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Foundation 2 year Scheme of WorkYearTermTopicF/PGuide HoursYEAR 10AUT 1ASSESSMENT 1 (Baseline) HYPERLINK \l "_Integers" Integers7Decimals4Coordinates4Angles, lines and triangles6AUT 2Reading scales and converting units5Collecting data4Charts and graphs5Symmetry, Similarity and Congruence4ASSESSMENT 2 SPR 1Types of Number8Introduction to algebra4Constructions 5SPR 2ASSESSMENT 3 YEAR 10 MOCK ExaminationPatterns and Sequences5Properties of quadrilaterals and parallel lines5Fractions7SUM 1Pie charts3Fractions, Decimals and Percentages4Applications of Percentages5Algebra using powers and brackets4SUM 2Ratio and Proportion6Linear equations and inequalities6Perimeter and Area7ASSESSMENT 4 EOY YEAR 10 ExaminationYEAR 11AUT 1ASSESSMENT 1 YEAR 11 (Baseline)3-D shapes4Real-life graphs5Straight line graphs4Compound Measures5AUT 2ASSESSMENT 2 Year 11 MOCK ExaminationTimetables and Distance-time graphs5Volume5Probability9Formulae7SPR 1ASSESSMENT 3 Mid YearAngles properties of Polygons5Transformations6Scatter graphs and Correlation5Averages and range7SPR 2Quadratic Graphs3Trial and Improvement3Circles5Pythagoras’ Theorem5ASSESSMENT 4 Pre-Exam SUM 1/2EXTERNAL GCSE MATHS EXAMINATIONModule 1Time: 6 – 8 hoursGCSE Tier:FoundationIntegersPRIOR KNOWLEDGE:The ability to order numbersAn appreciation of place valueExperience of the four operations using whole numbersKnowledge of integer complements to 10 and to 100Knowledge of strategies for multiplying and dividing whole numbers by 2, 4, 5 and 10OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUnderstand and order integersWrite numbers in words and writing numbers from wordsAdd and subtract integersRecall all multiplication facts to 10 × 10, and use them to derive quickly the corresponding division factsMultiply or divide any number by powers of 10Multiply and divide integersUse inverse operations (use one calculation to find the answer to another)Use brackets and the hierarchy of operations (BIDMAS)Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 (and that zero has no reciprocal because division by zero is undefined)Add, subtract, multiply and divide negative numbersRound whole numbers to the nearest: 10, 100, 1000, …Check calculations by rounding, eg 29 31 30 30Check answers by reverse calculation, eg if 9 23 = 207 then 207 9 = 23DIFFERENTIATION & EXTENSIONEstimate answers to calculations involving the four rules of operationDirected number work with multi-step calculationsEncourage effective use of a calculatorTry investigations with digits 3, 7, 5 and 2 and challenge students to find the biggest number, smallest odd number, the largest sum or product etcNOTESPresent all working clearlyFor non-calculator methods, ensure that remainders are shown as evidence of workingShow what is entered into your calculator, not just the answerTry different methods from traditional ones eg Russian or Chinese methods for multiplicationIncorporate Functional Elements whenever and wherever possible and always round measures to an appropriate degree of accuracyModule 2Time: 3 – 5 hoursGCSE Tier:FoundationDecimalsN aAdd, subtract, multiply and divide any numberN jUse decimal notation and recognise that each terminating decimal is a fractionN uApproximate to specified or appropriate degrees of accuracyPRIOR KNOWLEDGE:The concepts of a decimalThe four operationsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUnderstand place value, identifying the values of the digitsWrite decimals in ascending order of sizeApproximate decimals to a given number of decimal places or to one significant figureAdd and subtract decimalsMultiply and divide decimal numbers by integers and decimal numbersKnow that, eg 13.5 0.5 = 135 5Check their answers by rounding, and know that eg 29 31 30 30DIFFERENTIATION & EXTENSIONPractise long multiplication and division without using a calculatorMental maths problems with negative powers of 10 eg 2.5 0.01, 0.001Directed number work with decimal numbersUse decimals in real-life problems as much as possible eg Best Buys Use functional examples such as entry into theme parks, cost of holidays, sharing the cost of a mealMoney calculations that require rounding answers to the nearest pennyMultiply and divide decimals by decimals with more than 2 d.p.Round answers to appropriate degrees of accuracy to suit the context of the questionNOTESAdvise students not to round decimals, used in calculations, until stating in the final answerFor non-calculator methods ensure that remainders are shown as evidence of workingStudents need to be clear about the difference between decimal places and significant figuresLink decimals to Statistics and Probability, eg the mean should not be rounded, the probability of all events occurring is equal to 1Link decimals to Reading scales and converting units (module 5) and Compound measures (module 25)Module 3Time: 3 – 5 hoursGCSE Tier:FoundationCoordinatesA kUse the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric informationPRIOR KNOWLEDGE:Directed numbersParallel and perpendicular linesOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUse axes and coordinates to specify points in all four quadrants in 2-DIdentify points with given coordinatesIdentify coordinates of given points (NB: Points may be in the first quadrant or all four quadrants) Find the coordinates of points identified by geometrical information in 2-DFind the coordinates of the midpoint of a line segment, AB, given the coordinates of A and BDIFFERENTIATION & EXTENSIONThere are plenty of sources of good material here such as animal pictures with coordinates, games like Connect 4 using coordinatesThis topic can be delivered in conjunction with the properties of quadrilaterals NOTESClear presentation of graphs with axes correctly labelled is importantModule 4Time: 5 – 7 hoursGCSE Tier:FoundationAngles, lines and triangles GM aRecall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and vertically opposite anglesGM bUnderstand and use the angle properties of trianglesGM tMeasure and draw lines and anglesGM uDraw triangles and other 2-D shapes using a ruler and a protractorPRIOR KNOWLEDGE:An understanding of angles as a measure of turningThe ability to use a ruler and a protractorOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSMeasure and draw lines, to the nearest mmMeasure and draw angles, to the nearest degreeEstimate sizes of anglesRecall and use properties of angles:at a pointangles at a point on a straight line, including right anglesvertically opposite anglesFind the size of missing angles at a point or at a point on a straight lineDistinguish between acute, obtuse, reflex and right anglesName anglesGive reasons for calculationsUse geometric language appropriatelyIdentify points, lines and anglesUse two letter notation for a line and three letter notation for an angleRecall and use properties of perpendicular linesMark perpendicular lines on a diagramUnderstand the proof that the angle sum of a triangle is 180°Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two verticesDistinguish between scalene, equilateral, isosceles and right-angled trianglesUnderstand and