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Step-by-step methods for every topic, Years 4–10. Read the method, then practise it.

Year 4

34 guides
Grammar and PunctuationvisualSimple, Compound and Complex SentencesAC9E4LA06Grammar and PunctuationvisualPunctuating DialogueAC9E4LA12Grammar and PunctuationvisualSynonyms and AntonymsAC9E4LA11ReadingvisualFinding the Answer in the TextAC9E4LY05ReadingvisualWorking Out What Is Not SaidAC9E4LY05ReadingvisualFact and OpinionAC9E4LA02WritingvisualBuilding a ParagraphAC9E4LY06WritingvisualPlanning a StoryAC9E4LE05WritingvisualWriting to PersuadeAC9E4LY03FractionsvisualCounting Fractions on a Number LineAC9M4N04FractionsvisualEquivalent FractionsAC9M4N03MeasuringvisualReading Scales and Part MarksAC9M4M01MeasuringvisualTime, am and pm, and How LongAC9M4M03MeasuringvisualNaming AnglesAC9M4M04MeasurementvisualArea and PerimeterAC9M4M02More NumbervisualOdd and Even NumbersAC9M4N02More NumbervisualMultiplying and Dividing by 10, 100 and 1000AC9M4N05More NumbervisualRounding and EstimatingAC9M4N07NumbervisualPlace ValueAC9M4N05NumbervisualFractions of a WholeAC9M4N03More OperationsvisualAdding and Subtracting Big NumbersAC9M4N06More OperationsvisualMultiplication Facts and Division FactsAC9M4A02More OperationsvisualNumber Sentences and Missing NumbersAC9M4A01More OperationsvisualAlgorithms and Number PatternsAC9M4N09OperationsvisualMultiplicationAC9M4N06OperationsvisualDecimals: TenthsAC9M4N01Shape and PositionvisualShapes Made From ShapesAC9M4SP01Shape and PositionvisualGrid References and PathsAC9M4SP02Shape and PositionvisualLine and Rotational SymmetryAC9M4SP03Data and ChancevisualPictographs and Column GraphsAC9M4ST01Data and ChancevisualWhich Graph Works BestAC9M4ST02Data and ChancevisualDoing a SurveyAC9M4ST03Data and ChancevisualHow Likely Is It?AC9M4P01Data and ChancevisualDoing It Again and AgainAC9M4P02

Year 5

32 guides
Number PatternsvisualInverse Operations and Fact FamiliesAC9M5A01Number PatternsvisualMissing Numbers in Times and DivideAC9M5A02Grammar and PunctuationvisualMain and Dependent ClausesAC9E5LA05Grammar and PunctuationvisualCommas and ApostrophesAC9E5LA09Grammar and PunctuationvisualSimile, Metaphor and PersonificationAC9E5LE04ReadingvisualSkimming and ScanningAC9E5LY04ReadingvisualSummarising a TextAC9E5LY05ReadingvisualPoint of ViewAC9E5LE03WritingvisualLinking ParagraphsAC9E5LA04WritingvisualBacking Up an OpinionAC9E5LA02WritingvisualWriting a DescriptionAC9E5LA06FractionsvisualEquivalent FractionsAC9M5N03MeasuringvisualChoosing the Right UnitAC9M5M01MeasuringvisualPerimeter and AreaAC9M5M02Measuringvisual12-Hour and 24-Hour TimeAC9M5M03MeasuringvisualEstimating and Measuring AnglesAC9M5M04More NumbervisualOrdering DecimalsAC9M5N01More NumbervisualFactors, Multiples and DivisibilityAC9M5N02More NumbervisualAdding and Subtracting FractionsAC9M5N05More NumbervisualMixed Numerals and Comparing FractionsAC9M5N03More NumbervisualEstimating and Solving Word ProblemsAC9M5N08NumbervisualLong MultiplicationAC9M5N06NumbervisualPercentagesAC9M5N04OperationsvisualDivision with RemaindersAC9M5N07Shape and PositionvisualNets of 3D ObjectsAC9M5SP01Shape and PositionvisualCoordinates and DirectionsAC9M5SP02Shape and PositionvisualSlides, Flips and TurnsAC9M5SP03Data and ChancevisualCollecting and Checking DataAC9M5ST01Data and ChancevisualLine Graphs Over TimeAC9M5ST02Data and ChancevisualPlanning an InvestigationAC9M5ST03Data and ChancevisualEqually Likely or NotAC9M5P01Data and ChancevisualRepeating an ExperimentAC9M5P02

