to use Mathematical skills within a real or problem solving scenario. Students will be encouraged to engage in group dialogue and pursue their own individual solution to these tasks. Initial mistakes are used as learning opportunities and through questioning, dialogue and next step marking student learning is facilitated to ensure progress for all. Pupils are encouraged to communicate their solutions and be able where appropriate to prove mathematical conclusions.
Contact time will be 4 hours a week for Yr 7 students with exception of students identified as needing further support where they will be given a further 2 hours a week to ensure the foundation principles of number are strong and can be applied in problem solving and real life scenarios.
At Yr 8 students will have 5 hours on contact time a week. Learning will be further supported by a range of independent home learning tasks that will range from skill consolidation, watching videos to support learning (flipping the classroom) and working on individualised feedback.
Key Stage 4
KS4 Exam Board: Edexcel
Mathematics is undergoing an exciting transition at Key Stage 4 with a new government led curriculum model for students beginning the GCSE course in 2015/16. The new curriculum is bigger than ever before and covers both a broader spectrum of topics as well as increasing the level of rigour and challenge at all levels. At Lipson we see this as an opportunity to redevelop our current curriculum model and ensure it reflects the very best mix of Mathematical skills, content and application to ensure all students taking the course leave not only with the qualifications they deserve but with a passion for Mathematics.
The most notable changes to the GCSE course is the way in which pupils attainment is both assessed and reported. The historical grades of A* to G will be replaced with a number system ranging from 1 to 9 with 1 representing the lowest outcome and 9 the current highest outcome. For those more familiar with the A* to G system a rough comparison between the two systems is shown in diagram below.
Content and Assessment
All students at Lipson will engage in a linear GCSE course and will be assessed by a final examination in the end of year 11. To reflect the broader and larger curriculum content both the learning time and the time spent in examinations has been increased. All Lipson pupils will have 5 hours a week of Mathematics teaching and learning time during years 9, 10 and 11. The examination is now assessed by 3 summative examinations each lasting 1.5 hours each. These will be sat in separate examination sessions with one paper being non-calculator and the other two being calculator papers.
Students will be encouraged to develop confidence in mathematics and to recognise the importance of
mathematics in their own lives and to society. Our aim is that students will be enabled to;
- develop fluent knowledge, skills and understanding of mathematical methods
- 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.
The breakdown of the different components of the course are split into five different attainment domain as outlined in the Pie Charts below. The relative emphasis on each domain changes depending on the Tier of entry that is selected for each student.
Number - Students will develop their numeracy skills to ensure they can apply different number operations and forms into a range of contexts and problems. This is not a stand alone topic and will be taught throughout the year with the context of the other objective domains Eg When considering presenting data in a pie chart we make the links to fractions, percentages and proportional reasoning. The notational use and manipulation of fractions, percentages, decimals and ratio and the relationship between the different forms of number will be explored by all students. To support their work in other subjects students will be encouraged to use specific scientific notation such as standard form in the appropriate contexts as well as being introduced to the use of both rational and irrational numbers and their notation.Effective numerical methods will be considered and practical mental techniques such as estimation and rounding answers to appropriate degrees of accuracy. Some pupils will also begin to quantify the potential error in such estimations and link this to their algebraic work on inequalities. The course explores number properties such as factors, multiples and primes which will help to build an appreciation for some of the other techniques we consider such as simplifying fractions.
Algebra - The fundamental basis of problem solving is the use of algebra and pupils will grow in their confidence and ability to express mathematical problems using algebraic notation. Pupils will explore how to manipulate, represent, describe and where appropriate present these on a graph. Links are made to the pupils understanding of the number system such as indices. Here we develop and explore the rules and indices and how we can use these to simplify expressions and calculate complex equations. The course encourages pupils to explore relationships and where appropriate make generalisations which can often be expressed algebraically. A variety of graphical representations will be considered and how to analyse graphs will be a key component to the course.
