# Mathematics Curriculum Map

AUT 1AUT 2SPR 1SPR 2SUM 1SUM 2YEAR 7Number is at the heart of our Year 7 curriculum as this enables students to be successful in all other strands of Mathematics at KS4 and KS5. In Year 7 the curriculum is strongly linked to the KS2 curriculum to enable students to build on their prior learning and connect their prior knowledge to new concepts. Calculator use is discouraged throughout Year 7 to encourage further fluency with the four basic operations of addition, subtraction, multiplication and division. As there is considerable overlap of content from Key Stage 2 there are no amendments to the Year 7 Curriculum for 2020-21 but students may need to spend longer reviewing Key Stage 2 concepts than in previous years. Due to the additional teaching time in Summer 2 probability is now introduced from the last half term of Year 7. ADDITION & SUBRACTIONAdd and subtract negative numbersUse positive and negative numbers in contextSimplify expressions by collecting like termsFind the perimeter of shapesFind equivalent fractionsConvert between mixed numbers and improper fractionsAddition and Subtraction of fractionsMULTIPLICATION & DIVISIONCompare multiplication and division methodsMultiply and Divide Negative NumbersMultiplication and Division of FractionsFind the area of a rectangle, triangle, parallelogram and trapeziumOrder of operations Use divisibility rulesANGLESDraw and measure anglesFind angles on a straight line, around a point, vertically opposite, in triangles and quadrilateralsAngles in parallel linesBearingsCOORDINATE GEOMETRYPlot and read Cartesian coordinatesUnderstand the equations of vertical and horizontal linesFind simple rules connecting x and y coordinatesReflect, rotate, enlarge and translate shapes on a Cartesian gridROUNDING & ESTIMATIONInvestigate place valueSolve problems involving large numbers.Solve problems that require assumptions to be madeRounding to decimal placesRounding to significant figuresEstimationLimits of AccuracyApplying Limits of Accuracy to problemsCommon AssessmentSTATISTICS & PROBABILITY Solve problems using averagesRead & interpret pie chartsCompare frequency graphs and pie chartsExpressing probability in numbers Probability of single events YEAR 8In Year 8 students build on their knowledge and skills gained from Year 7 and KS2 through learning about how to use bar models to understand proportional relationships. Many more algebraic concepts are introduced to enable links to be established between geometry and algebraic manipulation. Calculator use is encouraged in Year 8 alongside regular opportunities for students to practise their mental Maths when appropriate. Students starting Year 8 in September 2020 may not have a deep and connected understanding of some significant concepts from the Spring and Summer Year 7 curriculum. Relevant concepts required for success in Year 8 are reintroduced at appropriate times throughout the year from the Year 7 curriculum. As in Year 7 additional probability concepts have been added to Summer 2 that follows on from Year 7 due to the additional curriculum time. PROPORTIONAL REASONINGSolve problems involving ratioFind percentages of amountsFind percentage increase and decreaseDevelop understanding of ratio tablesUse ratio tables to solve proportional word problemsEXPRESSIONS, EQUATIONS & INEQUALITIESIdentify prime numbersTo find the HCFPrime factorisation Using prime factorisation to calculate HCF and LCM Use basic index rulesUse algebraic conventionsMultiply single bracketsFactorise single bracketsForm equations and inequalitiesUse different representations for equationsSolve linear equationsSolve word problems that lead to linear equationsRatio and Algebra problems Solve linear inequalitiesCommon Assessment 12D GEOMETRYRounding to decimal places and significant figures (From Year 7 Summer 1) Find the area of compound shapesSolve word problems involving areasUnderstand the relationship between the circumference and radius of the circleFind the circumference of a circle given a radius or diameterFind the radius of diameter of a circle given the circumferenceFind the length of arcsFind the area of a circle given a radius or diameterFind the radius or diameter of a circle given the areaFind the area and perimeter of compound shapes involving circles.SEQUENCESFind patterns in spatial sequencesFind different ways of describing