Year 6

31 guides
Patterns and RulesvisualGrowing Patterns and Their RulesAC9M6A01Patterns and RulesvisualBrackets and Order of OperationsAC9M6A02Patterns and RulesvisualAlgorithms That Make NumbersAC9M6A03Grammar and PunctuationvisualEmbedded ClausesAC9E6LA05Grammar and PunctuationvisualThe Comma's Three JobsAC9E6LA09Grammar and PunctuationvisualEmotive and Figurative LanguageAC9E6LA08ReadingvisualComparing Two TextsAC9E6LE02ReadingvisualSpotting BiasAC9E6LA02ReadingvisualHow Structure Serves PurposeAC9E6LY03WritingvisualPlanning an ArgumentAC9E6LY06WritingvisualChoosing Stronger VerbsAC9E6LA06WritingvisualMaking Writing FlowAC9E6LA04MeasuringvisualConverting Metric UnitsAC9M6M01MeasuringvisualArea of a RectangleAC9M6M02MeasuringvisualTimetables and JourneysAC9M6M03More NumbervisualOrdering Fractions and Saying WhyAC9M6N03More NumbervisualAdding and Subtracting DecimalsAC9M6N04More NumbervisualMultiplying and Dividing Decimals by 10AC9M6N06More NumbervisualPercentages and DiscountsAC9M6N07More NumbervisualEstimating and Money ProblemsAC9M6N08NumbervisualNegative NumbersAC9M6N01NumberfullAdding and Subtracting FractionsAC9M6N05Shape and PositionvisualAngles on a Line and at a PointAC9M6M04Shape and PositionvisualCross-Sections and the Four QuadrantsAC9M6SP01Shape and PositionvisualTessellationsAC9M6SP03StatisticsvisualMean, Median, Mode and RangeAC9M6ST01StatisticsvisualComparing Two Data SetsAC9M6ST01StatisticsvisualStatistics in the MediaAC9M6ST02StatisticsvisualPlanning and Refining an InvestigationAC9M6ST03StatisticsvisualThe Probability ScaleAC9M6P01StatisticsvisualMore Trials, Closer ResultsAC9M6P02

Year 7

48 guides
AlgebraLike Terms and Collecting ThemAC9M7A02AlgebraExpanding BracketsAC9M7A02AlgebraSubstituting into FormulasAC9M7A01AlgebraSolving Equations and CheckingAC9M7A03AlgebraTables of Values and Plotting PatternsAC9M7A05AlgebraSimplifying and SubstitutingAC9M7A02AlgebrafullAngle RelationshipsAC9M7M04DecimalsDecimal Place Value and OrderingAC9M7N04DecimalsAdding and Subtracting DecimalsAC9M7N06DecimalsMultiplying and Dividing DecimalsAC9M7N06ComprehensionFinding the Answer, and Quoting ItAC9E7LA02ComprehensionInference — P.E.E.AC9E7LY05Essay WritingThe Paragraph — P.E.E.L.AC9E7LA04Essay WritingThe Narrative EssayAC9E7LE07LiteratureCharacter QuestionsAC9E7LE05LiteraturePoetry — What to Look ForAC9E7LE06Transactional WritingThe Formal LetterAC9E7LA03Transactional WritingThe Formal EmailAC9E7LY06FractionsEquivalent Fractions and SimplifyingAC9M7N04FractionsComparing and Ordering FractionsAC9M7N04FractionsAdding and Subtracting FractionsAC9M7N06FractionsMultiplying and Dividing FractionsAC9M7N06GeometryAngle Sums of Triangles and PolygonsAC9M7M05GeometryClassifying Triangles and QuadrilateralsAC9M7SP02GeometryTransformations on the Cartesian PlaneAC9M7SP03GeometryTwo-Dimensional Views and Sorting AlgorithmsAC9M7SP01Area and VolumeArea of Triangles and ParallelogramsAC9M7M01Area and VolumeVolume of PrismsAC9M7M02MeasurementfullCircles — Circumference and AreaAC9M7M03Number & AlgebrafullOrder of OperationsAC9M7N06Number & AlgebrafullAdding and Subtracting IntegersAC9M7N07Number & AlgebrafullSolving Two-Step EquationsAC9M7A03Number & AlgebrafullSquare Numbers and Square RootsAC9M7N01Number PropertiesIndex Notation and PowersAC9M7N02Number PropertiesPrime Factorisation, HCF and LCMAC9M7N02Number PropertiesPowers of 10 and EstimationAC9M7N03PercentagesFractions, Decimals and PercentagesAC9M7N04PercentagesFinding a Percentage of a QuantityAC9M7N06PercentagesPercentage Increase and DecreaseAC9M7N09Ratio and FinanceRatios and SimplifyingAC9M7N08Ratio and FinanceDividing a Quantity in a RatioAC9M7N08Ratio and FinanceProfit, Loss, Discount and GSTAC9M7N09Statistics and ProbabilityMean, Median, Mode and RangeAC9M7ST01Statistics and ProbabilityChoosing the Best Measure of CentreAC9M7ST01Statistics and ProbabilityData Displays and Stem-and-Leaf PlotsAC9M7ST02Statistics and ProbabilityPlanning a Statistical InvestigationAC9M7ST03Statistics and ProbabilityProbability of Single-Step EventsAC9M7P01Statistics and ProbabilityChance Experiments and SimulationsAC9M7P02

