Secondary: Key Stage 4 l.academy
MathematicsSecondary: Key Stage 468531255023350Curriculum plan 2020-2190000081324001. Curriculum PrinciplesAs mathematics teachers we want our pupils to reach fluency in what we are teaching them. In mathematics, fluency requires a deep understanding of concepts and the ability to apply them flexibly and with automaticity. The mathematics curriculum uses multiple representations to help make connections across concepts to help build a deep conceptual understanding. By making consistent use of the same core representations we will scaffold pupils’ thinking to help them understand abstract mathematical concepts. The curriculum will also include intelligent practice that is designed to help pupils develop automaticity in their mathematics.We also aim for our pupils to be able to use the precise language of mathematics, as distinct from everyday language. The curriculum will do this by explicitly teaching mathematical vocabulary and introducing core sentence structures with which to express, connect, reason with and apply mathematical structures and ideas. Finally, we also aim for our pupils to be able to think mathematically. The tasks and activities used in the curriculum teach pupils the components of mathematical thinking: to sort and classify, compare and contrast, specialise and generalise, to make conjectures and to prove them. Below are the set of principles we have used to build this curriculum, with these ambitions for our pupils in mind.Coherence and flexibilityWe strive to support schools by offering a maths curriculum that can fit alongside a range of existing structures. However, complete flexibility over unit ordering is impossible due to the cumulative nature of mathematics and the importance of prior knowledge. We have grouped lessons into units: coherent sequences of 5 or more lessons. Although each lesson can be accessed individually, explicit connections are made to earlier lessons and later lessons in the same unit. This is because the connections between mathematical concepts are so vital to deepening understanding. Knowledge organisationThe units in the maths curriculum have been organised by strand. We have also created a set of sequences for pupils targeting different grades at GCSE and who are at different stages in KS4, organised based on the topics that are most useful for the GCSE course.Inclusive and ambitiousWe know the difference it makes when children believe they “can do” maths. We are guided by the principles of the National Curriculum to ensure that every pupil, regardless of starting point, develops their fluency, reasoning and problem solving. Our activities are scaffolded so all children can succeed. Pupils are offered frequent opportunities to be and feel successful in their maths education.We develop conceptual understanding by always building new understanding on what pupils already know, by representing concepts in different ways, and by making connections between concepts. The mathematics curriculum makes consistent use of the same core representations across year groups to help pupils connect prior learning to new learning. These representations are selected to make key mathematical structures and ideas accessible to all pupils, no matter what their starting points. To support every child to communicate mathematically, pupils are introduced to core sentence structures with which to express, connect, reason with and apply?mathematical?structures and ideas.??Pupil engagementYou learn maths by thinking about maths. Our lessons include mathematical tasks which have multiple solutions. Mathematical thinking is woven into the units using scaffolds and prompts such as ‘what is the same and what’s different?’, ‘is it sometimes, always or never true?’ and ‘which could be the odd one out?’