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Skills with a written lesson, by school stageMathematics K–10: 236 of 236 skills have a lesson. Kindergarten: 6 of 6; Years 1–2: 14 of 14; Years 3–4: 13 of 13; Years 5–6: 15 of 15; Years 7–8: 46 of 46; Years 9–10: 142 of 142. English K–10: 325 of 363 skills have a lesson. Kindergarten: 57 of 57; Years 1–2: 52 of 52; Years 3–4: 71 of 71; Years 5–6: 71 of 71; Years 7–8: 57 of 57; Years 9–10: 17 of 55.Mathematics K–10236 of 236 skills have a lessonKindergarten6 of 6Years 1–214 of 14Years 3–413 of 13Years 5–615 of 15Years 7–846 of 46Years 9–10142 of 142English K–10325 of 363 skills have a lessonKindergarten57 of 57Years 1–252 of 52Years 3–471 of 71Years 5–671 of 71Years 7–857 of 57Years 9–1017 of 55Has a lessonNot written yetSource: the platform’s skill trees and lessonfilesSkills with a written lesson, by school stageMathematics K–10: 236 of 236 skills have a lesson. Kindergarten: 6 of 6; Years 1–2: 14 of 14; Years 3–4: 13 of 13; Years 5–6: 15 of 15; Years 7–8: 46 of 46; Years 9–10: 142 of 142. English K–10: 325 of 363 skills have a lesson. Kindergarten: 57 of 57; Years 1–2: 52 of 52; Years 3–4: 71 of 71; Years 5–6: 71 of 71; Years 7–8: 57 of 57; Years 9–10: 17 of 55.Mathematics K–10236 of 236 skills have a lessonKindergarten6 of 6Years 1–214 of 14Years 3–413 of 13Years 5–615 of 15Years 7–846 of 46Years 9–10142 of 142English K–10325 of 363 skills have a lessonKindergarten57 of 57Years 1–252 of 52Years 3–471 of 71Years 5–671 of 71Years 7–857 of 57Years 9–1017 of 55Has a lessonNot written yetSource: the platform’s skill trees and lesson files

