# 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

 Working with number & Geometric Reasoning (6 weeks) Skills Review the rules on indices with numbers and with algebraic expressions. Review converting between ordinary numbers and numbers in standard form and calculate, compare, and order numbers in standard form Use a ruler and compass to construct angles, triangles, other regular polygons, the perpendicular bisector of a line, the shortest distance from a point to a line, and the bisector of an angle Use congruency arguments as a form of deductive reasoning. Draw a locus and use loci to solve problems Use chains-of-reasoning to support explanations in algebraic and geometric proof 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. Indeed, it could be that as much new geometry is being devised by geometers working outside of established university mathematics departments as within.

## autumn 2

 Statistics and Algebra (6 weeks) Skills Find the quarter and the interquartile range from stem-and-leaf diagrams Draw and interpret box plots, cumulative frequency tables, stem-and-leaf diagrams and histograms; find and interpret the median, quartiles and interquartile range, frequency density Understand frequency density in them Experience the Capture/recapture method and know why it is used Know that iterative means carrying out a repeated action. Experience an iterative process to accurately calculate the solutions to a quadratic equation. Understand the effect of transformations on quadratic equation in its function form relationship between translating a graph and the change in its function notation Knowledge Know the relationships between box-plots, cumulative frequency diagrams and histograms. Know the differences and similarities between ‘cumulative’ and ‘accumulative’. Know that the area under a velocity-time graph is the distance travelled. Know that the tangent to a curve graph is a straight line that touches the graph at a point. the gradient at a point on a curve is the gradient of the tangent at that point. Know that the straight line that connects two points on a curve is called a chord. the gradient of the chord gives the average rate of change and can be used to find the average speed on a distance-time graph. 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.

## 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.