. Throughout the curriculum, all pupils have opportunities to sort and classify, compare and contrast, specialise and generalise, to make conjectures and to prove them. Motivation through learningWe believe that mathematics is inherently interesting and that all children?are?entitled?to?a genuine experience of mathematics. The tasks and activities that?pupils?engage with?harness?innate ways of thinking?and develop the habits of mind that?are?drawn?upon when?being?mathematical. Problem solving?is at the heart of every lesson with opportunities to investigate, explore and reason.??2. Subject structure overviewThe Mathematics Key Stage 4 structure is organised into the 4 strands of Number(N), Algebra(A), Shape and Space(S) and Handling Data/Probability(D). These are organised into units of 4 lessons. These units will develop the pupils’ previous learning at Key Stage 3. The units have been designed to allow for flexibility of order, however in some cases there are suggested prior units. Units that are in bold are for Higher Tier pupils only.StrandUnit #Unit NamePrior UnitN1Directed Numbers N24 Rules of Number N3Rules of Indices (numbers) N4Standard Form (Writing and converting) N5Standard Form 4 operations N6Factors Multiples and Primes N7Venn Diagrams N8HCF and LCM N9Types of Numbers N10Fraction Equivalents N11Fractions 1 (adding and subtracting) N12Fractions 2 (multiplying and dividing) N13Fraction Change N14Percentages N15Percentage Increase and Decrease N16Repeated Percentage Increase N17FDP Equivalents N18Decimals N19Rounding and Estimating N20Ratios (all these include 1 or 2 examples of using x and y) N21Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy) N22Negative and Fractional Indices N23Surds (Simplifying) N24Adding surdsN23N25Multiplying SurdsN24N26Dividing and Rationalising surdsN25N27Upper and Lower Bounds N28Recurring decimals StrandUnit #Unit NamePrior UnitA1Collecting Terms and Simple Expansion A2Expand and Simplify Brackets A3Rules of Indices A4Solving Equations 1 (One step, Two Step and Brackets) A5Solving Equations 2 (Simple algebraic fractions) A6Substitution and Rearranging formulae A7Factorising (single bracket) A8Factorise and Solve a Quadratic (a=1) A9Solve Inequalities and Represent on Number Line A10Linear Sequences A11Simple Graphs (Linear from a table) A12Straight Line Graphs (y=mx+C) A13Quadratic Graphs (a=1) A14Simultaneous Equations (Linear) A15Straight line graphs 2 (Parallel Lines) A16Travel Graphs A17Compound Measures A18Cubic and Reciprocal Graphs A19Algebraic Fractions A20Factorise and solve quadratics(a > 1) A21Further Quadratic equations A22One linear and one quadratic simultaneous equations A23Quadratic sequences and Inequalities A24Further Algebra (Change the subject/Binomial expansion) A25Higher Straight lines (Perpendicular Lines) A26Quadratic graphs 2 (a>1) A27Other Graphs (Trig, Exponential and Transformations) A28Further graphs (Gradients/Area of curves) A29Circle Graphs A30Graphs of inequalities A31Direct and Inverse Proportion A32Further Algebraic Fractions S19A33Algebraic Proof A34Solve equations numerically (Iteration) A35Functions StrandUnit #Unit NamePrior UnitS1Reflection S2Rotation and Enlargement S3Pythagoras Theorem 1 S4Pythagoras Theorem 2S3S5Area and Perimeter S6Circles S7CylindersS6S8Volume and Surface Area 1 (Prisms) S9Angle Facts S10Parallel Lines and Polygons 1 S11Polygons 2 (Interior and Exterior)S10S12Translate and Vectors 1 S13Vectors 2S12S14Bearings S15Views and Maps S16Constructions and Loci S17Loci S18Similarity S19Parts of Circles 1 (Semi and quarter circles)S19S20Parts of Circles 2 (Arcs and Sectors) S21Volume and Surface Area 2 S22Trigonometry 1 S23Trigonometry 2S23S24Trigonometry 3S24S25Enlargement and Similarity S26Volume and Surface Area Higher 3 S27Circle Theorems 1 S28Circle Theorems 2S27S29Advanced Trigonometry 1 S30Advanced Trigonometry 2S29S31Advanced Trigonometry 3S30S32Vectors Higher 1 S33Vectors Higher 2 and Congruent TrianglesS32StrandUnit #Unit NamePrior UnitD1Frequency charts (Data Collection, Bar and Pictograms) D2Averages (From a list and tables, Stem and Leaf) D3Charts and Tables (Pie Chart and Two way tables) D4Scatter Diagrams and Frequency Trees D5Probability 1 ( Scale and equally likely events) D6Probability 2 (Sample space, Venn