Year 8

35 guides
AlgebraExpanding, Factorising and SimplifyingAC9M8A01AlgebraLinear Equations and InequalitiesAC9M8A02AlgebraModelling and Graphing Linear RelationsAC9M8A03ComprehensionUsing Evidence and QuotationsAC9E8LY03ComprehensionTone and Imagery — How Writing WorksAC9E8LE05Essay WritingThe Descriptive EssayAC9E8LE06Essay WritingThe Argumentative EssayAC9E8LA03LiteratureTheme QuestionsAC9E8LE01LiteratureSetting, Mood and AtmosphereAC9E8LE03Transactional WritingThe Formal ReportAC9E8LA04Transactional WritingThe ReviewAC9E8LY06GraphsStraight Line GraphsAC9M8A02GraphsDrawing a Line — Table MethodAC9M8A02GraphsDrawing a Line — Gradient Intercept MethodAC9M8A02GraphsDrawing a Line — Dual Intercept MethodAC9M8A02MeasurementPerimeter and Area of Composite ShapesAC9M8M01MeasurementCircumference and Area of a CircleAC9M8M03MeasurementTime Zones and DurationAC9M8M04Number & MeasurementfullPythagoras' TheoremAC9M8M06Number & MeasurementfullExponent LawsAC9M8N02Number & MeasurementfullPercentages: Discount, Profit and GSTAC9M8N05Number & MeasurementfullRates, Speed and Unit ConversionAC9M8M05NumberRational, Irrational and RecurringAC9M8N01NumberFour Operations with IntegersAC9M8N04NumberPercentage Increase, Decrease and ProfitAC9M8N05NumberRatios and Rates in ContextAC9M8M07SolidsfullVolume and Surface Area of PrismsAC9M8M02GeometryCongruence and SimilarityAC9M8SP01GeometryProperties of QuadrilateralsAC9M8SP02GeometryPosition in Three DimensionsAC9M8SP03Statistics and ProbabilityHow Data Is CollectedAC9M8ST01Statistics and ProbabilityRandom and Non-Random SamplingAC9M8ST02Statistics and ProbabilityPlanning a Fair InvestigationAC9M8ST04Statistics and ProbabilityComplementary EventsAC9M8P01Statistics and ProbabilityTwo Events: Tables, Trees and VennAC9M8P02

Year 9

40 guides
Algebra — Equations & SurdsSimultaneous EquationsAC9M10A02Algebra — Equations & SurdsSurdsAC9M9N01AlgebraIndex LawsAC9M9A01AlgebraExponential EquationsAC9M9A01AlgebraExpanding — FOILAC9M9A02AlgebraFactorising — Common Factor & GroupingAC9M9A02AlgebraFactorising — Difference of Two SquaresAC9M9A02AlgebrafullFactorising TrinomialsAC9M9A02AlgebraSimplifying Algebraic FractionsAC9M9A02Analytical GeometryGradients — Comparing Gradients of Two LinesAC9M9A03Analytical GeometryGradients — Determining the Gradient from Another LineAC9M9A03Analytical GeometryDetermine a Straight Line EquationAC9M9A03DatafullScatter Plots and CorrelationAC9M9ST04ComprehensionEvaluation — Do You Agree?AC9E9LY03ComprehensionSummary — Finding the PointsAC9E9LY04Essay WritingThe Discursive EssayAC9E9LA04Essay WritingOpenings and EndingsAC9E9LE06LiteratureUnseen Poetry — The Full MethodAC9E9LE05LiteratureThe Literature Essay AnswerAC9E9LE04Transactional WritingLetter of Application and CVAC9E9LY06Transactional WritingThe Formal SpeechAC9E9LY07MeasurementVolume and Surface Area of Prisms and CylindersAC9M9M01MeasurementScientific NotationAC9M9M02MeasurementError in MeasurementAC9M9M04MeasurementDirect Proportion, Rates and ScaleAC9M9M05ProbabilityfullProbability with Venn DiagramsAC9M9P02QuadraticsGraphing Quadratic FunctionsAC9M9A04QuadraticsSolving Quadratic EquationsAC9M9A04QuadraticsModelling with Linear and Quadratic FunctionsAC9M9A05SimilarityfullSimilar Triangles and Scale FactorAC9M9M03SimilarityfullProbability TreesAC9M9P01GeometryWhy the Trig Ratios Are ConstantAC9M9SP01GeometryEnlargement and What It PreservesAC9M9SP02GeometryAlgorithms from Constructions and TheoremsAC9M9SP03Statistics and ProbabilityReading Survey Reports CriticallyAC9M9ST01Statistics and ProbabilityComparing Multiple Data SetsAC9M9ST03Statistics and ProbabilityCompound Events With and Without ReplacementAC9M9P01Statistics and ProbabilitySimulating Compound EventsAC9M9P03TrigonometryThe BasicsAC9M9M03TrigonometryCalculate an Identity Without a CalculatorAC9M9M03

