Alderman Peel

High School

Wells-Next-The-Sea   Norfolk

Mathematics

Faculty Staff and roles

Mr W Boyce: Director of Learning

Mrs H Barker: Teacher of Mathematics

Mr D Bridge: Teacher of Mathematics

Mr M Drews: Teacher of Mathematics

Mrs T Lear: Teaching Assistant

 

Overview

 

The creators of the hit US crime drama Numb3rs encapsulated it when they said:

« We all use maths every day; to predict weather, to tell time, to handle money. Maths is more than formulas or equations; it's logic, it's rationality, it's using your mind to solve the biggest mysteries we know. »

Whilst pupils here may not quite be working on solving the biggest maths mysteries we know, we very much hope that the maths they encounter in class will prove to be both enjoyable and useful.

When Ofsted visited us at the end of 2012 they noted that students were achieving particularly well in mathematics. They stated that mathematics is well taught and cited the improvement and achievement of SEND students who make considerable gains in maths.

Since 2012 things have continued to improve. In 2013 the maths department achieved its best ever GCSE results with 68% of students gaining at least a grade C in maths. In 2014 the figure rose again to 70% and in 2015 we broke the record again with 74% of students achieved at least a grade C in maths. And this year’s results look to be ever better! This is a trend which already sees our young people achieving results which are among the best in Norfolk.

We also pride ourselves on having a successful record in ensuring that our students make at least 3 levels progress from KS2 – with significant numbers making 4 levels progress in their time here.

We are very proud of how well our students do. However, our target is to be the best performing comprehensive High school in Norfolk.

 

Every Child Matters 

 

Every child really does matter in the mathematics department at Alderman Peel. From Year 7, when we set the foundations for future academic success, we strive to ensure that each and every lesson is a worthwhile and enjoyable experience for all of the students in it.

We pride ourselves on knowing each and every one of the children we teach – and not just their names! By taking a real interest in pupils’ well-being we are also looking after their academic progress.

We track progress, informally and constantly - and each half-term students sit a short classroom-based test on the work they have covered, with results then communicated to parents termly.

We value good behaviour in lessons. Children learning maths in happy and well behaved classes have every chance of reaching their potential. Every child has the right to be educated in a friendly and well-ordered environment.

Happy children make for better learners. 

KS3

We have a scheme of work which uses the Essential Maths series of textbooks www.elmwoodpress.co.uk to provide pupils with a wide and comprehensive experience of the foundations of maths.

For those interested, the New National Curriculum KS3 programme of Study can be found here.

 

At GCSE:

We use Edexcel as our examination board. Students follow a two year course, building upon the skills and knowledge that they have learnt and developed at Key Stage 3, with testing taking place through three exams at the end of Year 11.

Students studying Higher tier can gain grades 5-9 and students taking the Foundation tier can gain grades 1-5.

Further details of the Edexcel Maths GCSE, including full course specifications and some past examination papers are available from the Edexcel website. www.edexcel.org.uk

 

Number 

Pupils will learn 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, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

    §    use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

    §    use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

    §    recognise and use relationships between operations including inverse operations

    §    use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

        interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive

or negative integer or zero

        work interchangeably with terminating decimals and their corresponding fractions 

        define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

    §    interpret fractions and percentages as operators

    §    use standard units of mass, length, time, money and other measures, including with decimal quantities

    §    round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

        use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b

    §    use a calculator and other technologies to calculate results accurately and then interpret them appropriately

    §    appreciate the infinite nature of the sets of integers, real and rational numbers.

 

Algebra 

Pupils will learn to:

    §    use and interpret algebraic notation, including:

        ab in place of a × b

        3y in place of y + y  + y and 3 × y

        a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b

         a  in place of a ˜ b

    §    coefficients written as fractions rather than as decimals

    §    brackets

    §    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

    §    model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

    §    use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

    §    work with coordinates in all four quadrants

    §    recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

    §    interpret mathematical relationships both algebraically and graphically

    §    reduce a given linear equation in two variables to the standard form y = mx + c; 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 and to find approximate solutions of simultaneous linear equations

    §    find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

    §    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 will learn 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; express the division of a quantity into two parts as a ratio

    §    understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

    §    relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

    §    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 measures 

Pupils will learn 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 (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

    §    describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

    §    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 [for example, equal lengths and angles] using appropriate language and technologies

    §    identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

    §    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, and use known results to obtain simple proofs

        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 will learn to:

    §    record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

    §    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 will learn to:

    §    describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

    §    construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

    §    describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.