diagrams and experimental) D7Probability 3 (tree diagrams) D8Higher Probability (conditional and Further Set Notation) D9Higher Data 1 (CF and Box Plots) D10Histograms D11Data Collection Higher 3. Suggested sequenceYear 10 Pupils 2020-21Provided is a suggested sequence for pupils who may follow this course for two years to sit their GCSE exam in June 2022. There are three possible pathways available:i) Foundation for pupils aiming for a Grade 4ii) Core for pupils who will take the Higher Tier paper but are aiming for a grade 5 or 6 iii) Higher Tier for pupils aiming for a Grade 7+. If units are labelled in red then they are a combination of the units given in section 2.There are 39 weeks of content provided here for pupils to study in year 10: Week TopicFoundation (Aiming for 4)Higher (Aiming for 7/8/9)Core (Aiming for 5/6)1Number 1Directed numbersSimplifying surdsDirected numbers2Four RulesAdding surdsRules of Indices with numbers3Types of NumberMultiplying surdsStandard form 4Rules of indices with numbersDividing and rationalising surdsStandard form operations5Algebra 1Collecting like terms, simplifyingSolving equations 2Collecting, indices, expand and simplify, solving equations 16Expand and simplifyAlgebraic fractionsSolving equations 27IndicesFactorise and solve quadratic a = 1Adding and Subtracting fractions8Solving equations 1Factorise and solve quadratic a > 1Algebraic fractions9Solving equations 2Substitution and rearrange formulaeFactorise and solve quadratic a = 110Substitution and rearrange formulaeFurther algebraSubstitution and rearrange formulae11Shape 1ReflectionsSimilarityRotation and enlargement12Rotation and enlargementTrigonometry 1Similarity13Pythagoras 1Trigonometry 2Pythagoras 114Pythagoras 2Trigonometry 3Pythagoras 215Number 2Factors multiples and primesTypes of Number and Rules of IndicesFactors multiples and primes16Venn diagramsFractional and negative indicesVenn diagrams17HCF and LCMRecurring decimalsHCF and LCM18Rounding and EstimatingUpper and lower boundsRounding and estimating19Algebra 2Factorise 1Straight line graphsSimple graphs20Factorise 2Straight line graphs 2Straight line graphs21InequalitiesHigher straight linesStraight line graphs 222Linear sequencesLinear simultaneous equationsLinear simultaneous equations23Number & StatisticsFraction equivalentsScatter diagrams and frequency trees and AveragesScatter diagrams and frequency trees24Fractions 1Higher data 1Averages25Fractions 2Probability 2Higher data 126Fraction changeHigher ProbabilityProbability 227Algebra 3Simple graphsFurther quadratic equationsQuadratic graphs28Straight line graphsQuadratic graphsQuadratic graphs 229Quadratic graphs 1Quadratic graphs 2Ratio 1 and 230PercentagesQuadratic sequencesPercentages, increase and decrease31Shape and NumberPercentage Increase and decreaseOne linear and one quadratic simultaneous equationsRepeated percentage change32Repeated percentage changeParts of a circle 1/2Fractions 1, 2 and Fractional Change33FDP EquivalentsVolume and Surface Area 1Parts of circle 134Decimals Volume 2Parts of circle 235Rounding and EstimatingSurface Area 2Cylinders36RatioVolume and Surface Area 2Area and perimeter37Area and perimeterAdvanced Trig 1Trigonometry 138CirclesAdvanced Trig 2Trigonometry 239Volume and surface area 1Advanced Trig 3Trigonometry 3There are then 24 weeks of content provided for pupils in year 11: Week TopicFoundation (Aiming for 4)Higher (Aiming for 7/8/9)Core (Aiming for 5/6)1ShapeAngle factsCircle Theorems 1Revise - angles, polygons, bearings2Parallel Lines and Polygons 1Circle Theorems 2Circle Theorems 13Polygons 2Constructions and LociCircle Theorems 24Number & AlgebraStandard form - writing and convertingSolve equations numerically Simplifying surds5Standard form - four operationsDirect and inverse proportionAdding surds6Ratio 2FunctionsFunctions7Revise - Solving equationsFurther algebraic fractionsQuadratic sequences8Simultaneous equationsAlgebraic ProofRevise - simultaneous equations9Statistics and ProbabilityFrequency chartsCircle graphsCharts and