Quick Links # Maths

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### Mathematics Departmental Statement

The mission of the mathematics department is to provide an environment where students can learn and become competent users of mathematics and mathematical applications.

It will aim to promote an equal opportunity of learning experiences throughout all topics within the key stages.  Students will be encouraged to look at and investigate mathematics in day to day contexts.  Moreover, the department will contribute to the development of students as mathematical thinkers, enabling them to become lifelong learners, to continue to grow in their chosen professions, and to function as productive citizens.

##### KS4: Revision Links

Link to Mrbartonmaths e-book of notes and examples Link to mrbartonmaths.com/gcsetakeaway KS3:

Through the mathematics content students should be taught to:

1. Develop fluency.
2. Reason mathematically.
3. Solve problems.

### Subject content

Number

Pupils should be taught to:

• understand and use place value for decimals, measures and integers of any size
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
• use the concepts and vocabulary of prime numbers, factors (or divisors), multiples
• use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, mixed numbers
• use integer powers and associated real roots (square, cube and higher)
• work interchangeably with terminating decimals and their corresponding fractions (such
• define percentage as ‘number of parts per hundred’
• interpret fractions and percentages as operators
• use standard units of mass, length, time, money and other measures
• round numbers and measures to an appropriate degree of accuracy
• use approximation through rounding to estimate answers

Algebra

Pupils should be taught to:

• use and interpret algebraic notation
• substitute numerical values into formulae and expressions, including scientific
• formulae
• understand and use the concepts and vocabulary of expressions, equations,
• inequalities, terms and factors
• simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms, multiplying a single term over a bracket, taking out common factors, expanding products of two or more binomials, understand and use standard mathematical formulae; rearrange formulae to change the subject
• use algebraic methods to solve linear equations in one
• work with coordinates in all four quadrants
• interpret mathematical relationships both algebraically and graphically
• calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
• use linear and quadratic graphs to estimate values of y for given values of x and vice versa
• generate terms of a sequence from either a term-to-term or a position-to-term rule
• recognise arithmetic sequences and find the nth term
• recognise geometric sequences and appreciate other sequences that arise.

Ratio, proportion and rates of change

Pupils should be taught to:

• change freely between related standard units [for example time, length, area, volume/capacity, mass]
• use scale factors, scale diagrams and maps
• express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
• use ratio notation, including reduction to simplest form
• divide a given quantity into two parts in a given part:part or part:whole ratio
• solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
• solve problems involving direct and inverse proportion, including graphical and
• algebraic representations
• use compound units such as speed, unit pricing and density to solve problems.

Geometry and Measure

Pupils should be taught to:

• derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
• calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
• draw and measure line segments and angles in geometric figures, including
• interpreting scale drawings
• derive and use the standard ruler and compass constructions
• describe, sketch and draw using conventional terms and notations:
• use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
• derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures
• identify properties of, and describe the results of, translations, rotations and reflections
• identify and construct congruent triangles, and construct similar shapes by
• enlargement, with and without coordinate grids
• apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• understand and use the relationship between parallel lines and alternate and
• corresponding angles
• derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
• apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem
• use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve
• problems involving right-angled triangles
• use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
• interpret mathematical relationships both algebraically and geometrically.

Probability

Pupils should be taught to:

• record, describe and analyse the frequency of outcomes of simple probability
• experiments
• understand that the probabilities of all possible outcomes sum to 1
• enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
• generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Statistics

Pupils should be taught to:

• describe, interpret and compare observed distributions of a single variable
• construct and interpret appropriate tables, charts, and diagrams
• describe simple mathematical relationships between two variables.

### SPIRITUAL, MORAL, SOCIAL AND CULTURAL DEVELOPMENT

We strongly support the school policy of SMSC development.

The teaching of mathematics supports the spiritual, moral, social and cultural development in a number of ways:

• Through what is taught - encouragement of the wonder and awe of the beauty of mathematics, the simplicity of mathematics, the complexities of mathematics, the particular qualities of mathematics…
• Through how it is taught – explorations, investigations,…
• Through how we work - create the atmosphere and the opportunity to ask questions, reward and encourage,…
• Through what we offer - participation in extracurricular activities, mathematics classrooms with interesting wall displays...

### GCSE qualification

All students in Year 10 and 11 will follow the AQA course of study in Mathematics, leading to a GCSE qualification.

The Mathematics teaching in the school aims to introduce students to the many and varied aspects of Mathematics, to stimulate interest in mathematical ideas, to develop useful mathematical skills and to lay sound foundations for future development.

All students will follow a course appropriate to their level of ability in covering the National Curriculum and GCSE syllabus.

The examination course will have two levels of entry. Higher Tier and Foundation Tier. The Scheme of Assessment is linear with three question papers at each tier to be taken in the same examination series in June of Year 11 as detailed below:

GCSE Mathematics has a Foundation tier (grades 1 - 5) and a Higher tier (grades 3 - 9). Students must take three question papers at the same tier. All question papers must be taken in the same series.

The information in the table is the same for both Foundation and Higher tiers. The subject content section shows the content that is assessed in each tier.

 Paper 1: non calculator + Paper 2: calculator + Paper 3: calculator What’s assessed Content from any part of the specification may be assessed What’s assessed Content from any part of the specification may be assessed What’s assessed Content from any part of the specification may be assessed How it’s assessed · Written exam: 1 hour 30 mins · 80 marks · Non-calculator · 33⅓% of the GCSE             Mathematics assessment How it’s assessed · Written exam: 1 hour 30 mins · 80 marks · Calculator allowed · 33⅓% of the GCSE             Mathematics assessment How it’s assessed · Written exam: 1 hour 30 mins · 80 marks · Calculator allowed · 33⅓% of the GCSE             Mathematics assessment Questions A mix of question styles, from short, single mark questions to multi step problems. The mathematical demand increases as the student progresses through the paper. Questions A mix of question styles, from short, single mark questions to multi step problems. The mathematical demand increases as the student progresses through the paper. Questions A mix of question styles, from short, single mark questions to multi step problems. The mathematical demand increases as the student progresses through the paper.

Prospective employers regard maths as a prime qualification and in many careers a mathematics qualification is part of the entry requirements.

### Useful Web Links Click on the link above to visit the new BBC Bitesize pages.