Maths

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)

mathstwitter

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

(DfE Programmes of Study)

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

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