Mathematics

Powerful Knowledge

In KS4 the curriculum aims to ensure that all students:

Develop fluency

• consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots
• select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π, use of standard form and application and interpretation of limits of accuracy
• consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions
• extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities
• move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic, reciprocal functions
• use mathematical language and properties precisely

Reason mathematically

• extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically
• extend their ability to identify variables and express relations between variables algebraically and graphically
• make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments
• reason deductively in geometry, number and algebra, including using geometrical constructions
• interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
• explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally
• assess the validity of an argument and the accuracy of a given way of presenting information

Solve problems

• develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

• develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts
• make and use connections between different parts of mathematics to solve problems
• model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions
• select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem

In addition those students who are studying higher tier maths cover the following additional content:

Develop fluency

• consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include fractional indices
• select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving and surds
• consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include expressions involving surds and algebraic fractions
• move freely between different numerical, algebraic, graphical and diagrammatic representations, including exponential and trigonometric functions

Reason mathematically

• begin to use algebra to support and construct proofs

Literacy

Teachers are the role model in the classroom and therefore use correct mathematical terms during their lessons.

Students are taught correct mathematical terminology and are encouraged to use such vocabulary when giving answers and during class discussions.

When introducing new mathematical terms the root, prefix or suffix of the word is discussed with students so they can understand how many mathematical terms have originated from Greek or Latin.

In addition, the new maths GCSE, with its increased focus on real world problem solving, demands higher literacy skills. It is therefore imperative that we ensure students understand key mathematical terms and raise their literacy so they can access the exam questions and demonstrate their true mathematical ability.

When considering literacy we also consider mathematical literacy. This is the ability to use numbers to help solve real-world problems. By developing mathematical literacy, students are able to understand the language of mathematics. Knowing and understanding the language of mathematics is important because maths is everywhere. Maths is a fundamental tool we use to understand the world we live in.

School Context

Students will be offered a wide variety of opportunities and experiences that widen their appreciation of

mathematics and the world around it. These will include:

• Developing an appreciation of some aspects of finance and more creative mathematics
• National competitions such as the UK Mathematics Individual Challenge and Team challenges
• Local competitions such as AMSP Team challenges
• Maths lectures such as the Maths Inspiration events
• Code breaking competitions with opportunities to visit Bletchley Park
• Origami
• Maths in different cultures
• Opportunities to further explore mathematical ideas with key exponents in the mathematics community
• Students will be encouraged to read extracts around mathematics
• Students have access to a number of recreational mathematics books that contain several puzzles and challenges that they can work on at any time

Assessment

Formative assessment takes place through a variety of methods. Within lessons students’ progress is assessed through teacher questioning, mini whiteboard work, low stakes quizzes and self, peer or teacher marking of work. Homework tasks alternate each week between a paper based assignment and Sparx Maths that tests students’ understanding of either their current topic or a past topic.

When students have been set a task on Sparx Maths it is marked automatically by the software giving students instant feedback. Teachers then review the work that has been completed and provide written feedback to the students on what they need to do to improve. Where whole class misconceptions are identified time is then allocated within lessons to re-cover this topic.

Starters are predominantly used for retrieval practice and where gaps in students’ knowledge are found teachers set aside future lesson time to re teach this topic and allow further practice. Where it is noticed that only a handful of students are struggling with understanding a prior learned topic we set up tutor time interventions with these students to work with them on this topic and increase their understanding and confidence.

Students sit topic tests at the end of each unit. These are peer marked during the lesson and then reviewed by the teacher. FIT tasks are then provided in a subsequent lesson alongside individual and whole class feedback to allow students time to improve their knowledge and skills. Areas of difficulty are noted by the class teacher and included in retrieval practice starters in future lessons.

Students sit summative assessments three times per year. These assessments cover all prior learning. Results are analysed and used to create forthcoming starters, plan additional teaching of topics and identify students who require intervention.

Careers

Maths is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment.

Posters detailing potential careers in Maths are displayed around the department and students are encouraged to ask about the mathematical content in a range of careers. Where explicit links can be made between a topic and how this could be used in the workplace, relevant resources or examples are used or discussed within lessons. However as a department we are conscious that when using real life contexts we may have to modify or simplify the complex mathematics in order for our students to understand and are wary of making this appear contrived.

The importance of being numerate in every job and the impact this has on career prospects and salary is discussed with students at various points in the curriculum. For example when studying displaying data a variety of poor graphs are shown and analysed to demonstrate how statistics can be used to manipulate data.

In KS4 we also discuss the ways in which students can continue studying maths beyond their GCSEs and specifically talk about Core Maths as an option for those who do not want to study purely theoretical or abstract maths. Core maths can be applied on a day-to-day basis, whether in work, study or life and can help with other A level subjects, in particular with science, geography, business studies, economics and psychology.

Specific careers that involve a high degree of maths are: accountant, architect, actuary, bank manager, business adviser, credit manager, economist, financial advisor, insurance account manager, insurance underwriter, investment analyst, revenue officer, management accountant, management consultant, money adviser, mortgage adviser, pensions manager, stockbroker, tax advisor, web developer, games developer, lawyer, event manager, journalist, media programmer, doctor, nurse, copywriter, data analyst, chemical engineer, mechanical engineer, civil engineer, research scientist, statistician, self employed business owner.