Maths

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Daniel Prowse - Head of Maths - daniel.prowse@swale.at

The only way to learn mathematics is to do mathematics

PAUL HALMOS


Subject Overview

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.

In KS3 pupils are taught in ability groups which match their strengths and interests with regards to mathematics.  The KS3 mathematics curriculum at Peacehaven Community School aims to develop character by ensuring 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

In KS3 we want students to have a broad, comprehensive and firm foundation of the basics of mathematics. This includes appreciation of the key topics that they will encounter and require to develop at KS4.

At KS4 students will develop their problem solving skills enabling them to become reflective learners. They are enabled to apply the concepts and skills acquired at KS3 within the spiral curriculum adding more depth and complexity with each rotation.  We aim to give them the best opportunities to learn the KS4 curriculum, to have the best possible outcomes for their GCSE examinations in year 11 and to make them confident and responsible members of the school and wider community. The sequencing of the curriculum enables students to build on their knowledge and skills towards agreed end points.

The mathematics curriculum at Peacehaven Community School aims to develop character by ensuring that all pupils:

Develop fluency

  • consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots {and fractional indices}

  • select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π {and surds}, use of standard form and application and interpretation of limits of accuracy

  • consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, {and expressions involving surds and algebraic fractions}

  • extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities

  • use mathematical language and properties precisely

Reason mathematically

  • extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically

  • extend their ability to identify variables and express relations between variables algebraically and graphically

  • make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments {and proofs}

  • 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 express their arguments formally

  • assess the validity of an argument and the accuracy of a given way of presenting information.

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 contexts

  • make and use connections between different parts of mathematics to solve problems

  • model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions 

  • select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem.

Throughout the whole school curriculum we embed a reflective assessment cycle which incorporates assessment of prior knowledge which leads to gap analysis. This allows for targeted and focused teaching and formative assessment to ensure every opportunity is given to close any gaps. Enabling students and teachers to monitor and reflect on progress made and can be used to inform interventions and next steps.

Using the detailed knowledge that this generates we are able to engage parents / carers in the education of their child.

KS3

Students have maths for 4 lessons each week.

Year 7

In terms 1&2 students will cover sequences, algebraic notation, equality and equivalence, place value and ordering and FDP equivalence.

In terms 3&4 students will cover addition and subtraction, multiplication and division, fractions and percentages of amounts, directed number and addition and subtraction of fractions.

In terms 5&6 students will cover constructing, measuring and using geometric notation, developing geometric reasoning, developing number sense, sets and probability and prime numbers and proof.

Year 8

In terms 1&2 students will cover proportional reasoning, rounding and estimation, indices and roots, HCF, LCM and prime factor decomposition, venn diagrams, equations, sequences, graphs, pythagoras, angle reasoning and angles in polygons.

In terms 3&4 students will cover construction of triangles and quadrilaterals, bearings, constructions and loci, fractions, decimals and percentages, fractions and percentages of a quantity, ratio and speed, distance and time.

In terms 5&6 students will cover circumference and area of circles, 3D solids and their nets, surface area and volume.

KS4

Students have maths for 5 lessons a week in year 10 and 4 lessons a week in year 11, OCR is the exam board and their specification can be found here:

https://www.ocr.org.uk/qualifications/gcse/mathematics-j560-from-2015/

Year 9

In terms 1&2 students will cover sampling and organising data, bar charts and pictograms, pie charts, averages and spread 1, place value and rounding, 4 operations, directed numbers, BIDMAS, estimation, calculator skills, substitution and forming expressions, simplifying expressions, laws of indices, expanding and factorising single brackets, pythagoras and trigonometry.

In terms 3&4 students will cover fractions and decimals, F.D.P conversion, fractions of amounts, percentages of amounts, 4 operations with fractions, percentage change, frequency diagrams, averages from grouped data, scatter graphs and correlation, time series graphs, relative frequency, expected outcomes, theoretical probability and mutually exclusive and exhaustive events.

In terms 5&6 students will cover measures and bearings, angle properties and parallel lines triangles and quadrilaterals, congruence and similarity, angles in polygons, constructions and loci, substitution into formulae, form and rearrange formulae, equations, identities and functions and expand and factorise quadratics.

Year 10

In terms 1&2 students will cover column vectors, transformations, area of triangles and quadrilaterals, area and circumference of circles, solving linear equations, solving quadratic equations, simultaneous equations, inequalities, laws of indices, 4 operations with fractions, calculations with pi and standard form.

In terms 3&4 students will cover F.D.P. in proportion, ratio, percentage change, factors, multiples and primes, prime factor decomposition, LCM, HCF and Venn diagrams, powers and roots.

In terms 5&6 students will cover co-ordinates, plot graphs, equation of a straight line, real life graphs, 3D solid names and terminology, plans and elevations, volume of a prism, surface area and cones and spheres.

Year 11

In terms 1&2 students will length, mass and capacity, speed and density, upper and lower bounds, sets, possibility space, tree diagrams, sequence rules, finding the nth term, special sequences, properties of quadratic functions, sketching functions, real life graphs, compound units, direct proportion, inverse proportion and growth and decay

In terms 3&4 students will undertake revision applicable to their group and tier of entry specific to their needs

In term 5 students will work on exam technique, revise and undertake their first GCSE paper

Homework

Homework is set once a week for each class, however the length of the homework increases from 30 minutes in year 7 to 60 minutes in year 11.

Most homework tasks will be set on mathswatch, an internet based resource, where there are video clips to support the completion of the homework

ADD LINK

Additional Resources

https://www.mathsgenie.co.uk/gcse.html

Maths genie is a website where there are topic based questions with solutions and video clips to support understanding. It is free and split by grade to allow appropriate material to be used depending on ability.

https://vle.mathswatch.co.uk/vle

As stated previously mathswatch is a subscription website that we have signed up to that also allows students to further their understanding of topics by watching video clips and undertaking interactive examples.

Key Words

Foundation Higher