Ratio, proportion and rates of change - This objective domain is a new element to the GCSE which explicitly ensures pupils explore the use and practical application of ratio and scales in such contexts as analysing best buys. Scales in a range of practical contexts will be considered to ensure pupils feel confident manipulating this form of mathematical notation. Direct links to scientific concepts such as speed, density and proportionality will be considered. The effects of using repeated fraction, decimal or percentage changes is considered and related directly to financial contexts like interest rates, compound interest and reverse percentages changes.
Geometry and Measures - This element of the course will ensure key vocabulary is fluent for students when describing geometric shapes or analysing measures such as time, money or mass. Geometrical reasoning will be developed in describing, analysing and providing key shapes properties and relationships including angle rules, transformations, perimeter, area and volume. The application of key famous formulae and theorems such as Pythagoras’ theorem, trigonometric functions and circle theorems are also considered.
Statistics and Probability - Probability will explore the use of fractional notation to describe the mathematical likelihood of specific outcomes. Both single and combined events are considered and the real life application and dangers of these are considered in contexts such as gambling. Students will develop the ability to mathematical reason using these models of future outcomes or behaviour and interpret them to make predictions and manage future potential risks.
Statistics use a similar skill set that looks to analyse situations and explores how to logical engage in a data handling cycle to collect, analyse, represent and conclude the findings for statistical enquiries. Specific analytical techniques are taught including a variety of methods of calculating an average and to consider the consistency of data distribution. Pupils will develop a variety of methods for representing data and will be able to both select the most appropriate method and be able to interpret statistical representations from which they may draw conclusions.
Routes through Mathematics at Lipson
Our unique banding routes through Mathematics allows flexibility and bespoke routes through Mathematics to suit our learners needs.
This band will engage in the higher tier curriculum with the aim to prepare these students so that they can engage in Mathematics at the highest level in any future education such as A Level Mathematics. Initially the will engage just with the GCSE content during Year 9 and then in year 10 will be introduced to Further Mathematics concepts. This will enable these students to gain a second separate and distinct Lv 2 qualification in Further Mathematics. This covers more advanced Mathematical principles and is the very best way to prepare students who would look to engage in either A’level Mathematics or further education courses that have a significant Mathematical content. Our students currently have enjoyed great success with this additional qualification that complements the GCSE content and helps to challenge and develop well rounded and very able Mathematicians.
This group is designed to challenge our able Mathematicians and ensure they achieve strongly within GCSE Mathematics. Often students within this band benefit from focusing solely on the Higher GCSE content and will study content upto and including the new grade 9. We have ensured that Band 2 mirrors exactly with Band 1 during year 9 so that changes can be made up until the beginning of year 10. This is intended to ensure as much flexibility within the banding system as possible.
Band 3 is designed for students who will benefit from building their Mathematical confidence and engage in a 2 year course looking at the full range of Mathematical principles at the foundation stage. These pupils will look to master these skills upto and including the new grade 5. You will notice that this grade overlaps on both tiers and therefore to ensure students are not limited to this grade alone they explore a wide range of carefully selected Higher Tier GCSE content in year 11 that will build upon the secure knowledge developed through years 9 and 10.
This band is designed for students who again will benefit from a strong focus on both the foundation GCSE course content and the further development of Numeracy techniques that will allow our learners to feel empowered and numerate in everyday mathematical challenges both in the home and the workplace. This band has been designed to be flexible such that it strongly mirrors the content in Band 3 to ensure students can move between bands if it is identified that such a move would better meet their learning needs. would be better met.
Key Stage 5
KS5 Exam Board
The KS5 curriculum is balanced between core modules and applied topics.
Yr 12 pupils will engage in 3 modules
C1 - Introduction to Advanced Mathematics,
To build on and develop the techniques students have learnt at GCSE so that they acquire the fluency
required for advanced work. For example looking at coordinate geometry and Binomial Distributions
C2 - Concepts of Advanced Mathematics
To introduce students to a number of topics which are fundamental to the advanced study of
mathematics. These include introducing the concepts behind integration and differentiation.