spatial sequencesFind the nth term of linear sequencesAll about Fibonacci3D GEOMETRYUse isometric paper to draw 3D shapesDraw plans and elevations of 3D shapesFind the volume of cuboidsFind the volume of shapes made from cuboidsUse nets to find the surface Area of cuboidsIdentifying Pyramids and prismsFind the volume of prismsFind the volume of pyramids and cones Find the volumes of spheres and compound shapes Common Assessment 2STATISTICS & PROBABILITYPlot Scatter diagramsInterpret scatter diagramsUnderstand correlation and causationExpressing probability in numbers (From Year 7 Summer 2) Probability of single events (From Year 7 Summer 2) Understanding Mutually Exclusive Events Relative Frequency Using Sample Space Diagrams Independent Events Drawing and using Tree Diagrams YEAR 9In Year 9 students are introduced to additional algebraic manipulation to enable students to solve coordinate geometry and further 2D/3D geometric problems. Students starting Year 9 in September 2020 may not have a deep and connected understanding of some Year 8 concepts that are required for the Year 9 curriculum. When appropriate and necessary these concepts have been added to the Year 9 curriculum at relevant times. Some concepts from Year 8 are connected to learning in Year 10 and these concepts will be amended within the curriculum plan for the academic year 2021-22. ALGEBRAIC MANIPULATION Multiply out two or more bracketsFactorise quadratic expressionsCancel algebraic fractionsMultiply and divide algebraic fractionsAdd and subtract algebraic fractionsCommon Assessment 1 FURTHER COORDINATE GEOMETRYUse multiple representations of straight linesUnderstanding and using y = mx + cUnderstand the link between parallel and perpendicular linesANGLES, CONSTRUCTION & CONGRUENCE Know and use angle rules for parallel linesKnow and use angles in polygonsUnderstand when shapes tessellateConstruct trianglesIdentify when triangles are congruentConstruct bisectors and angles using compasses and rulersQUADRATIC EXPRESSIONS, EQUATIONS & GRAPHS Drawing Quadratic GraphsFinding roots of quadratic equations by factorisingForm and Solve Quadratic Equation by factorising by (a =1)Form and Solve Quadratic Equation by factorising (a>1)Complete the SquareUsing the Quadratic FormulaPYTHAGORAS, SURDS & SURFACE AREAFinding the hypotenuseFinding a shorted sidePythagoras ProblemsIntroducing SurdsSimplifying SurdsManipulating SurdsRationalising Surds 3D PythagorasSurface Area of PyramidsArea and Circumference of Circles Surface Area of Cuboids (from Year 8 Summer 1)Area and Circumference of Circles (From Year 8 Spring 1)Surface Area of Cylinders Surface Area of Cones Common Assessment 2PROBABILITY & VENN DIAGRAMS Sample Space Diagrams (from Year 8 Summer 2)Drawing Tree Diagrams (from Year 8 Summer 2)Using Tree Diagrams without replacement (from Year 8 Summer 2)Frequency TreesVenn Diagram NotationFinding probabilities from a Venn DiagramsYEAR 10During Year 10 students build on prior learning from subsequent years to learn about Trigonometry and its applications. Additional algebraic techniques are introduced to provide students with more tools for solving complex problems. Statistical representations are explored with opportunities for students to analyse data in a variety of ways. The foundation/higher pathways are to be introduced from the start of Year 10 this academic year to enable more time for lower attaining students to close the gaps in their knowledge. In addition to this some concepts will be moved to Year 11 Autumn 1 for higher students in 2021-2022 to enable more time to deepen and connect learning of key concepts from lockdown. Please note that Science Skills is now Spring 1 and Sequences 7 Graphs is Summer 1, this is to improve the Further Maths scheme of learning, TRIGONOMETRY, SURDS & PYTHAGORASUse trigonometric ratios to find missing lengths and angle sin triangles Finding the hypotenuse (From Year 9 Summer 1)*Finding a shorted side *Pythagoras Problems *Introducing Surds *Simplifying Surds*Manipulating Surds*Expanding brackets with surds *Find exact values for sin theta, cos theta and tan theta for key angleSolving area problems using Pythagoras and TrigonometryHIGHER ONLYRationalising Surds (From Year 9 Summer 1) Use the Sine and Cosine rules to find missing lengths and angles. Find the area of triangles using trigonometry CIRCLES & EQUATIONSSolving and forming simultaneous equations by eliminationCalculate arc lengths, angles and areas of sectorsDrawing Quadratic GraphsFinding roots of quadratic equations by factorisingForm and Solve Quadratic Equation by factorising. HIGHER ONLYQuadratic Equation by factorising (a>1)*Solving and forming simultaneous equations by substitutionEquation of a CircleFinding the intersection of lines and curvesSCIENCE SKILLSRelated CalculationsNegative Indices?Standard FormSolve problems involving measure such as speed, density and pressure.Changing UnitsSurface Area of Prisms, cylinders, cones and spheres.?