Maths Department

The mathematics department at SCCBS supports all pupils’ potential for achievement, providing them with a solid foundation of mathematical skills, whilst promoting a sense of wonder about the beauty of mathematics.

“Mathematics is the alphabet with which God has written the universe”

Galileo (1564 – 1642)

The Mathematics Department at St Columba’s will provide for all students mathematical experiences through spiritual, moral, cultural and social contexts – irrespective of their background, ability or race. These experiences should help the students to acquire the mathematical skills and understanding they need as they journey through life. Mathematics plays an important role in our lives. It is used in everyday activities such as buying food and clothes, keeping time and playing games.

All students at St Columbas study mathematics. We aim to provide a wide range of mathematical experiences enabling students to:

• acquire skills in mathematical thinking;

• develop conﬁdence in using and applying mathematics and to appreciate its challenges and aesthetic satisfaction within wider contexts;

• develop positive attitudes to mathematics and an understanding of its nature and purpose in a variety of relevant contexts;

• progress appropriately through a challenging programme of work differentiated to meet individual needs;

• develop, initiate and enjoy working cooperatively, collaboratively and individually.

Students are encouraged to develop their thinking skills and approaches to problem solving and enquiry using a range of techniques. The development of an understanding of number and its application, in particular the development of mental strategies and the use of appropriate language is a priority.

The following exemplification can be found at www.gov.uk

**Purpose of study**

Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

**Aims**

The national curriculum for mathematics aims to ensure that all pupils:

become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

**Information and communication technology (ICT)**

Calculators should not be used as a substitute for good written and mental arithmetic. They should therefore only be introduced …. to support pupils’ conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure.

**Spoken language**

The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others, and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.

As specified in the DfE Mathematics Programmes of Study, pupils at both Key Stage 3 and Key Stage 4, through the mathematics content, will develop fluency, reason mathematically and solve problems. These three key skills are expanded on here:

**Working mathematically**

Through the mathematics content, pupils will:

**Develop fluency**

• consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots

• select and use appropriate calculation strategies to solve increasingly complex problems

• use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships

• substitute values in expressions, rearrange and simplify expressions, and solve equations

• move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]

• develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

• use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics

**Reason mathematically**

• extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

• extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically

• identify variables and express relations between variables algebraically and graphically

• make and test conjectures about patterns and relationships; look for proofs or counter-examples

• begin to 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 begin to express their arguments formally

**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 mathematics

• begin to model situations mathematically and express the results using a range of formal mathematical representations

• select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems

A wide range of teaching methods are used, in order to meet the varying needs of students. Included are whole class, small group and individualised learning approaches. Active involvement in mathematical experiences, in real and relevant contexts is essential for the mathematical development of our students. We are committed to providing a broad, balanced, relevant and knowledge-rich curriculum for all our students, presented at a level appropriate to the needs and ability of the individual.

**An overview of the Mathematics Curriculum: **

Year 7 | |

Autumn Term 1 | Numbers and the number system Counting and comparing Calculating |

Autumn Term 2 | Visualising and constructing Investigating properties of shapes Algebraic proficiency |

Spring Term 1 | Exploring fractions, decimals and percentages Proportional reasoning Patterns |

Spring Term 2 | Measuring space Investigating angles Calculating fractions, decimals and percentages |

Summer Term 1 | Solving equations and inequalities Calculating space Checking, approximating and estimating |

Summer Term 2 | Mathematical movement Presentation of data Measuring data |

Year 8 | |

Autumn Term 1 | Numbers and the number system Calculating Visualising and constructing |

Autumn Term 2 | Understanding risk I Algebraic proficiency |

Spring Term 1 | Exploring fractions, decimals and percentages Proportional reasoning Patterns |

Spring Term 2 | Investigating angles Calculating fractions, decimals and percentages Solving equations and inequalities |

Summer Term 1 | Calculating space Calculating space Algebraic proficiency: visualising |

Summer Term 2 | Understanding risk II Presentation of data Measuring data |

Year 9 | |

Autumn Term 1 | Calculating Visualising and constructing Algebraic proficiency |

Autumn Term 2 | Proportional reasoning Patterns Solving equations and inequalities I |

Spring Term 1 | Calculating space Conjecturing Algebraic proficiency |

Spring Term 2 | Solving equations and inequalities II Understanding risk Presentation of data |

Summer Term 1 | BEGIN GCSE SPECIFICATION: GCSE 1a. Calculations, checking and rounding GCSE 1b. Indices, roots, reciprocals and hierarchy of operations GCSE 1c. Factors, multiples, primes, standard form and surds |

Summer Term 2 | GCSE 2a. Algebra: the basics, setting up, rearranging and solving equations GCSE 2b. Sequences |

Year 10 GCSE Foundation | |

Autumn Term 1 | Integers and place value Decimals Indices, powers and roots Factors, multiples and primes Algebra: the basics Expressions and substitution into formulae |

Autumn Term 2 | Tables, charts and graphs Pie charts Scatter graphs Fractions, decimals and percentages Percentages |

Spring Term 1 | Equations and inequalities Sequences Properties of shapes, parallel lines and angle facts Interior and exterior angles of polygons |

Spring Term 2 | Statistics, sampling and the averages Perimeter, area and volume |

Summer Term 1 | Real-life graphs Straight-line graphs Transformations |

Summer Term 2 | Ratio Proportion Right-angled triangles: Pythagoras and trigonometry |

Year 10 GCSE Higher | |

Autumn Term 1 | Averages and range Representing and interpreting data and scatter graphs Fractions and percentages Ratio and proportion |

Autumn Term 2 | Polygons, angles and parallel lines Pythagoras’ Theorem and trigonometry |

Spring Term 1 | Graphs: the basics and real-life graphs Linear graphs and coordinate geometry Quadratic, cubic and other graphs |

Spring Term 2 | Perimeter, area and circles 3D forms and volume, cylinders, cones and spheres Accuracy and bounds Transformations Constructions, loci and bearings |

Summer Term 1 | Solving quadratic and simultaneous equations Inequalities Probability |

Summer Term 2 | Multiplicative reasoning Similarity and congruence in 2D and 3D |

Year 11 GCSE Foundation | |

Autumn Term 1 | Probability Multiplicative reasoning |

Autumn Term 2 | Plans and elevations Constructions, loci and bearings Quadratic equations: expanding and factorising Quadratic equations: graphs |

Spring Term 1 | Circles, cylinders, cones and spheres Fractions and reciprocals Indices and standard form |

Spring Term 2 | Similarity and congruence in 2D Vectors Rearranging equations, graphs of cubic and reciprocal functions Simultaneous equations |

Summer Term 1 | Consolidation, revision and practice of all topics in preparation for external examinations |

Year 11 GCSE Higher | |

Autumn Term 1 | Graphs of trigonometric functions Further trigonometry Collecting data Cumulative frequency, box plots and histograms |

Autumn Term 2 | Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics Circle theorems Circle geometry |

Spring Term 1 | Changing the subject of formulae (more complex), Algebraic fractions, Solving equations arising from algebraic fractions, Rationalising surds, Proof |

Spring Term 2 | Vectors and geometric proof Reciprocal and exponential graphs; Gradient and area under graphs Direct and inverse proportion |

Summer Term 1 | Consolidation, revision and practice of all topics in preparation for external examinations |

NB: the above lists are not exhaustive. We aim to include investigational and enrichment tasks throughout the school year. We are also committed to supporting the school’s designation as a Financial Education Centre of Excellence and will include financial awareness topics where appropriate.

Last updated: June 19, 2017 at 11:25 am