 # Blackfen School for Girls

Raising aspirations - releasing potential # Mathematics

KEY STAGE 3 - YEAR 7 AND 8

Year 7 and 8 are set by ability and follow an accelerated curriculum in Mathematics which enables them to take their end of Key stage 3 Teacher Assessment in the Summer Term of year 8. The Scheme of Work they follow is based on Kangaroo Maths (http://www.kangaroomaths.com), depending on their level students follow schemes at the following stages;

Stage 6 (support year 7)

 Term Topics and Key Concepts Autumn 1 Number and the number system use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions   Counting and comparing order positive and negative integers, decimals and fractions use the symbols =, ≠, <, >, ≤, ≥ Autumn 2 Calculating understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals) apply the four operations, including formal written methods, to integers and decimals use conventional notation for priority of operations, including brackets recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)   Visualizing and constructing use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries use the standard conventions for labelling and referring to the sides and angles of triangles draw diagrams from written description   Investigating properties of shapes identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language   Algebraic proficiency: tinkering understand and use the concepts and vocabulary of expressions, equations, formulae and terms 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, a/b in place of a ÷ b, brackets simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket where appropriate, interpret simple expressions as functions with inputs and outputs substitute numerical values into formulae and expressions use conventional notation for priority of operations, including brackets Spring 1 Exploring fractions, decimals and percentages express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 define percentage as ‘number of parts per hundred’ express one quantity as a percentage of another   Proportional reasoning use ratio notation, including reduction to simplest form divide a given quantity into two parts in a given part:part or part:whole ratio   Pattern sniffing generate terms of a sequence from a term-to-term rule   Measuring space use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.) use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts measure line segments and angles in geometric figures Spring 2 Investigating angles apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles   Calculating fractions, decimals, percentages apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively compare two quantities using percentages solve problems involving percentage change, including percentage increase/decrease Summer 1 Solving equations and inequalities recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) solve linear equations in one unknown algebraically Calculating space use standard units of measure and related concepts (length, area, volume/capacity) calculate perimeters of 2D shapes know and apply formulae to calculate area of triangles, parallelograms, trapezia calculate surface area of cuboids know and apply formulae to calculate volume of cuboids understand and use standard mathematical formulae   Checking, approximating and estimating round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures) estimate answers; check calculations using approximation and estimation, including answers obtained using technology recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) Summer 2 Mathematical movement work with coordinates in all four quadrants understand and use lines parallel to the axes, y = x and y = -x solve geometrical problems on coordinate axes identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation describe translations as 2D vectors   Presentation of data interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use   Measuring data interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean and mode) and spread (range)

Stage 7 (year 7)

 Term Topics and Key Concepts Autumn 1 Numbers and the number system use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions   Counting and comparing order positive and negative integers, decimals and fractions use the symbols =, ≠, <, >, ≤, ≥   Calculating understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals) apply the four operations, including formal written methods, to integers and decimals use conventional notation for priority of operations, including brackets recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) Autumn 2 Visualizing and constructing use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries use the standard conventions for labelling and referring to the sides and angles of triangles   Investigating properties of shapes identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language   Algebraic proficiency: tinkering understand and use the concepts and vocabulary of expressions, equations, formulae and terms 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, a/b in place of a ÷ b, brackets simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket where appropriate, interpret simple expressions as functions with inputs and outputs substitute numerical values into formulae and expressions use conventional notation for priority of operations, including brackets   Exploring fractions, decimals and percentages express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 define percentage as ‘number of parts per hundred’ express one quantity as a percentage of another Spring 1 Proportional reasoning use ratio notation, including reduction to simplest form divide a given quantity into two parts in a given part:part or part:whole ratio   Pattern sniffing generate terms of a sequence from a term-to-term rule     Measuring space use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.) use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts measure line segments and angles in geometric figures Spring 2 Investigating angles Measure accurately Convert between measures Solve problems involving measurement   Calculating fractions, decimals and percentages apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively compare two quantities using percentages solve problems involving percentage change, including percentage increase/decrease Summer 1 Solving equations and inequalities recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) solve linear equations in one unknown algebraically   Calculating space use standard units of measure and related concepts (length, area, volume/capacity) calculate perimeters of 2D shapes know and apply formulae to calculate area of triangles, parallelograms, trapezia calculate surface area of cuboids know and apply formulae to calculate volume of cuboids understand and use standard mathematical formulae   Checking, approximating and estimating round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures) estimate answers; check calculations using approximation and estimation, including answers obtained using technology recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)   Mathematical movement work with coordinates in all four quadrants understand and use lines parallel to the axes, y = x and y = -x solve geometrical problems on coordinate axes identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation describe translations as 2D vectors Summer 2 Presentation of data interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use

Stage 8 (top year 7 and year 8)