use the angle properties of trianglesFind a missing angle in a triangle, using the angle sum of a triangle is 180?Use the side/angle properties of isosceles and equilateral trianglesUnderstand and use the angle sum of trianglesMake accurate drawing of triangles and other 2-D shapes using a ruler and a protractorMake an accurate scale drawing from a diagramDIFFERENTIATION & EXTENSIONExplore other angle properties in triangles, parallel lines or quadrilaterals, in preparation for future topicsNOTESMake sure that drawings are neat, accurate and labelledGive students a lot of drawing practice, and encourage students to check their drawingsAngles should be accurate to within 2° and lengths accurate to the nearest mmModule 5Time: 4 – 6 hoursGCSE Tier:FoundationReading scales and converting unitsGM oInterpret scales on a range of measuring instruments, and recognise the inaccuracy of measurementsGM tMeasure and draw linesGM pConvert measurements from one unit to anotherGM mUse scale drawingsPRIOR KNOWLEDGE:An awareness of the imperial system of measuresStrategies for multiplying and dividing by 10 (for converting metric units)OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSInterpret scales on a range of measuring instruments inc mm, cm, m, km, ml, cl, l, mg, g, kg, tonnes, °CIndicate given values on a scaleKnow that measurements using real numbers depend upon the choice of unit Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either directionConvert units within one systemConvert metric units to metric units (Metric equivalents should be known)Convert imperial units to imperial units (NB: Conversion between imperial units will be given)Convert between metric and imperial measuresKnow rough metric equivalents of pounds, feet, miles, pints and gallonsEstimate conversionsDIFFERENTIATION & EXTENSIONThis could be made a practical activity, by collecting assorted everyday items and weighing and measuring to check the estimates of their lengths, weights and volumesUse the internet to find the weights, volumes and heights of large structures such as buildings, aeroplanes and shipsTake the opportunity to do some real measuring/estimating around schoolUse conversions for height and weight of students, cars, bridges. Combine with simple scales such as 1 cm to 1 m for classrooms, playing fields, bedrooms and ask them to draw a plan of their ideal design for their bedrooms including the furniture NOTESMeasurement is essentially a practical activityUse a range of everyday objects to bring reality to lessonsUse Functional Elements as a source of practical activities Module 6Time: 3 – 5 hoursGCSE Tier:FoundationCollecting dataSP aUnderstand and use statistical problem solving process/handling data cycleSP bIdentify possible sources of biasSP cDesign an experiment or surveySP dDesign data-collection sheets distinguishing between different types of dataSP eExtract data from printed tables and listsSP fDesign and use two-way tables for discrete and grouped dataPRIOR KNOWLEDGE:An understanding of why data needs to be collectedExperience of simple tally chartsSome idea about different types of graphsExperience of inequality notation and signsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSSpecify the problem and planDecide what data to collect and what statistical analysis is neededCollect data from a variety of suitable primary and secondary sourcesUse suitable data collection techniquesProcess and represent the dataInterpret and discuss the dataUnderstand how sources of data may be biasedIdentify which primary data they need to collect and in what format, including grouped dataConsider fairnessUnderstand sample and populationDesign a question for a questionnaireCriticise questions for a questionnaireDesign and use data-collection sheets for grouped, discrete and continuous dataCollect data using various methodsSort, classify and tabulate data and discrete or continuous quantitative dataGroup discrete and continuous data into class intervals of equal widthExtract data from lists and tablesDesign and use two-way tables for discrete and grouped dataUse information provided to complete a two way tableDIFFERENTIATION & EXTENSIONCarry out a statistical investigation of their own, including designing an appropriate means of gathering the dataSome guidance needs to be given to stop students choosing limited investigations, eg favourite football teamNOTESFor Functional Elements activities, it is worth collecting data at different times of the day, eg to compare types of shopper in a centre. Get data from holiday brochures to compare resorts for temp, rainfall and type of visitorEmphasise the differences between primary and secondary data. Mayfield High data can be used as an example of secondary dataDiscuss sample size and mention that a census is the whole population. In the UK, the census is every year that ends in ‘1’, so the next census is in 2011If students are collecting data as a group, then they should use the same procedureEmphasise that continuous data is data that is measured, eg temperatureModule 7Time: 4 – 6 hoursGCSE Tier:FoundationCharts and graphsSP gProduce charts and diagrams for various data typesSP iInterpret a wide range of graphs and diagrams and draw conclusionsSP lCompare distributions and make inferencesPRIOR KNOWLEDGE:An understanding of why data needs to be collected and some idea about different types of graphsOBJECTIVES By the end of the module the student should be able to:TOPICS/CLASSDraw:PictogramsComposite bar chartsComparative and dual bar chartsFrequency polygons,Histograms with equal class intervalsFrequency diagrams for grouped discrete dataLine graphsInterpret:composite bar chartscomparative and dual bar chartsstem and leaf diagramsscatter graphsfrequency polygonsFrom pictograms, bar charts, line graphs and histograms with equal class intervals:read off frequency valuescalculate total populationfind greatest and least valuesRecognise simple patterns and characteristic relationships in bar charts, line graphs and frequency polygonsUse dual or comparative bar charts to compare distributionsDIFFERENTIATION & EXTENSIONCarry out a statistical investigation of their own and use an appropriate means of displaying the resultsUse a spreadsheet to draw different types of graphsCollect examples of charts and graphs in the media which have been misused, and discuss the implications NOTESReiterate that clear presentation with axes correctly labelled is important, and to use a ruler to draw straight linesStem and leaf diagrams must have a keyShow how to find the median and the mode from a stem and leaf diagramMake comparisons between previously collected dataEncourage student to work in groups and present their charts (useful display material for classrooms/corridors)Use Excel Graph wizardConsider Functional Elements by comparing rainfall charts, distributions of ages in cinemas etcModule 8Time: 3 – 5 hoursGCSE Tier:FoundationSymmetry, Similarity and CongruenceGM eRecognise reflection and rotation symmetry of 2-D shapes GM fUnderstand congruence and similarityPRIOR KNOWLEDGE:Basic idea of shapeOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSRecognise reflection