tables10AveragesProbability 3 (tree diagrams)Revise - data (mean table, CF charts)11Charts and tablesHigher Probability (conditional)Probability 312Scatter diagramsHistogramsHigher Probability (conditional)13Probability Data Collection HigherHistograms14GraphsProbability 2Revise - Linear and Quadratic GraphsStraight line graphs 215Probability 3Cubic and Reciprocal GraphsQuadratic graphs 216Straight line graphs 2Other graphsCubic and Reciprocal Graphs17Quadratic graphs 1Further graphsTravel graphs18Travel graphsGraphs of inequalitiesGraphs of inequalities19Compound measuresCompound measuresCompound measures20Shape and NumberTranslate and vectors 1Volume and Surface area 3Volume and Surface Area 1 & 221Vectors 2Translate and vectorsTranslate and vectors 122BearingsVectors 2Vectors 223Views and mapsHigher vectors 1Constructions24Constructions Higher vectors 2Loci25LociEnlargement and similarityRevisionYear 11 Pupils 2020-21Provided is a suggested sequence for pupils who can follow this course for one year. This is an “express” sequence to consider that there has been disrupted learning in 2019-20. There are 3 possible pathways available:i) Foundation for pupils aiming for a Grade 4ii) Core for pupils who will take the Higher Tier paper but are aiming for a grade 5 or 6 iii)Higher Tier for pupils aiming for a Grade 7+. If units are labelled in red then they are a combination of the units given in section 2.Week TopicAiming for a 4Aiming for 5/6Aiming for 7/8/91Number 1Directed Numbers and 4 rules, Rounding and EstimatingTypes of Number, Roots and indicesFractional indices2Fractions 1 and 2Rounding and EstimatingUpper and lower bounds3Algebra 1Expand and Simplify, Factorise Linear, Solving Equations 1 and 2Solving Equations 1 and 2Algebraic Fractions4InequalitiesFactorise and solve a quadratic (a>1)5Factorise and solve a quadratic (a=1)Further quadratics equations6FDP Percentages and FPD EquivalencePercentage Increase/DecreaseRecurring decimals7Shape 1Angle Facts and Parallel LinesAngle Facts and Parallel LinesCircle theorems 18Polygons 1 and 2Polygons 1 and 2Circle theorems 29Graphs Simple Graphs and Straight Line Graphs 1Straight line graphs 1/2Quadratic Graphs, Cubic and reciprocal graphs, Circle Graphs10Quadratic Graphs and Travel GraphsQuadratic Graphs, Cubic and reciprocal graphsStraight line Graphs 2, Higher Straight lines11Ratio and proportionRatioRatio 1 and 2Compound Measures/ Direct and Inverse Proportion12Ratio 2Compound Measures/ Direct and Inverse ProportionFurther Graphs13Shape 2Area and Perimeter, CirclesParts of circle 1/2Parts of circle 1/214Volume and Surface Area 1 Volume and surface 2 and Views and MapsVolume and surface 2 and 315DataCharts and tables and Frequency ChartsScatter graphs and Frequency Trees and AveragesHigher Data Collection16Scatter graphs and Frequency Trees and AveragesHigher Data 1Histograms17Algebra 2Substitution and rearranging formulae and rules of indicesSubstitution and rearranging formulae and rules of indicesQuadratic Sequences and Further Algebra18Linear SequencesLinear and Quadratic sequencesAlgebraic Proof and Functions19Pythagoras and TrigonometryPythagoras 1Pythagoras 1 and 2Advanced Trigonometry 1,2 and 320Pythagoras 2Trigonometry 1 and 221Number 2Factors, Multiples and Primes/ Venn DiagramsRepeated Percentage ChangeSimplify Surds and Add Surds22Standard Form Convert/4 OperationsStandard Form - 4 operationsMultiply and Divide Surds23ProbabilityProbability 1 and 2Probability 2 and 3Higher Probability24TransformationsBearings/ReflectionRotation and EnlargementEnlargement and Similarity25Rotation and EnlargementSimilarityOther graphs (Transforming)26ConstructionsViews and Maps/ConstructionsConstructions and LociConstructions and Loci27Algebra 3Solving Equations 2Simultaneous EquationsSimultaneous Equations Linear/Quadratic28Simultaneous EquationsSimultaneous Equations Linear/QuadraticSolve equations numerically29VectorsTranslate and vectors 1Vectors 2Higher Vectors 1 and 2 ................
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