 Term Topics and Key Concepts Autumn 1 Numbers and the number system use the concepts and vocabulary of prime numbers, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures) interpret standard form A × 10n, where 1 ≤ A < 10 and n is an integer   Calculating apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative use conventional notation for priority of operations, including brackets, powers, roots and reciprocals   Visualising and constructing measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement interpret plans and elevations of 3D shapes use scale factors, scale diagrams and maps Autumn 2 Understanding risk I relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale record describe and analyse the frequency of outcomes of probability experiments using tables construct theoretical possibility spaces for single experiments with equally likely outcomes and use these to calculate theoretical probabilities apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one   Algebraic proficiency: tinkering use and interpret algebraic notation, including: a²b in place of a × a × b, coefficients written as fractions rather than as decimals understand and use the concepts and vocabulary of factors simplify and manipulate algebraic expressions by taking out common factors and simplifying expressions involving sums, products and powers, including the laws of indices substitute numerical values into scientific formulae rearrange formulae to change the subject   Exploring fractions, decimals and percentages work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8) Spring 1 Proportional reasoning express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations) identify and work with fractions in ratio problems understand and use proportion as equality of ratios express a multiplicative relationship between two quantities as a ratio or a fraction use compound units (such as speed, rates of pay, unit pricing) change freely between compound units (e.g. speed, rates of pay, prices) in numerical contexts relate ratios to fractions and to linear functions   Pattern sniffing generate terms of a sequence from either a term-to-term or a position-to-term rule deduce expressions to calculate the nth term of linear sequences   Investigating angles understand and use alternate and corresponding angles on parallel lines derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) Spring 2 Calculating fractions, decimals and percentages interpret fractions and percentages as operators work with percentages greater than 100% solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics calculate exactly with fractions   Solving equations and inequalities solve linear equations with the unknown on both sides of the equation find approximate solutions to linear equations using a graph Summer 1 Calculating space compare lengths, areas and volumes using ratio notation calculate perimeters of 2D shapes, including circles identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr² calculate areas of circles and composite shapes know and apply formulae to calculate volume of right prisms (including cylinders)   Algebraic proficiency: visualizing plot graphs of equations that correspond to straight-line graphs in the coordinate plane identify and interpret gradients and intercepts of linear functions graphically recognise, sketch and interpret graphs of linear functions and simple quadratic functions plot and interpret graphs and graphs of non-standard (piece-wise linear) functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance and speed Summer 2 Understanding Risk II apply systematic listing strategies record describe and analyse the frequency of outcomes of probability experiments using frequency trees enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams construct theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments   Presentation of data interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data use and interpret scatter graphs of bivariate data recognise correlation   Measuring data interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers) apply statistics to describe a population

Stage 9 (top year 8)

 Term Topics and Key Concepts Autumn 1 Calculating calculate with roots, and with integer indices calculate with standard form A × 10n, where 1 ≤ A < 10 and n is an integer use inequality notation to specify simple error intervals due to truncation or rounding apply and interpret limits of accuracy   Visualizing and constructing 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) use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line construct plans and elevations of 3D shapes Autumn 2 Algebraic proficiency: tinkering understand and use the concepts and vocabulary of identities know the difference between an equation and an identity simplify and manipulate algebraic expressions by expanding products of two binomials and factorising quadratic expressions of the form x² + bx + c argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments translate simple situations or procedures into algebraic expressions or formulae   Proportional reasoning solve problems involving direct and inverse proportion including graphical and algebraic representations apply the concepts of congruence and similarity, including the relationships between lengths in similar figures change freely between compound units (e.g. density, pressure) in numerical and algebraic contexts use compound units such as density and pressure   Pattern sniffing recognise and use Fibonacci type sequences, quadratic sequences Spring 1 Solving equations and inequalities understand and use the concepts and vocabulary of inequalities solve linear inequalities in one variable represent the solution set to an inequality on a number line   Calculating space identify and apply circle definitions and properties, including:  tangent, arc, sector and segment calculate arc lengths, angles and areas of sectors of circles calculate surface area of right prisms (including cylinders) calculate exactly with multiples of π know the formulae for: Pythagoras’ theorem, a² + b² = c², and apply it to find lengths in right-angled triangles in two dimensional figures Spring 2 Conjecturing use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs   Algebraic proficiency: visualising identify and interpret gradients and intercepts of linear functions algebraically use the form y = mx + c to identify parallel lines find the equation of the line through two given points, or through one point with a given gradient interpret the gradient of a straight line graph as a rate of change recognise, sketch and interpret graphs of quadratic functions recognise, sketch and interpret graphs of simple cubic functions and the reciprocal function  y = 1/x with x ≠ 0 plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration Summer 1 Solving equations and inequalities II solve, in simple cases, two linear simultaneous equations in two variables algebraically derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution find approximate solutions to simultaneous equations using a graph   Understanding risk calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions enumerate sets and combinations of sets systematically, using tree diagrams understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size Summer 2 Presentation of data interpret and construct tables, charts and diagrams, including tables and line graphs for time series data and know their appropriate use draw estimated lines of best fit; make predictions Understand that correlation does not indicate causation; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing

KEY STAGE 4 – YEARS 9 TO 11

In Year 9 all students start their GCSE Mathematics course. They will complete the course in Year 11 and take the final examination in June 2019.