symmetry of 2-D shapesIdentify and draw lines of symmetry on a shapeRecognise rotation symmetry of 2-D shapesIdentify the order of rotational symmetry of a 2-D shapeDraw or complete diagrams with a given number of lines of symmetryDraw or complete diagrams with a given order of rotational symmetryUnderstand congruenceIdentify shapes which are congruentUnderstand similarityIdentify shapes which are similar, including all circles or all regular polygons with equal number of sidesRecognise that all corresponding angles in similar shapes are equal in size when the corresponding lengths of sides are not equal in sizeDIFFERENTIATION & EXTENSIONInvestigate Rangoli Patterns, which is a good source of display work Ask students to find their own examples of symmetry, similarity and congruence in real-lifeNOTESEquations of lines of symmetry are covered later in courseReinforce accurate drawing skills and measurementUse tracing paper or mirrors to assist with symmetry questionsModule 9Time: 7 – 9 hoursGCSE Tier:FoundationTypes of numberN cUse the concepts and vocabulary of factor (divisor), multiple, common factor, Highest Common Factor (HCF), Least Common Multiple (LCM), prime number and prime factor decompositionN dUse the terms square, positive and negative square root, cube and cube rootN eUse index notation for squares, cubes and powers of 10N fUse index laws for multiplication and division of integer powersPRIOR KNOWLEDGE:Number complements to 10 and multiplication/division factsRecognise basic number patternsExperience of classifying integersOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSRecognise even and odd numbersIdentify factors, multiples and prime numbers Find the prime factor decomposition of positive integers Find the common factors and common multiples of two or three numbers Find the Lowest common multiple (LCM) and Highest common factor (HCF) of two number Recall integer squares up to 15 × 15 and the corresponding square rootsRecall the cubes of 2, 3, 4, 5 and 10Find squares and cubes Find square roots and cube roots Use index notation for squares and cubesUse index notation for powers of 10Find the value of calculations using indicesDIFFERENTIATION & EXTENSIONCalculator exercise to check factors of larger numbersFurther work on indices to include negative and/or fractional indicesUse prime factors to find LCMUse a number square to find primes (sieve of Eratosthenes)Calculator exercise to find squares, cubes and square roots of larger numbers (using trial and improvement)NOTESAll of the work in this module can be easily reinforced by using it as ‘starters’ or ‘plenaries’Calculators should be used only when appropriateThere are plenty of investigative work using squares like ‘half time’ scoresFor extension, work could introduce simple ideas on standard formModule 10Time: 3 – 5 hoursGCSE Tier:FoundationIntroduction to algebraA aDistinguish the different roles played by letter symbols in algebra, using the correct notationA bDistinguish in meaning between the words ‘equation’, ‘formula’ and ‘expression’A cManipulate algebraic expressions by collecting like termsPRIOR KNOWLEDGE:Experience of using a letter to represent a numberAbility to use negative numbers with the four operationsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUse notation and symbols correctlyWrite an expressionSimplify algebraic expressions in one or more like terms, by adding and subtractingUnderstand the difference between the word ‘equation’, ‘formula’, and ‘expression’Multiply and divide with variables and numbersDIFFERENTIATION & EXTENSIONLook at patterns in games like ‘frogs’, eg Total moves = R × G + R + GLook at methods to understand expressions, eg there are ‘b’ boys and ‘g’ girls in a class, what is the total ‘t’ number of students in the class Further work, such as collecting like terms involving negative terms, collecting terms where each term may consist of more than one letter eg 3ab + 4abNOTESEmphasise correct use of symbolic notation, eg 3x rather than 3 xPresent all work neatly and use the appropriate algebraic vocabularyModule 11Time: 4 – 6 hoursGCSE Tier:FoundationConstructionsGM vUse straight edge and a pair of compasses to carry out constructionsGM wConstruct lociPRIOR KNOWLEDGE:Knowledge of types of triangleKnowledge of the difference between a line and a regionOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUse straight edge and a pair of compasses to do standard constructions such asConstruct a triangleConstruct an equilateral triangleUnderstand, from the experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are notConstruct the perpendicular bisector of a given lineConstruct the perpendicular from a point to a lineConstruct the bisector of a given angleConstruct angles of 60?, 90?, 30?, 45?Draw parallel linesConstruct diagrams of everyday 2-D situations involving rectangles, triangles, perpendicular and parallel linesDraw and construct diagrams from given instructionsA region bounded by a circle and an intersecting lineA given distance from a point and a given distance from a lineEqual distances from 2 points or 2 line segmentsRegions which may be defined by ‘nearer to’ or ‘greater than’Find and describe regions satisfying a combination of lociDIFFERENTIATION & EXTENSIONTry to do this module as practically as possible using real life situations eg horses tethered to ropes, mobile phone masts etcUse the internet to source ideas for this moduleUse loci problems that require a combination of lociNOTESAll constructions should be presently neatly and accuratelyA sturdy pair of compasses is essentialConstruction lines should not be erased as they carry valuable method marksAll lines should be correct to within 2 mm and angles correct to 2° Module 12Time: 4 – 6 hoursGCSE Tier:FoundationPatterns and sequencesA iGenerate terms of a sequence using term-to-term and position to-term definitions of the sequenceA jUse linear expressions to describe the nth term of an arithmetic sequencePRIOR KNOWLEDGE:Know about odd and even numbersRecognise simple number patterns, eg 1, 3, 5, ...Writing simple rules algebraicallyRaise numbers to positive whole number powersOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSGenerate simple sequences of odd or even numbersFind the missing numbers in a number pattern or sequenceFind the nth term of a number sequenceUse the nth number of an arithmetic sequenceFind whether a number is part of a given sequenceContinue a sequence derived from diagramsUse a calculator to produce a sequence of numbersDIFFERENTIATION & EXTENSIONMatch-stick problems Use practical real life examples like ‘flower beds’Sequences of triangle numbers, Fibonacci numbers etcExtend to quadratic sequences whose nth term is an2 + b and link to square numbersNOTESEmphasise good use of notation 3n means 3 nWhen investigating linear sequences, students should be clear on the description of the pattern in words, the difference between the terms and the algebraic description of the nth termModule 13Time: 4 – 6 hoursGCSE Tier:Foundation Properties of quadrilaterals and parallel linesGM d Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombusGM bUnderstand