Year 10

54 guides
AlgebraExpanding and FactorisingAC9M10A01AlgebraCompleting the Square and the DiscriminantAC9M10A01AlgebraSimultaneous Equations AlgebraicallyAC9M10A02AlgebraSolving Quadratic Equations by FactorisingAC9M10A01Data and ProbabilityScatterplots and AssociationAC9M10ST03Data and ProbabilityTree Diagrams, Independence and VennAC9M10P01Data and ProbabilityDepreciation, Inflation and CurrencyAC9M10A04ComprehensionLiteral Questions and QuotingAC9E10LY05ComprehensionInference Questions — P.E.E.AC9E10LY05ComprehensionEvaluation QuestionsAC9E10LY03ComprehensionAppreciation Questions — N.Q.E.L.AC9E10LA03ComprehensionSummary WritingAC9E10LY05Essay WritingThe Reflective Essay — Writing with VoiceAC9E10LE08Essay WritingPlanning and Editing Under Time PressureAC9E10LA04LiteratureComparing Two TextsAC9E10LE06LiteratureContext and InterpretationAC9E10LE03Transactional WritingThe News ArticleAC9E10LY06Transactional WritingThe Letter to the EditorAC9E10LA08Financial MathsSimple Interest and Hire PurchaseAC9M10A04Financial MathsCalculate Investment InterestAC9M10A04Financial MathsInvestments with Multiple RatesAC9M10A04Graphs and FunctionsSketching a Parabola and TransformationsAC9M10A05Graphs and FunctionsExponentials, Hyperbolas and CirclesAC9M10A03Graphs and FunctionsDistance, Midpoint and Line RelationshipsAC9M10A02FunctionsThe Parabola — Given the Turning PointAC9M10A05FunctionsThe Parabola — Given the InterceptsAC9M10A05GeometryPythagoras in Three DimensionsAC9M10M03GeometryCongruence and Similarity ProofsAC9M10SP01GeometryCircle TheoremsExtensionGeometryDeductive Reasoning and ProofAC9M10SP01Inequalities and RegionsLinear Inequalities on a GraphAC9M10A02Inequalities and RegionsSimultaneous Equations from a GraphAC9M10A02LogarithmsfullLogarithmsExtensionMeasurementAngles of Elevation and DepressionAC9M10M03MeasurementSurface Area and Volume of Composite SolidsAC9M10M01MeasurementMeasurement Error and AccuracyAC9M10M04MeasurementLogarithmic ScalesAC9M10M02MeasurementModelling with Proportion and ScalingAC9M10M05Algebra & TrigonometryThe Quadratic FormulaAC9M10A01Algebra & TrigonometrySine Rule and Cosine RuleExtensionNetworksNetworks and ConnectednessAC9M10SP02NetworksAlgorithms on NetworksAC9M10SP03NumberApproximation and Exact ValuesAC9M10N01PatternsArithmetic SequenceExtensionPatternsGeometric SequenceExtensionData and ProbabilityTwo-Way TablesAC9M10ST04Data and ProbabilityConditional ProbabilityAC9M10P01Data and ProbabilitySimulating Conditional ProbabilityAC9M10P02StatisticsBoxplots and Comparing DistributionsAC9M10ST02StatisticsfullBias in Statistical ClaimsAC9M10ST01StatisticsfullRunning a Statistical InvestigationAC9M10ST05StatisticsfullStandard DeviationExtensionSurds and IndicesSimplifying and Operating with SurdsAC9M10A01Surds and IndicesIndex Laws and Rational IndicesAC9M10A01