Candidates for this qualification are entered for one of two tiers.

Higher Tier: graded 1 – 9

Foundation Tier: grade 1 - 5

Exam Board: Edexcel

Year 9 Scheme of Work 2018-2019

Year 9 students will do the following assessments during the year:

• Autumn 1 assessment (one paper)
• January Year 9 examinations (non-calculator and calculator papers)
• Easter assessment (one paper)
• End of Year examinations (non-calculator and calculator papers)

 Half Term Foundation Unit of Work Higher Unit of Work Accelerated Higher Unit of Work Autumn 1 Integers and Place Value Decimals Indices, powers and roots Calculations, checking and rounding Indices and roots Factors, multiples and primes Indices and standard form Calculations, checking and rounding Indices and roots Factors, multiples and primes Indices and standard form Algebra basics Equations Sequences Autumn 2 Factors, multiples and primes Algebra basics Expanding and factorising single brackets Substitution and expressions Algebra basics Equations Sequences Averages and range Algebra basics Equations Sequences Averages and range Representing and interpreting data Scatter graphs Fractions Percentages Ratio and proportion Polygons, angles and parallel lines Pythagoras’ theorem and trigonometry Spring 1 Tables Charts and graphs Fractions Representing and interpreting data Scatter graphs Fractions Graphs and real life graphs Linear graphs and coordinate geometry Quadratic, cubic and other  graphs Spring 2 Pie charts Scatter Graphs Fractions, decimals and percentages Percentages Fractions Percentages Ratio and proportion Perimeter, area and circles 3D forms and volume Accuracy and bounds Summer 1 Equations Inequalities Polygons, angles and parallel lines Pythagoras’ theorem and trigonometry Transformations Constructions, loci and bearings Summer 2 Sequences Properties of shape, parallel lines and angle facts Interior and exterior angles of polygons Graphs and real life graphs Linear graphs and coordinate geometry Quadratic, cubic and other  graphs Solving quadratic and simultaneous equations Inequalities Probability

Year 10 Scheme of Work 2018-2019

Year 10 students will do the following assessments during the year:

• Autumn 1 assessment (one paper)
• Autumn 2 assessment (one paper)
• Spring 1 assessment (one paper)
• Spring 2 assessment (one paper)
• Year 10 Summer PPE examinations (one non-calculator and two calculator papers)

 Half Term Foundation Units of Work Higher Units of Work Accelerated Higher Units of Work Autumn 1 Equations Inequalities Properties of shapes, parallel lines and angles Pythagoras’ theorem and trigonometry Graphs and real life graphs Pythagoras’ theorem and trigonometry Graphs of trigonometric functions Real life graphs Other graphs Autumn 2 Interior and exterior angles of polygons Perimeter and area 3D forms and volume Real life graphs Linear graphs and coordinate geometry Quadratic, cubic and other graphs Perimeter, area and circles 3D forms and volumes 3D forms and volume Accuracy and bounds Transformations Constructions, loci and bearings Spring 1 Straight line graphs Transformations Accuracy and bounds Transformations Constructions, loci and bearings Solving quadratic and simultaneous equations Inequalities Probability Multiplicative reasoning Spring 2 Pythagoras’ theorem and trigonometry Probability Multiplicative reasoning Solving quadratic and simultaneous equations Inequalities Probability Similarity and congruence Further trigonometry Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics Summer 1 Plans and elevations Constructions, loci and bearings Multiplicative reasoning Similarity and congruence Circle theorems Circle geometry Changing the subject of the formula Summer 2 Quadratic equations: expanding and factorising Quadratic graphs Graphs of trigonometric functions Further trigonometry Vectors and geometric proof

Year 11
Students in Year 11 are focused on the completion of their GCSE studies we offer Linear Foundation and Higher (Edexcel).

In Year 11, students will complete the GCSE schemes of work in the Autumn term and then the will work through a programme of revision and prepare for their exams by completing past papers. Students are also expected to design their own independent revision programmes to assist them in achieving their full potential. They will sit their final examination in June.

The following websites are useful to aid students to achieve their potential;

www.edexcel.com

www.bbc.co.uk/bitesize/

www.mymaths.co.uk

www.corbettmaths.com

 Foundation Units of Work Higher Units of Work Accelerated Higher Units of Work Constructions, loci and bearings Quadratic equations Quadratic graphs Circles, cylinders, cones and spheres Fractions and reciprocals Similarity and congruence Vectors Rearranging formulae Graphs of trigonometric  functions Further trigonometry Quadratics Circle theorems Circle geometry Rearranging more complex formulae Vectors and geometric proof Reciprocal and exponential graphs Circle geometry Rearranging more complex formulae Vectors and geometric proof Reciprocal and exponential graphs