 # 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 7 (year 7)

 Term Topics and Key Concepts Autumn 1 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 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 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 Counting and comparing order positive and negative integers, decimals and fractions use the symbols =, ≠, <, >, ≤, ≥   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 Spring 1 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 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 Spring 2 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 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 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) 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 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 Find the mode of set of data Find the median of a set of data including when there are an even number of numbers in the data set Calculate the mean from a frequency table Find the mode from a frequency table Find the median from a frequency table Calculate and understand the range as a measure of spread (or consistency) Analyse and compare sets of data, appreciating the limitations of different statistics (mean, median, mode, range)

Stage 8 (top year 7 and year 8)

 Term Topics and Key Concepts Autumn 1 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 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 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 Autumn 2 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 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 Spring 1 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) 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 Spring 2 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) 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 2020

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 2019-2020

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 2019-2020

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 Statistics and sampling The averages Perimeter and area Graphs and real life graphs Quadratic, cubic and other graphs Perimeter, area and circles Probability Multiplication reasoning Similarity and congruence in 2D and 3D trigonometry Graphs of trigonometric functions Autumn 2 3D forms and volume Real life graphs Straight line graphs 3D forms and volumes Accuracy and bounds Transformations Constructions, loci and bearings Similarity and congruence in 2D and 3D Collecting data Cumulative frequency, box plots and histograms Spring 1 Transformations Ratio proportion Solving quadratic and simultaneous equations Inequalities Probability Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics Circle theorems Circle geometry Spring 2 Pythagoras’ theorem and trigonometry Probability Multiplicative reasoning Similarity and congruence Changing the subject of the formula Vectors and geometric proof Summer 1 Multiplicative reasoning Plans and elevations Constructions, loci and bearings Graphs of trigonometric functions Further trigonometry Reciprocal and exponential graphs; Gradient and area under graphs Summer 2 Quadratic equations: expanding and factorising Collecting data Direct and inverse proportion

GCSE Statistics

Students learn the EDEXCEL Higher tier scheme of work .

Year 10

 Term Unit(s) of Work Summary Autumn 1 Data Population and sampling Collecting discrete data Students learn the key definitions of statistical words, how to sample data. Autumn 2 Planning and collecting data Qualitative and discrete data Students will learn how to collect continuous, qualitative and discrete data. Spring 1 Continuous data Tabulation Measures of central tendency – mode, median and mean Students will convert raw data to summary statistics, design, construct and present summary tables. Spring 2 Measures of dispersion Box plots, skewness, calculating and representing outliers Students will learn how to calculate – range, quartiles, interquartile range, interpercentile range, inter-decile range, standard deviation and boxplots. Summer 1 Scatter graphs Time series Introduction to probability Students will learn in detail the different aspects of a scatter graph and time series. Know how to interpret them in real life context and relate information to exam questions. Summer 2 Complete a mock controlled assessment Students will learn how to complete a controlled assessment , learning about how to write statistical information.

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

www.mathswatch.co.uk

www.mathsgenie.co.uk

 Foundation Units of Work Higher Units of Work Accelerated Higher Units of Work Quadratic graphs Circles, cylinders, cones and spheres Fractions and reciprocals Similarity and congruence Vectors Rearranging formulae Cumulative frequency, box plots and histograms Graphs of 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

GCSE Statistics

Students learn the EDEXCEL Higher tier scheme of work .

Year 11

 Term Unit(s) of Work Summary Autumn 1 Calculating moving averages, seasonal and cyclic trends Students will learn how to display data on a time series graph and use seasonal variation, moving averages and make predictions. Autumn 2 Simple probability and theoretical probability Students will learn how to use probability rules to support them in investigations  and relating the information to exam questions. Spring 1 Interpreting index numbers in context and simple calculations Binomial distribution Students will learn how index and weighted index numbers are using in contexts. Also interpreting data related to rates of change over time. Spring 2 Normal distribution and standardised scores Quality assurance Students will learn how to compare different data sets using appropriate calculated or given measure of spread.  Know the characteristics of the normal distribution and standardised score. Summer 1 Revision for exam