and use the angle properties of parallel and intersecting lines, triangles and quadrilateralsGM rUnderstand and use bearingsPRIOR KNOWLEDGE:Know that angles in a triangle add up to 180?Know that angles at a point on a straight line sum to 180°Know that a right angle = 90°OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSRecall the properties and definitions of special types of quadrilaterals, including symmetry propertiesList the properties of each, or identify (name) a given shapeDraw sketches of shapesName all quadrilaterals that have a specific propertyIdentify quadrilaterals from everyday usageClassify quadrilaterals by their geometric propertiesUnderstand and use the angle properties of parallel linesMark parallel lines on a diagramFind missing angles using properties of corresponding and alternate anglesUnderstand and use the angle properties of quadrilateralsUse the fact that angle sum of a quadrilateral is 360?Give reasons for angle calculationsUse three figure-bearings to specify directionMark on a diagram the position of point B given its bearing from the point AGive a bearing between the points on a map or scaled planGiven the bearing of point A from point B, work out the bearing of B from ADIFFERENTIATION & EXTENSIONPractical activities help with the understanding of the properties and proofs – games like ‘Guess who I am?’Use the angle properties of triangles to find missing angles in combination s of trianglesExplore other properties in triangles, quadrilaterals and parallel lines NOTESAll diagrams should be presently neatly and accuratelyStudents should have plenty of practice drawing examples to illustrate the properties of various shapesFor bearings and scaled drawings, angles should be correct to 2° and lines accurate to 2 mmModule 14Time: 6 – 8 hoursGCSE Tier:FoundationFractions N hUnderstand equivalent fractions, simplifying a fraction by cancelling all common factorsN iAdd and subtract fractionsN bOrder rational numbersN jUse decimal notation and understand that decimals and fractions are equivalentN kRecognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimalsPRIOR KNOWLEDGE:Multiplication factsAbility to find common factorsA basic understanding of fractions as being ‘parts of a whole unit’Use of a calculator with fractionsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSVisualise a fraction diagrammaticallyUnderstand a fraction as part of a wholeRecognise and write fractions in everyday situationsFind fractions of amountsWrite a fraction in its simplest form and recognise equivalent fractionsCompare the sizes of fractions using a common denominatorAdd and subtract fractions by using a common denominatorWrite an improper fraction as a mixed fractionConvert between fractions and decimalsDIFFERENTIATION & EXTENSIONCareful differentiation is essential as this topic is dependent on the student’s abilityRelate simple fractions to percentages and vice versaWork with improper fractions and mixed numbers, eg divide 5 pizza’s between 3 peopleSolve word problems involving fractions and in real life problems, eg finding the perimeter using fractional valuesLink fractions with probability questionsNOTESRegular revision of fractions is essentialDemonstrate how to use the fraction button on a calculator, in order be able to check solutionsUse real-life examples whenever possibleModule 15Time: 3 – 4 hourGCSE Tier:FoundationPie chartsSP gDraw and produce pie chartsSP iInterpret pie chartsSP lCompare distributions and make inferencesPRIOR KNOWLEDGE:Measuring and drawing anglesFractions of simple quantitiesOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSRepresent data in a pie chartInterpret data in a pie chartUnderstand that the frequency represented by corresponding sectors in two pie charts is dependent upon the total populations represented by each of the pie chartsFrom pie chartsfind the total frequencyfind the size of each categoryDIFFERENTIATION & EXTENSIONUse this module to refresh memories on frequency and tally tablesPractise the ability to divide by 20, 30, 40, 60 etcThis can be delivered as a practical module that could lead to wall display- remind about of bias, eg only asking their friends which band they like Compare pie charts for, eg boys and girls, to identify similarities and differencesAsk students to combine two pie chartsNOTESAngles for pie charts should be accurate to within 2° Module 16Time: 3 – 5 hoursGCSE Tier:FoundationFractions, Decimals and Percentages N hUnderstand equivalent fractions in the context of ‘hundredths’ N lUnderstand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportionsN oInterpret fractions, decimals and percentages as operatorsN uApproximate to a specified or appropriate degree of accuracyN vUse calculators effectively and efficientlyPRIOR KNOWLEDGE:Four operations of numberThe concepts of a fraction and a decimalNumber complements to 10 and multiplication tablesAwareness that percentages are used in everyday lifeOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUnderstand that a percentage is a fraction in hundredthsConvert between fractions decimals and percentagesWrite one number as a percentage of another numberCalculate the percentage of a given amountDIFFERENTIATION & EXTENSIONConsider fractional percentages of amounts eg 12.5% = 0.125 =Consider percentages which convert to recurring decimals (eg 33%), and situations which lead to percentages of more than 100%Use fraction, decimal and percentage dominos or follow me cards.Investigate into the many uses made of percentages, particularly in the media Practise the ability to convert between different formsNOTESUse Functional Elements questions using fractions, eg off the list price when comparing different sale pricesKeep using non-calculator methods, eg start with 10%, then 1% in order to required percentagesModule 17Time: 4 – 6 hoursGCSE Tier:FoundationApplications of percentagesN lUnderstand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportionsN mUse percentagesN oInterpret fractions, decimals and percentages as operatorsN vUse calculators effectively and efficientlyPRIOR KNOWLEDGE:Four operations of numberThe concepts of a fraction and a decimalNumber complements to 10 and multiplication tablesAwareness that percentages are used in everyday lifeOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUse percentages to solve problemsConvert between fractions, decimals and percentages to find percentage changeFind a percentage of a quantity in order to increase or decreaseUse percentages in real-life situationsVATvalue of profit or losssimple interestincome tax calculationsDIFFERENTIATION & EXTENSIONUse a mixture of calculator and non-calculator methodsUse ideas for wall display, students make up their own poster to explain say a holiday reductionUse functional skills questions to look at questions in contextCombine multipliers to simplify a series of percentage changesProblems which lead to the necessity of rounding to the nearest penny, eg real-life contextsInvestigate comparisons between simple and compound interest calculationsNOTESUse plenty of practical examples that can be linked to Functional Elements, eg VAT calculationsModule 