(From Year 9 Summer 1)Volume of prisms, cylinders, cones, pyramids & spheres.? HIGHER ONLY Fractional Indices?Index Laws in ContextApproximate the gradient of a curve at a given point and the area under a graph.Interpret these values in real-life problems including kinematic graphs.Further volume and surface area problems.?Common Assessment 1SEQUENCES AND GRAPHSUsing iterative methods to generate sequencesnth term of linear sequenceSequences and Ratio?Combining Ratios?1:n?Unit Pricing Solve Direct and Inverse Proportion ProblemsRecognise different types of graphs HIGHER ONLY Quadratic SequencesIterative methodsQuadratic InequalitiesCompound FunctionsInverse Functions?Recognise and draw cubic and reciprocal functionsRecognise and draw graphs of exponential functionsRecognise and sketch translations and reflections of graphs. DELVING INTO DATAWorking with averages and rangeEstimating the Mean from a grouped Frequency Table?Constructing and Interpreting Pie ChartsUse tables and line graphs to represent time seriesHIGHER ONLY Construct and Interpret Cumulative Frequency Tables and GraphsConstruct and Interpret BoxPlotsConstruct and Interpret HistogramsFURTHER PROBABILITY & COMBINATORICSCombinationsUnderstanding independent events (From Year 9 Summer 2) Using Two way tables Using Tree Diagrams (From Year 9 Summer 2) HIGHER ONLY Conditional Probability from Tree Diagrams Conditional Probability from Venn Diagrams Algebraic Probability problems Common Assessment 2YEAR 11Students starting Year 11 in September 2020 may not have a deep and connected understanding of concepts from the Spring and Summer terms from the Year 10 curriculum. The more challenging concepts from the Year 10 curriculum are planned into the Year 11 Higher curriculum accordingly. Each of the four half terms are deliberately light to ensure we can respond to any gaps in knowledge and understanding uncovered through low stakes testing and homework past papers. Foundation tier students have covered the majority of GCSE content by this point, as QLA data from end of Year 10 mocks is missing this year students will be following the “Select 16” curriculum. The “Select 16” curriculum has been developed from the “Focussed 15” GCSE resit curriculum that was created by looking at examination data to identify topics that Grade 4 students have mastered but Grade 3 students have not! The 16 interconnected topics vary in size and difficulty and build over time to give a rounded, solid level of mathematical understanding. The 16 topics need to be covered this year but teacher judgement dictates the speed of delivery to suit their students; the division of topics here is only a guide. FOUNDATION Types of Number Rounding and Estimation Using Number Simplify and SolveHIGHER Surface Area and Volume (From Year 10 Spring 1) Transformations Similar Shapes Vector Geometry FOUNDATION Percentages Representing Data Averages and Spread Right-angled TrianglesHIGHER Function Notation (From old Year 10 Summer 1)*Compound Functions*Inverse Functions *Quadratic Sequences *Using Iteration to solve equations*FOUNDATION Measures Perimeter, Area and Volume Ratio & Proportion HIGHER Construct and Interpret Cumulative Frequency Tables and Graphs (From Year 10 old Spring 2)*Construct and Interpret BoxPlots*Construct and Interpret Histograms*FOUNDATION Probability Angle Properties Working with Graphs TransformationsHIGHERTo be determined from Mock QLA Level 2 FURTHER MATHS KS4 students are given the opportunity to study Further Mathematics GCSE to help the transition for further learning of Mathematics beyond Year 11. The curriculum has been planned to enable this to be taught alongside the Year 10 programme of study. For example, Autumn 1 concepts only require pre-requisite knowledge from the Year 9 concepts. Expanding