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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

unit overview - autumn term

Autumn 1: Reasoning in Angles (3 weeks) and Probability (3 weeks)

Skills

  • Review of angles including angle-chasing accompanied with chains-of-reasoning (finding quantities by deductive reasoning about properties) and is a useful introduction to proof.

Derive and utilise circle theorems for increased complexity angle-chasing accompanied with chains-of-reasoning 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.

  • Use sample spaces, two-way tables, tree diagrams and Venn diagrams to visualize combinations of independent or dependent events and to calculate conditional probability, probabilities of repeated events and repeated events without replacement.

Knowledge

  • The central idea of mathematics in general and geometry in particular, is the study of invariance. Most theorems in geometry can be seen as resulting from the study of what change is permitted that leaves some relationships or properties invariant.  For example, knowing that the angle in a semicircle, is an invariant 90 degrees provided that the point being moved remains on the circle; if it moves inside the circle, the angle is greater than 90 degrees, if it is outside it is less, which could mean that a valid definition of a circle would be the locus of points that subtend an angle of 90 degrees to the ends of a line segment.
  • Geometry consists of three kinds of cognitive process: visualisation processes (for example, the visual representation of a geometrical statement), construction processes (when using tools, be these ruler and compass, or computer-based), and reasoning processes. Knowing that circle theorems require spatial thinking and visualisation and as well as deductive reasoning involving transformation or congruency arguments. These aspects are not separate; each gives rise to the other and each only exists in relation to the other.

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 wide-ranging 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.

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 A-Level 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.