18Time: 3 –5 hoursGCSE Tier:FoundationAlgebra using powers and bracketsN fUse the index laws for multiplication and division of integer powersA cManipulate algebraic expressions by collecting like terms, by multiplying a single term over abracket, and by taking out common factorsPRIOR KNOWLEDGE:Squares and cubesExperience of using a letter to represent a numberAbility to use negative numbers with the four operationsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUse index laws to simplify and calculate the value of numerical expressions involving multiplication and division of Multiply a single algebraic term over a bracketWrite expressions using squares and cubesUse simple instances of index lawsFactorise algebraic expressions by taking out common factorsDIFFERENTIATION & EXTENSIONUse various investigations leading to generalisations, eg:Indices – cell growth, paper foldingBrackets – pond borders 4n + 4 or 4(n + 1)Football league matches n? – n or n(n – 1)NOTESUse everyday examples that lead to generalisationsModule 19Time: 5 – 7 hoursGCSE Tier:FoundationRatio and proportionN pUse ratio notation, including reduction to its simplest form and its various links to fraction notationN tDivide a quantity in a given ratioGM mUse and interpret maps and scale drawingsN qUnderstand and use number operations and inverse operationsPRIOR KNOWLEDGE:Using the four operationsAbility to recognise common factorsKnowledge of fractionsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUnderstand what is meant by ratioWrite a ratio in its simplest form; and find an equivalent ratioSolve a ratio problem in context, eg recipesShare a quantity in a given ratioUnderstand and use examples in direct proportionInterpret map/model scales as a ratioSolve problems involving money conversions, eg ?’s to Euros etcDIFFERENTIATION & EXTENSIONConsider maps: draw a plan of the schoolFurther problems involving scale drawing, eg find the real distance in metres between two points on 1 : 40000 mapPlan a housing estate with variety of different sized housesCurrency calculations using foreign exchange ratesHarder examples involving multi-stage problemsLink ratios and proportion to Functional Elements, eg investigate the proportion of different metals in alloys, the ingredients needed for recipes for fewer or more people, mixing cement, planting forests, comparing prices of goods here and abroad, Best buy type questionsNOTESStudents often find ratios with 3 parts difficultModule 20Time: 5 – 7 hoursGCSE Tier:FoundationLinear equations and inequalitiesA dSet up and solve simple equationsN qUnderstand and use number operations and the relationships between them including inverse operations and the hierarchy of operationsA gSolve linear inequalities in one variable and represent the solution set on a number linePRIOR KNOWLEDGE:Experience of finding missing numbers in calculationsThe idea that some operations are ‘opposite’ to each otherAn understanding of balancingExperience of using letters to represent quantitiesBe able to draw a number lineAn understanding of fractions and negative numbersOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSSet up simple equationsRearrange simple equationsSolve simple equationsSolve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equationSolve linear equations which include brackets, those that have negative signs occurring anywhere in the equation, and those with a negative solutionSolve linear equations in one unknown, with integer or fractional coefficientsUse linear equations to solve word problemsSolve simple linear inequalities in one variable, and represent the solution set on a number lineUse the correct notation to show inclusive and exclusive inequalitiesDIFFERENTIATION & EXTENSIONDerive equations from practical situations (such as finding unknown angles in polygons or perimeter problems)Solve equations where manipulation of fractions (including negative fractions) is requiredNOTESRemind students about work on patterns and sequences that have linear resultsStudents need to realise that not all equations can be solved by ‘trial and improvement’ or by observation. The use of a formal method of solving equations is very important Remind students of the need to set their work out clearly, keeping the equal signs in lineModule 21Time: 6 – 8 hoursGCSE Tier:FoundationPerimeter and areaGM xCalculate perimeters and areas of shapes made from triangles and rectanglesGM nUnderstand the effect of enlargement for perimeter and area of shapesGM pConvert between units and area measuresPRIOR KNOWLEDGE:Names of triangles, quadrilaterals Knowledge of the properties of rectangles, parallelograms and trianglesConcept of perimeter and areaUnits of measurementFour operations of number OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSMeasure shapes to find perimeters and areasFind the perimeter of rectangles and trianglesFind the perimeter of compound shapesFind the area of a rectangle and triangleRecall and use the formulae for the area of a triangle, rectangle and a parallelogramCalculate areas of compound shapes made from triangles and rectanglesFind the area of a trapezium by using the formulaSolve a range of problems involving areas including cost of carpet type questionsConvert between units of areaDIFFERENTIATION & EXTENSIONFurther problems involving combinations of shapesUse practical examples from functional papers on topics such as returfing a garden, carpeting a room, laying carpet tiles on a floor Perimeter questions could use skirting board, wallpaper, planting a border of a gardenNOTESDiscuss the correct use of language and units, particularly when method marks are for the correct unit of measureEnsure that students can distinguish between perimeter and areaPractical examples help to clarify the concepts, eg floor tiles etcModule 22Time: 3 – 5 hoursGCSE Tier:Foundation3-D shapesGM kUse 2-D representations of 3-D shapesGM xCalculate the surface area of a 3-D shapePRIOR KNOWLEDGE:The names of standard 2-D and 3-D shapesOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSIdentify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and coneKnow the terms face, edge and vertexUse 2-D representations of 3-D shapesUse isometric gridsDraw nets and show how they fold to make a 3-D solidUnderstand and draw front and side elevations and plans of shapes made from simple solidsGiven the front and side elevations and the plan of a solid, draw a sketch of the 3-D solidDIFFERENTIATION & EXTENSIONMake solids using equipment such as clixi or multi-linkDraw shapes made from multi-link on isometric paperBuild shapes from cubes that are represented in 2-DEuler’s theoremA useful topic for a wall display-pupils tend to like to draw 3-D shapes and add interest by using a mixture of colours in the elevationsNOTESAccurate drawing skills need to be reinforcedSome students find visualising 3-D object difficult, so using simple models will helpModule 23Time: 4 – 6 hoursGCSE Tier:FoundationReal-life graphsA rConstruct linear functions from real-life problems and plotting their corresponding graphsA sDiscuss, plot and interpret graphs (which may be non-linear) modelling real