Mathematics
subject overview
Mathematics can be applied in practical tasks, real life problems and within mathematics itself. The aim of the course is to develop mathematical vocabulary, improve mental calculation and use a range of methods of computation and apply these to a variety of problems.
The course of study should help you whether working individually or collaboratively to reason logically, plan strategies and improve your confidence in solving complex problems.
During Maths lessons you will learn how to:
 Use and apply maths in practical tasks, real life problems and within mathematics itself.
 Develop and use a range of methods of computation and apply these to a variety of problems.
 Develop mathematical vocabulary and improve mental calculation.
 Consider how algebra can be used to model real life situations and solve problems.
 Explore shape and space through drawing and practical work using a range of materials and a variety of different representations.
 Use statistical methods to formulate questions about data, represent data and draw conclusions.
Engage in practical and experimental activities in order to appreciate principles of probability. There is no coursework
Autumn 1
Reasoning in Angles (3 weeks) and Probability (3 weeks) 

Skills 
Derive and utilise circle theorems for increased complexity anglechasing accompanied with chainsofreasoning is a useful introduction to proof: deductive reasoning about properties Use experimentation, observation, frequency tables, relative frequency as well as theoretical probability to make predictions about expectations of future events.

Knowledge 

Rationale 
Geometry is one of the longest established branches of mathematics and remains one of the most important. Its development can be traced back through a wide range of cultures and civilisations with its origins in the surveying of land and in the design of religious and cultural artefacts. If anything, geometry is becoming more important across many fields. This is not only because of the wideranging applications of geometry in everything from robotics to CGI (computer generated imagery) movies, from crystallography to architecture, from neuroscience to the very nature of our universe, but also because new geometrical ideas are being generated within such diverse fields as these. The challenge of making sense of situations that are unpredictable pervades everyday living. Situations that lack information create conditions for uncertainty. Probability is one approach to reason about such uncertain situations. Uncertainty in some games and sports contests can be compelling and fun. A player who can reason about uncertainty will be able to adopt strategic approaches, which will improve the player’s success rate in the long term. Uncertainty is also apparent in everyday decision making. 
autumn 2
Developing algebra thinking and argumentation (6 weeks) 

Skills 

Knowledge 

Rationale 
Old Babylonian texts (17921750 b.c.e.) show a knowledge of how to solve quadratic equations, but it appears that ancient Egyptian mathematicians did not know how to solve them. Since the time of Galileo (1564 – 1642), they have been important in the physics of accelerated motion, such as free fall in a vacuum. The study of quadratics provides an arena for students to learn to go beyond visual assumptions and to use parameters as clues or tools to interrogate and display the characteristics of a function. 
spring 1
Proportional reasoning (6 weeks) 

Skills 
Draw and interpret Trigonometric graphs and functions

Knowledge 
y=kx, y=nkx and in y=1kx, y=1kn. 
Rationale 
Narrow ideas of ratio and proportion persist. These include ratio as the quotient of two numbers or the comparison as part to part and proportion as a comparison of part to whole or a comparison of ratios, with ‘proportional to’ indicating equality of ratios. These definitions complicate learners’ understanding of the constant relation between independent and dependent variables in proportional relations. The ratio between quantities is a comparison using the multiplicative relation, similar to the use of ‘difference’ to compare quantities in the additive relation. However, there is a crucial difference between ‘difference’ and ‘ratio’ which makes ratio significantly harder – its numerical form does not represent a magnitude in the same units as those it is comparing. When ratio can be counted the abstract nature of ratio is hidden in the concrete models and actions, but when it cannot be counted the ratio has significant imaginary qualities. Trigonometry (from the Greek for triangle measure) began as a branch of geometry, both for the practical task of surveying land and for astronomical calculations. Trigonometric functions are pervasive in many parts of pure and applied mathematics. Working on trigonometry is an important theme because it provides a context for developing a relational (as compared to instrumental) understanding of the component concepts. For example, understandings of ratio can develop through work on similar rightangled triangles and the notion of sine, cosine, and tangent as multipliers, understanding of angle as a measure of turn develops through extension beyond 90 degrees. Trigonometry offers an opportunity to work on the algebra of functions in a meaningful context instead of being tempted to provide mnemonics and transformation aids, or memorised formulae. 
spring 2
Vectors and compound measures (strengthening ratio & proportional reasoning) 

Skills 

Knowledge 

Rationale 
Vectors are a useful topic to develop ratio and proportional reasoning and other the key geometrical ideas of symmetry, invariance, transformation, similarity, and congruence, and use these ideas to enable learners to build sound spatial and geometrical reasoning skills which are encompassed in engineering and physics. 
summer 1
Representing algebraic functions (6 weeks) 

Skills 
Review of linear graphs (gradients and yintercepts); Investigate for parallel and perpendicular lines and make connections to (arithmetic) sequences and grapple with Geometric sequences and connections to growth and decay, strengthen ratio and proportional reasoning.

Knowledge 

Rationale 
The concept of algebraic functions is foundational to modern mathematics, and essential in related areas of the sciences. Algebraic functions are used in finance, engineering, and design to name three. Learning about the concept of algebraic function is complex, with many high performing students possessing weak function understandings. Conceptions and reasoning patterns needed for a strong and flexible understanding of functions are more complex than what is typically assumed by designers of curriculum. Students who think about functions only in terms of symbolic manipulations and procedural techniques are unable to comprehend a more general mapping of a set of input values to a set of output values; they also lack the conceptual structures for modelling function relationships in which the function value (output variable) changes continuously in tandem with continuous changes in the input variable. These reasoning abilities have been shown to be essential for representing and interpreting the changing nature of a wide array of function situations they are also foundational for understanding major concepts in advanced mathematics 
summer 2
Geometry and Locating ‘signals’ in ‘noisy’ data sets 

Skills 

Knowledge 

Rationale 
The scope of statistics spreads across the curriculum. Statistical reasoning draws on context and those contexts relate to many disciplines in the school curriculum. Making sense of mathematics involves describing, modelling, comprehending, and grappling with mathematical variation. Reasoning with statistics is a variant of mathematical variation and at the same time serves as a tool for making sense of data in other subject areas or to be used by citizens seeking to be better informed. Insofar as statistics is a tool for rooting out possible causes or associations, it is invaluable to the practice of many disciplines, albeit with added complexity. Statistics is a form of enquiry, centred on inference making when working with data arising out of experimentation or observation rather than simply computing numerical and graphical representations of data The notion of informal inferential reasoning is an essential tool for the modern statistically literate citizen who needs to be able to reason with and about data. 
knowledge Organiser
A knowledge organiser is an important document that lists the important facts that learners should know by the end of a unit of work. It is important that learners can recall these facts easily, so that when they are answering challenging questions in their assessments and GCSE and ALevel exams, they are not wasting precious time in exams focusing on remembering simple facts, but making complex arguments, and calculations.
We encourage all pupils to use them by doing the following:
 Quiz themselves at home, using the read, write, cover, check method.
 Practise spelling key vocabulary
 Further researching people, events and processes most relevant to the unit.