S1 - Statistics 1
To enable students to build on and extend the data handling and sampling techniques they have learnt
at GCSE and apply theoretical knowledge to practical situations using simple probability models. Also to give insight into the ideas and techniques underlying hypothesis testing.
Students will have 5 hours a week contact time and progress will be monitored through the use of end of chapter assessments and written next step feedback. Students will sit a mock examination in January of Year 12 in the C1 and the S1 modules.
Books are provided to support the learning of each module as well as access to the online resources provided by the examination board (http://new.integralmaths.org/).
Year 13 builds upon the concepts mastered at year 12 with respect to the core modules and students engage in
C3 - Methods of Advanced Mathematics
To build on and develop the techniques students have learnt at AS Level, with particular emphasis on
C4 - Applications of Advanced Mathematics
To develop the work in C1, C2 and C3 in directions which allow it to be applied to real world
problems. Also new ideas are introduced such as Complex vector work and differential equations,
D1 - Decision Mathematics 1
To give students experience of modelling and of the use of algorithms in a variety of situations and to develop modelling skills. These problems presented are diverse and require flexibility of approach. Students are expected to consider the success of their modelling, and to appreciate the limitations of their solutions.
The same level of support and resources continues as it was delivered in Year 12 as does a January mock and access to both textbooks and online resources.
In addition we offer Further Maths which is aimed towards the most able mathematicians to set them up for university courses which are linked to Science, Mathematics and Engineering.
In year 12 three modules are taken
FP1 - Further Concepts in for advanced mathematics
To develop an understanding of the rigour and technical accuracy needed for more advanced study of
mathematics. New ideas such as Complex numbers and Matices are shown to the students.
M1 - Mechanics 1
To introduce students to mathematical modelling and to the basic concepts in kinematics, statics and
dynamics which underlie the study of mechanics where students will be expected to formulate models, using the mechanics within the specification, and to show an appreciation of any assumptions made. They will also be expected to make simple deductions from the model and to comment on its usefulness. They will understand the particle model.
S2 - Statistics 2
To extend students’ ability to represent data in bivariate situations, with an emphasis on linear and
rank order modelling, and associated hypothesis testing.
To introduce continuous probability distributions through the Normal distribution.
In year 13 a further 3 Modules are undertaken
FP2 - Further Methods for advanced mathematics
To build on and extend students’ knowledge of Pure Mathematics and associated techniques. Including work on Matrices, Complex numbers and additional calculus techniques.
M2 - Mechanics 2
To build on the work in Mechanics 1 by extending the range of mechanics concepts which students
are able to use in modelling situations. Students will be able to use the rigid body model in simple
cases involving moments.
Students will be expected to formulate models, using the mechanics within this specification and that
for Mechanics 1, and to show an appreciation of any assumptions made; they will also be expected to
make simple deductions from the model and to comment on its usefulness.
The examination will test candidates’ knowledge of principles and of when they should be applied.
The examination will avoid excessive emphasis on algebraic or calculus skills, but candidates will be
expected to interpret simple algebraic expressions.
This module makes use of modelling and algorithms in a variety of situations. It includes more advanced techniques
for linear programming and solving problems in networks. Logic gates, truth tables and decision trees are introduced.
How do we enrich our subject outside the classroom?
At KS3, we offer a mine craft club where students can test their mathematical skills.
At KS4 and KS5, we offer opportunities to complete workshops run by the university and we also offer some students the opportunity to take an additional GCSE in statistics.
All year groups also compete in national mathematics competitions run by the UK Mathematics Trust.
Meet the team
Vicky Connor – Head of Maths
Wendy Haydon – Second in Maths
Joe Lincoln – PP and SEND Progress Champion
Matt Tamlyn -Teacher of Maths
Emily Pooley - Teacher of Maths
Tammy Bailey-Teacher of Maths
Bianca Lewis -Teacher of Maths
Brian Malone -Teacher of Maths
Alec Bithersea-Teacher of Maths