situationsPRIOR KNOWLEDGE:Experience at plotting points in all quadrantsExperience at labelling axes and reading scalesOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSDraw graphs representing ‘real’ examples like filling a bath/containersInterpret and draw linear graphs, including conversion graphs, fuel bills etcSolve problems relating to mobile phone bills with fixed charge and price per unitInterpret non-linear graphs like the number of cans in a vending machine at times throughout the dayDIFFERENTIATION & EXTENSION800100116205008001004273550080010084455004572001570355008001008445500Use open ended questions that test student awareness of what intersections mean, eg mobile phone bills Use spreadsheets to generate straight-line graphs and pose questions about gradient of linesUse ICT packages or graphical calculators to draw straight line graphs and quadratic graphsNOTESClear presentation is important with axes clearly labelledStudents need to be able to recognise linear graphs and also be able to recognise when their graph is incorrectLink graphs and relationships in other subject areas, eg science, geographyStudents should have plenty of practice interpreting linear graphs for Functional Elements problemsModule 24Time: 3 - 5 hoursGCSE Tier:FoundationStraight line graphsA lRecognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding gradientsPRIOR KNOWLEDGE:Experience at plotting points in all quadrantsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSDraw, label and put suitable scales on axesRecognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate planePlot and draw graphs of functionsPlot and draw graphs of straight lines of the form y = mx + cFind the gradient of a straight line from a graphInterpret gradients from real life graphs eg for height of bath water vs time, the gradient is the rate of fillingDIFFERENTIATION & EXTENSIONPlot graphs of the form y = mx + c where pupil has to generate their own table and set out their own axesUse a spreadsheet to generate straight-line graphs, posing questions about the gradient of linesUse a graphical calculator or graphical ICT package to draw straight-line graphs102870066675000685800203835000102870043815000Use some examples from the last module to interpret gradient and interceptCharge in ?’sFor hire of a skip the intercept is delivery charge and theand the gradient is the cost per dayTime in daysFind the equation of a straight line through two pointsNOTESCareful annotation should be encouraged. Label the coordinate axes and write the equation of the line on the graphCover horizontal and vertical line graphs as students often forget these (x = c and y = c)Link graphs and relationships in other subject areas, eg science and geographyInterpret straight line graphs in Functional ElementsLink conversion graphs to converting metric and imperial units and equivalentsModule 25Time: 4 – 6 hoursGCSE Tier:FoundationCompound measuresGM sUnderstand and use compound measuresN uApproximate to specified or appropriate degree of accuracyGM pConvert between speed measuresPRIOR KNOWLEDGE:Knowledge of metric units eg 1 m = 100 cmKnow that 1 hour = 60 mins, 1 min = 60 secondsExperience of multiply by powers of 10, eg 100 100 = 10 000OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSUse the relationship between distance, speed and time to solve problemsConvert between metric units of speed, eg km/h to m/sDIFFERENTIATION & EXTENSIONConvert imperial units to metric units, eg mph into km/h which would remind students that 5 miles = 8 kmAsk students to convert a 100m time of 10 secs into mphUse the internet and/or reference books to find weights, volumes and heights of large structures; such as prominent buildings, aeroplanes and shipsNOTESMeasurement is a practical activityAll working out should be shown with multiplication or division by powers of 10Use the distance/speed/time triangle (i.e. Drink Some Tea)Use Functional Elements for practice questions for this topic area, eg Best BuysLink to their work drawing and interpreting Module 26Time: 4 – 6 hoursGCSE Tier:FoundationTimetables and Distance/ time Graphs GM oInterpret scales on a range of measuring instruments, and recognise the inaccuracy of measurementsSP eExtract data from printed tables and listsA sInterpret graphs (which may be non-linear) modelling real-life situationsPRIOR KNOWLEDGE:Knowledge of metric units eg 1 m = 100 cmKnow that 1 hour = 60 mins, 1 min = 60 secondsKnow how to find speedKnow how to read scales, draw and interpret graphs OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSConvert between 12–hour and 24–hour hour clock timesRead bus and train timetables and plan journeysDraw distance time graphsInterpret distance time graphs and solve problemsDIFFERENTIATION & EXTENSIONDraw and interpret non linear curves like 400 m running trackMake up a graph and supply the commentary for itAsk students to plan and cost a holiday from a brochureNOTESClear presentation with axes labelled correctly is importantInterpret straight line graphs for Functional Elements problemsModule 27Time: 4 – 6 hoursGCSE Tier:FoundationVolumeGM aaCalculate volumes of right prisms and shapes made from cubes and cuboidsGM nUnderstand the effect of enlargement for perimeter, area and volume of shapes and solidsGM p Converting between volume measures, including cubic centimetres and cubic metresPRIOR KNOWLEDGE:Concept of volumeConcept of prismExperience of constructing cubes or cuboids from multi linkOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSFind volumes of shapes by counting cubesRecall and use formulae for the volume of cubes and cuboidsCalculate the volumes of right prisms and shapes made from cubes and cuboidsConvert between units of volumeDIFFERENTIATION & EXTENSIONLook at ‘practical’ examples with fish tanks/ filling containers, find the number of small boxes fitting into a large boxFurther problems involving a combination of shapesCylinders are left until later in the courseNOTESDiscuss the correct use of language and units. Remind students that there is often a mark attached to writing down the correct unitUse practical problems to enable the students to understand the difference between perimeter, area and volumeUse Functional Elements problems, eg floor tiles, optimisation type questions etcModule 28Time: 8 - 10 hoursGCSE Tier:FoundationProbability SP mUnderstand and use the vocabulary of probability and probability scaleSP nUnderstand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency SP oList all outcomes for single events, and for two successive events, in a systematic way andderive relative probabilitiesSP pIdentify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1SP sCompare experimental data and theoretical probabilitiesSP tUnderstand that if they repeat an experiment, they may ? and usually will ? get different outcomes, and that increasing sample size generally leads to better estimates of probabilityand population characteristics PRIOR KNOWLEDGE:Elementary fractions decimals and percentagesAbility to read from a two-way tableOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSDistinguish between events which are: impossible, unlikely, even