brackets using Pascal’s TriangleWorking with the straight lines Using Trigonometric identities to simplify expressions and proof further identities Using Trigonometric identities to solve trigonometric equations in given intervals Using factor Theorem to factorise cubic expressionsSolving linear equations in three unknownsEquation of a Circle with centre (a, b) Geometric Proof Differentiation Equations of Tangents and NormalsIncreasing and Decreasing Functions Stationary Points and Classification Sketching and Interpreting Curves using calculusLimiting value of a sequence Drawing piece-wise functions Domain and Range of a Function Y12 CORE MATHS This course prepares students for the varied contexts they are likely to encounter in vocational and academic study and in future employment and life. FERMI ESTIMATIONEstimate answers to calculations in unfamiliar contextsPERCENTAGESPercentages of an amountInterpret percentages as a fraction or decimalCompare two quantities Understand and use percentages greater than 100%Reverse percentagesSolve problems involving percentage increase and decreaseSimple interestCompound interest and depreciationINCOME TAX AND NATIONAL INSURANCECalculate tax, NI, Student Loan and pension paymentsDATA ANALYSISPrimary, secondary, qualitative and quantitative dataREPRESENTING DATACumulative Frequency and box plotsStem and leaf diagrams (including back to back)SPREADSHEETSUse of simple formulaeVOLUME AND SURFACE AREASurface area and volume of cones, spheres, pyramids and compound shapesSolve problems involving similar shapesAERPerform AER calculationsSolve problems involving savings and investments and AER calculationsEQUATION OF A STRAIGHT LINEGradient of a line connecting 2 pointsUnderstand and use y=mx+cREPRESENTING DATACalculate and interpret the mean, median and mode of a data setCalculate and interpret quartiles, percentiles, range, interquartile range and standard deviation of a data setAPRPerform APR calculationsSolve problems involving debt and APR calculationsPayday LoansOPTIONAL CONTENTFINANCIAL PROBLEMSUnderstand the effect of inflationUse iterative formulaeExchange ratesUnderstand how to budgetOPTIONAL CONTENTCRITICAL ANALYSISCritically analyse data used in the mediaLIMITS OF ACCURACYApply and interpret limits of accuracyAppreciate errors due to roundingOPTIONAL CONTENTBESPOKE REVISION / MOCK EXAMS Y12 AS Mechanics routeAS Mathematics extends students experience of mathematical techniques significantly, developing advanced analysis of mathematical problems and construction of related arguments and methods of proof. The Mechanics route ensures that students have the pre-requisite knowledge and understanding of calculus to be successful when solving problems involving kinematics. STRAIGHT LINES AND CIRCLESDistance between two points and midpointsThe equation of a straight lineParallel and perpendicular linesThe equation of a circleSolving problems with lines and circlesPROOFMathematical arguments and notationProof by deduction, exhaustion and counter-exampleBINOMIAL EXPANSIONUnderstanding the Binomial TheoremSolving problems involving binomial coefficientsApplications of the Binomial TheoremDIFFERENTIATIONSketching derivativesDifferentiation from first principalsRules of differentiationInterpreting derivatives and second derivativesSolving problems involving tangents, normal and stationary pointsOptimisationINTEGRATIONRules for integrationFinding the equation of a curveDefinite integralsCalculate the area between a curve and a lineVECTORSDescribe vectors using magnitude and directionAddition and subtraction of vectorsProblems involving equal and parallel vectorsUnderstand position and displacement vectorsUse vectors to solve geometrical problemsKINEMATICS IN ONE DIMENSIONDisplacement, velocity and accelerationCalculus and kinematicsDisplacement-time graphsVelocity-time graphsProblems involving kinematicsFORCES AND NEWTONS LAWSDeriving the constant acceleration formulaSolving problems involving the constant acceleration formula and vertical motionNewton’s Laws of motionProblems involving gravity and resultant forcesTypes of forces, gravity and weightForces in equilibriumFORCES AND NEWTONS LAWSNewton’s third lawNormal reaction forceSolving complex problems in involving equilibriumConnected particlesProblems involving pulleysBESPOKE REVISION / MOCK EXAMSSEQUENCES AND SERIESTerm-to-term and position-to-term