chance, likely, and certain to occurMark events and/or probabilities on a probability scale of 0 to 1Write probabilities in words, fractions, decimals and percentagesFind the probability of an event happening using theoretical probabilityFind the probability of an event happening using relative frequencyEstimate the number of times an event will occur, given the probability and the number of trialsUse theoretical models to include outcomes using dice, spinners, coinsList all outcomes for single events systematicallyList all outcomes for two successive events systematicallyUse and draw sample space diagramsAdd simple probabilitiesIdentify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1Use 1 ? p as the probability of an event not occurring where p is the probability of the event occurringFind a missing probability from a list or tableCompare experimental data and theoretical probabilitiesCompare relative frequencies from samples of different sizesDIFFERENTIATION & EXTENSIONUse this as an opportunity for practical workExperiments with dice and spinnersShow sample space for outcomes of throwing two dice (36 outcomes)Use ‘the horse race’/drawing pins/let students make their own biased dice and find experimental probabilityNOTESStudents should express probabilities as fractions, percentages or decimalsProbabilities written as fractions don’t need to be cancelled to their simplest formModule 29Time: 6 – 8 hoursGCSE Tier:FoundationFormulaeA fDerive a formula, substitute numbers into a formula and change the subject of a formulaPRIOR KNOWLEDGE:Understanding of the mathematical meaning of the words; expression, simplifying, formulae and equationExperience of using letters to represent quantitiesSubstituting into simple expressions using wordsUsing brackets in numerical calculations and removing brackets in simple algebraic expressionsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSDerive a simple formula, including those with squares, cubes and rootsUse formulae from mathematics and other subjects expressed initially in words and then using letters and symbols Substitute numbers into a formulaSubstitute positive and negative numbers into expressions such as 3x? + 4 and 2x?Change the subject of a formulaFind the solution to a problem by writing an equation and solving itDIFFERENTIATION & EXTENSIONUse negative numbers in formulae involving indicesVarious investigations leading to generalisations, eg the painted cube, Frogs, Pond BordersRelate to topic on graphs of real life functionsMore complex changing the subject, moving onto higher tier workApply changing of the subject to physics formulae, eg speed, density, equations of motionNOTESEmphasise the need for good algebraic notationShow a linear equation first and follow the same steps to rearrange a similarly structured formulaLink with Functional Elements problems in everyday problemsLink with formulae for area and volumeModule 30Time: 4 – 6 hoursGCSE Tier:FoundationAngle properties of polygonsGM cCalculate and use the sums of the interior and exterior angles of polygonsGM vUse straight edge and a pair of compasses to carry out constructionsPRIOR KNOWLEDGE:Angles on straight lines and in simple shapes OBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSCalculate and use the sums of the interior angles of polygonsUse geometrical language appropriately and recognise and name pentagons, hexagons, heptagons, octagons and decagonsKnow, or work out, the relationship between the number of sides of a polygon and the sum of its interior anglesKnow that the sum of the exterior angles of any polygon is 360°Calculate the size of each exterior/interior angle of a regular polygonConstruct for example a regular hexagon inside a circleUnderstand tessellations of regular and irregular polygonsTessellate combinations of polygonsExplain why some shapes tessellate and why other shapes do notDIFFERENTIATION & EXTENSIONStudy Escher drawings (possibly cross curricular with Art).Ask students to design their own tessellation, and explain why their shapes tessellateNOTESAll diagrams should be neatly presentedUse of tracing paper helps with tessellationsConsider real-life examples of tessellationsModule 31Time: 5 – 7 hoursGCSE Tier:FoundationTransformationsGM lDescribe and transform 2-D shapes using single or combined rotations, reflections, translations or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformationsPRIOR KNOWLEDGE:Recognition of basic shapesAn understanding of the concept of rotation, reflection and enlargementCoordinates in four quadrantsLinear equations parallel to the coordinate axes and y = ± xOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSDescribe and transform 2-D shapes using single rotationsUnderstand that rotations are specified by a centre and an (anticlockwise) angleFind the centre of rotationRotate a shape about the origin, or any other pointDescribe and transform 2-D shapes using single reflectionsUnderstand that reflections are specified by a mirror lineIdentify the equation of a line of symmetryDescribe and transform 2-D shapes using single translationsUnderstand that translations are specified by a distance and direction (using a vector) Translate a given shape by a vectorDescribe and transform 2-D shapes using enlargements by a positive scale factorUnderstand that an enlargement is specified by a centre and a scale factorScale a shape on a grid (without a centre specified) Draw an enlargementEnlarge a given shape using (0, 0) as the centre of enlargementEnlarge shapes with a centre other than (0, 0) Find the centre of enlargementRecognise that enlargements preserve angle but not lengthIdentify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sidesDescribe and transform 2-D shapes using combined rotations, reflections, translations, or enlargementsUnderstand that distances and angles are preserved under rotations, reflections and translations, so that any shape is congruent under any of these transformationsDescribe a transformationDIFFERENTIATION & EXTENSION Use squared paper to enlarge cartoon characters to make a displayNOTESEmphasise that students should describe the transformations fully Diagrams should be drawn in pencilTracing paper can be useful for rotationsModule 32Time: 5 – 6 hoursGCSE Tier:FoundationScatter graphs and correlationSP kRecognise correlation and draw and/or use lines of best fit by eye, understanding what these representSP jLook at data to find patterns and exceptionsPRIOR KNOWLEDGE:Plotting coordinates and scale An understanding of the concept of a variableRecognition that a change in one variable can affect anotherLinear graphsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSDraw and produce a scatter graph Look at data to find patterns and exceptionsDistinguish between positive, negative and zero correlation using lines of best fitInterpret correlation in terms of the problemUnderstand that correlation does not imply causalityDraw lines of best fit by eye and understand what it representsUse a line of best fit to predict values of one variable given values of the other variableDIFFERENTIATION & EXTENSIONVary the axes required on a scatter graph to suit the ability of the classCarry out a statistical investigation of their own including; designing an appropriate means of gathering the data, and an appropriate means of displaying the results eg height and length of armUse a spreadsheet, or other software, to produce scatter diagrams/lines of best fitInvestigate how the line of best fit is affected by the choice of scales on the axes, eg use car data with age and price of the same make of carNOTESThe line of best fit should pass through the coordinate representing the mean of the dataLabel all axes clearly and use a ruler to draw all straight linesRemind student the line of best fit does not necessarily go through the origin of the graphModule 33Time: 6 – 8 hoursGCSE Tier:FoundationAverages and RangeSP hCalculate median, mean, range, mode and modal class SP lCompare distributions and make inferencesSP uUse calculators efficiently and effectively, including statistical functionsSP gProduce ordered stem and leaf diagramsSP iDraw conclusions from graphs and diagramsPRIOR KNOWLEDGE:Mid point of a line segmentAddition and subtractionDifferent statistical diagramsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSCalculate the mean, mode, median and range for discrete dataCalculate the mean, mode, median and range from an ordered stem and leaf diagramProduce an ordered stem and leaf diagramCalculate the modal class and interval containing the median for continuous dataCalculate the mean, median and mode from a frequency tableEstimate the mean of grouped data using the mid-interval valueCompare the mean and range of two distributionsRecognise the advantages and disadvantages between measures of averageCalculate the mean of a small data set, using the appropriate key on a scientific calculatorDIFFERENTIATION & EXTENSIONFind the mean for grouped continuous data with unequal class intervalsCollect continuous data and decide on appropriate (equal) class intervals; then find measures of averageUse the statistical functions on a calculator or a spreadsheet to calculate the mean for continuous dataNOTESAsk class to do their own survey with data collection sheets, eg to find the average number of children per family in the classThe internet and old coursework tasks are a rich source of data to work with, eg Second-Hand Car Sales, Mayfield High data etcModule 34Time: 2 – 4 hoursGCSE Tier:FoundationQuadratic graphsA tGenerate points and plot graphs of simple quadratic functions, and use these to find approximate solutionsN vUse calculators effectively and efficientlyPRIOR KNOWLEDGE:Squaring negative numbersSubstituting numbers into algebraic expressionsPlotting points on a coordinate gridExperience of dealing with algebraic expression with brackets -BIDMASOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSSubstitute values of x into a quadratic function to find the corresponding values of yDraw graphs of quadratic functionsUse quadratic graphs to solve approximate solution of a quadratic equation from the graph of the corresponding quadratic functionDIFFERENTIATION & EXTENSIONDraw simple cubic and graphsSolve simultaneous equations graphically including a quadratic graph and a lineSolve simple projectile problems NOTESThe graphs of quadratic functions should be drawn freehand, and in pencil. Turning the paper often helps. Squaring negative integers may be a problem for some. Students will often forget the middle term of the expansion and they will need to be reminded of thisModule 35Time: 3 – 4 hoursGCSE Tier:FoundationTrial and improvementA hUse systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving themN uApproximate to a specified or appropriate degree of accuracyN v Use calculators effectively and efficientlyPRIOR KNOWLEDGE:Substituting numbers into algebraic expressionsDealing with decimals on a calculatorComparing/ordering decimalsOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSSolve algebraic equations involving squares and cubes eg x? + 3x = 40Solve ‘real life’ problems on areas and volumes, eg the length of a rectangular room is 2 m longer than the width. If the area is 30 m?, find the width.DIFFERENTIATION & EXTENSIONCan look at various calculator functions like ‘square root’ and ‘cube root’. Introduce by trial and improvementSolve functions of the form , and link with changing the subjectNOTESStudents should be encouraged to use their calculator efficiently by using the ‘replay’ or ANS/EXE function keysStudents to take care when entering negative values to be squaredStudents should write down all the digits on their calculator display and only round the final answer to the required degree of accuracyModule 36Time: 4 – 6 hoursGCSE Tier:FoundationCirclesGM iDistinguish between the centre, radius, chord, diameter, circumference, tangent, arc, sector and segmentGM zFind circumferences and areasN uApproximate to a specified or appropriate degree of accuracyN v Use calculators effectively and efficientlyPRIOR KNOWLEDGE:The ability to substitute numbers into formulaeOBJECTIVESBy the end of the module the student should be able to:TOPICS/CLASSRecall the definition of a circle and identify and draw parts of a circleDraw a circle given its radius or diameterFind circumferences of circles and areas enclosed by circlesRecall and use the formulae for the circumference of a circle and the area enclosed by a circleUse π ≈ 3.142 or use the π button on a calculatorFind the perimeters and areas of semicircles and quarter circlesFind the surface area and volume of a cylinderDIFFERENTIATION & EXTENSIONUse more complex 2-D shapes eg (harder) sectors of circles Approximate as Work backwards to find the radius/diameter given the circumference/areaApply to real life contexts with laps of running tracks and average speeds Make a label for a canHarder problems involving multi-stage calculationsDefine a circle by using the language of lociNOTESAll working should be clearly and accurately presented Use an pencil to draw all diagramsA sturdy pair of compasses is essentialModule 37Time: 4 – 5 hoursGCSE Tier:FoundationPythagoras’ Theorem Gm gUnderstand, recall and use Pythagoras’ theorem in 2-D A kCalculate the length of a line segmentN uApproximate to specified or appropriate degrees of accuracyN v Use calculators effectively and efficientlyPRIOR KNOWLEDGE:Knowledge of square and square rootsKnowledge of types of triangleOBJECTIVESBy the end of this module students should be able toTOPICS/CLASSUnderstand and recall Pythagoras’ TheoremUse Pythagoras’ theorem to find the hypotenuseUse Pythagoras’ theorem to find a sideUse Pythagoras’ theorem to find the length of a line segment from a coordinate gridApply Pythagoras’ theorem to practical situationsDIFFERENTIATION & EXTENSIONSee exemplar question involving times taken to cross a field as oppose to going around the edge.Try to find examples with ladders on walls, area of a sloping roof etcIntroduce 3-D Pythagoras (moving towards Higher Tier)NOTESA useful mnemonic for remembering Pythagoras’ Theorem is; ‘Square it, square it, add/subtract it, square root it’Students should not forget to state units for the answers ................
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