rulesSigma notationArithmetic sequences and seriesGeometric sequences and seriesInfinite geometric seriesMixed arithmetic and geometric problemsStatistics routeALGEBRAIC MANIPULATIONLaws of indicesSurdsQUADRATIC EQUATIONSSolving quadratic equationsGraphs of quadratic equationsCompleting the squareQuadratic inequalitiesThe discriminantDisguised quadraticsPOLYNOMIALSPolynomial divisionThe factor theoremSketching polynomial functionsGRAPHS, LINEAR AND QUADRATIC INEQUALITIESIntersections of graphsTransforming graphsReciprocal GraphsSketching inequalitiesTRIGONOMETRYGraphs of sine, cosine and tangent functionsTrigonometric identitiesSolving trigonometric equations in degreesTransformations of trigonometric graphsPROBABILITY AND STATISTICAL DISTRIBUTIONSMutually exclusive and independent probabilitiesProbability distributionsThe binomial distributionSTATISTICAL SAMPLING AND HYPOTHESIS TESTINGMethods of samplingHypothesis testing for the binomial distributionUnderstand critical regions for hypothesis testing. LOGARITHMSUnderstand the relationship between logarithms and indicesUnderstand the laws of logarithmsSolve exponential equations including disguised quadraticsEXPONENTIALSGraphs of exponential and logarithmic functionsSolve problems involving exponential functionsApproximate an exponential model as a straight lineDATA PRESENTATION AND REPRESENTATIONDraw and interpret statistical diagrams including histograms, cumulative frequency diagrams and box and whisker plotsStandard deviationCalculate and interpret the mean, standard deviation and variance from frequency tables. Interpret correlation coefficients and regression linesCalculate and determine outliersBESPOKE REVISION / MOCK EXAMSFUNCTIONSMappings and functionsDomain and rangeComposite functionsInverse functionsFURTHER TRANSFORMATIONS OF GRAPHSCombined graph transformationsThe modulus functionSolving modulus equations and inequalitiesY13 A2Mechanics route RADIAN MEASUREUnderstanding radians as an angle measureInverse trigonometric functionsSolving trigonometric equations in radiansModelling with trigonometric functionsArc length and sector areaSmall angle approximationsPROOFProof by contradictionCriticising proofBINOMIAL THEROEMBinomial theorem for fractional and negative powersExpansion of compound expressionsFURTHER DIFFERENTIATIONThe chain ruleThe product ruleThe quotient ruleImplicit differentiationDifferentiation of inverse functionsFURTHER APPLICATIONS OF CALCULUSConcave and convex curvesPoints of inflectionParametric equationsDifferentiating parametric equationsIntegrating parametric equationsConnected rates of changeFinding complex areas e.g. between 2 curves, between a curve and the y-axis. DIFFERNETIAL EQUATIONSSolving differential equations with 1 or 2 variablesModelling with differential equationsAPPLICATIONS OF VECTORSDescribing motion in two dimensionsConstant acceleration equationsCalculus with vectorsVectors in three dimensionsSolving geometrical problemsPROJECTILESModelling projectile motionThe trajectory of a projectileFORCES IN CONTEXTResolving forcesCoefficient of frictionMotion on a slopeMOMENTSThe turning effect of a forceEquilibriumBESPOKE REVISION / MOCK EXAMSStatistics RoutePARTIAL FRACTIONSSolving problems involving the factor theoremSimplifying rational functionsPartial fractions with distinct and repeated factorsTRIGNOMETRYCompound angle identitiesDouble angle identitiesFunctions in the form a sin x + b cos xReciprocal trigonometric functionsCALCULUS OF EXPONENTIAL AND TRIGONOMETRIC FUNCTIONSDifferentiationIntegrationFURTHER INTEGRATIONIntegration of secx, cosec x and cotxIntegration by substitutionIntegration by partsUsing trigonometric identities in integrationIntegration rational functionsNUMERICAL METHODSLocating roots of a functionThe Newton-Raphson method and its limitationsFixed-point iteration and its limitationsThe trapezium ruleFURTHER PROBABILITYSet notationVenn diagramsTwo-way tablesTree diagramsTHE NORMAL DISTRIBUTIONThe normal distributionThe inverse normal distributionFinding unknown μ or σModelling with the normal distributionFURTHER HYPOTHESIS TESTINGCalculating and interpreting probabilities using the normal distribution for a sampleHypothesis testing for the normal distributionHypothesis testing for correlation coefficientsBESPOKE REVISION / MOCK EXAMS ................

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