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English K–10 · Year 8

57 lessons in this selection

Learning tree for English K–10 · Year 8 57 skills · 11 topics · builds on 46 skills from earlier years
Learning tree for English K–10 · Year 857 skills in lanes by topic, in sequence from left to right. Each arrow runs from a skill to one that builds on it. The list that follows names every skill and what it builds on.Reading, viewing and listening to textsUnderstanding and responding to texts AUnderstanding and responding to texts BUnderstanding and responding to texts CEssay craft and composing written textsImaginative and poetic compositionRepresenting and multimodal compositionSentence-level grammar and punctuationWord-level language and spellingPlanning, monitoring, revising and reflectingSpeakingFrom earlier yearsStep 1Step 2Step 3Step 4Step 5Supports inferenceswith evidence fromthe textMonitors, repairs andevaluates owncomprehensionstrategiesSummarises andorganises the mainideas of a textChooses texts andreading approachesfor a purposeUses signposts andstructure to findinformation fastUses morphology andetymology to unlockunfamiliar wordsExplains howperspective is shapedby context andauthorial choiceIdentifies wherewords come fromRe-reads closely touncover main ideasand layers of meaningExplains a personalresponse and where itcomes fromReads strategically:pathways, contextcues and readingaloudExplores how cultureand time shapelanguage in textsSustains wide readingacross diverseperspectivesReflects on whatreading has taughtyouReads dialogue,quoted speech andreported speechAnalyses characterattributes,archetypes anddevelopmentExplains why anauthor structured atext the way they didAnalyses figurativelanguage, symbol andimagery in literatureAnalyses narrativeconventions and theexpectations they setCollects and usesnewly met words,includingmetalanguageAnalyses narrativevoice, focaliser andpersonAnalyses howcharacters areconstructed and whatthey representIdentifies imagery,simile, metaphor andpersonification andanalyses their effectAnalyses narrativeconventions and theidentities theydepictUnderstands texts asacts ofrepresentation anddescribes them withmetalanguageAnalyses images, filmand multimodal textsusing their codes andconventionsDistinguishes factfrom opinion,identifies bias andquestions the authorJudges argument,objectivity and theauthority of textsIdentifies therecurring messages inliteratureWeighs modality andshades of meaningbetween synonymsExplains how textsposition readers toaccept a point ofviewAnalyses howarguments areconstructed andevidencedExplains how culturalcontext shapes a textand its languageAnalyses personalvoice and how a textbuilds authorityIdentifies themes andexplains how theydevelop across a textDescribes thestylistic andaesthetic qualitiesof a textCompares andsynthesises texts onthe same topicExplains genre codesand the texts thatbreak themAnalyses genreconventions and howtexts exhibit orchallenge themAnalyses connectionsbetween texts,including adaptationsand appropriationsExplains why textsare valueddifferently indifferent contextsVaries sentence typeand length forclarity and effectsuited to textpurposeControls tense,referencing,substitution andparagraph transitionsacross a whole textUses metaphor,hyperbole, oxymoronand allusion foreffectChooses informativeformats and organisesideas into logicallysequenced paragraphsWrites objectivearguments, blendsthem with personalones, and presentsmultiple viewpointsTargets rhetoricaldevices and modalityto qualify orstrengthen argumentsBuilds a statement ofposition and logicallines of argument toa rhetoricalconclusionControls thestructural andgrammaticalconventions ofimaginative,informative andpersuasive writingStructures andsequences textscohesively andorients the reader inthe openingUses imagery,figurative languageand modality tocreate tone,atmosphere and moodDiscusses a centralidea from personaland objectivepositionsComposes persuasivetexts with a definingthesis, elaborationparagraphs and asynthesisingconclusionUses rhetoricallanguage to shapeideas and express aperspectiveWrites a structuredanalytical text withintroduction,supporting points andconclusionSupports argumentswith subjective andobjective evidence,and refutescounterargumentsEmbeds textualevidence withinsentences to supporta personalperspectiveComposes informativetexts that summariseconceptualinformationCrafts imaginativetexts with deliberatechoices of setting,character, voice andthemeSelects poetic formsto express ideasdescriptivelyCreates imaginativetexts that driveplot, developcharacter and buildplace and atmosphereSelects poetic formsand features toexpress ideas andpersonal perspectivesExperiments withunpredictablestructural featuresto engage a readerDevelops thematicelements around acentral complicationor conflictReshapes aspects oftexts to create newmeaningChooses multimodalfeatures for anaudience andacknowledges sourcesComposes visual andmultimodal texts thatcreate tone,atmosphere and moodUses appositives andnominalisation towrite succinctly andauthoritativelyEmbeds adjectivalclauses andrepositions adverbialclauses for effectUses parentheses,dashes and hyphens,and experiments withpunctuation foreffectUses capitals, commasand quotation marksconsistently across atextSelects noun groupsand verb forms tocontrol clarity andexpress modalityEmbeds adjectivalclauses and positionsadverbial phrases andclauses to clarifymeaningApplies a wide rangeof punctuation tocontrol clarity, paceand reader responseConstructs variedsentence structuresand controls the foursentence types forpurposeControls agreement,prepositions,articles,conjunctions, linkingdevices and pronounsfor cohesionControls active andpassive voice andtense for particularpurposesApplies punctuationconventions forquotations and citingsourcesUses Tier 2 and Tier3 vocabulary,synonyms and modalitywith controlAdds derivationalsuffixes andassimilated prefixesto base words androotsSegments unfamiliarmultisyllabic wordsand appliesinfrequent graphemesSelectstopic-specificvocabulary thatcontributes to thestylistic features ofwritingSpells unfamiliar,complex and technicalwords usingphonological,orthographic andmorphologicalknowledgeAssesses thereliability andauthority of sourceswhen researchingPlans hybrid textsand researches fromseveral sources usingprint or digitaltoolsJustifies authorialdecisions and editsown and others'writing againstcriteriaIntegratesinformation andperspectives fromdifferent sourcesinto informed textsUses model texts toplan and to shapecompositional choicesMonitors accuracy andresponds to verbaland written feedbackReflects on owncomposition usingtechnical vocabularyDevelops a coherentthesis for extendedanalytical andpersuasive textsPlans a logicalsequence of argumentsand sets goals atconceptual, text andparagraph levelProducesco-constructed textsthat representdifferent ideas andvaluesInitiates andsustains a discussionby questioning,building on andevaluating ideasApplies interactiveand active listeningstrategies and givesfeedback to a speakerPresents a researchedmultimodal argumentwith references andpersuasive techniquesWrites a persuasivetext with a statedposition, sequencedarguments and aconclusionDelivers apresentation suitedto purpose andaudience, moderatinglength, content andstyleExperiments withvolume, pace andintonation andrecognises the effecton the audienceParticipates ininformal, speculativeand exploratorydiscussion abouttexts and ideasDelivers a spokentext with control ofintonation, emphasis,volume, pace andtimingUses rhetoricalstrategies to engagean audience and evokean emotional responseCreates spoken,signed orcommunicated textsthat convey ideas andviewpoints to anaudience
  1. Reading, viewing and listening to texts

    1. Re-reads closely to uncover main ideas and layers of meaningBuilds on: Supports inferences with evidence from the text (Years 5–6); Summarises and organises the main ideas of a text (Years 5–6)
    2. Explores how culture and time shape language in textsBuilds on: Identifies where words come from (Years 5–6); Explains how perspective is shaped by context and authorial choice (Years 5–6)
    3. Explains a personal response and where it comes fromBuilds on: Chooses texts and reading approaches for a purpose (Years 5–6)
    4. Reads strategically: pathways, context cues and reading aloudBuilds on: Uses signposts and structure to find information fast (Years 5–6); Uses morphology and etymology to unlock unfamiliar words (Years 5–6)
    5. Sustains wide reading across diverse perspectivesBuilds on: Explains a personal response and where it comes from
    6. Reflects on what reading has taught youBuilds on: Sustains wide reading across diverse perspectives; Monitors, repairs and evaluates own comprehension strategies (Years 5–6)
  2. Understanding and responding to texts A

    1. Analyses how characters are constructed and what they representBuilds on: Analyses character attributes, archetypes and development (Years 5–6)
    2. Identifies imagery, simile, metaphor and personification and analyses their effectBuilds on: Analyses figurative language, symbol and imagery in literature (Years 5–6)
    3. Analyses narrative conventions and the identities they depictBuilds on: Analyses narrative conventions and the expectations they set (Years 5–6)
    4. Analyses narrative voice, focaliser and personBuilds on: Explains how perspective is shaped by context and authorial choice (Years 5–6); Reads dialogue, quoted speech and reported speech (Years 3–4)
    5. Understands texts as acts of representation and describes them with metalanguageBuilds on: Collects and uses newly met words, including metalanguage (Years 5–6); Explains how perspective is shaped by context and authorial choice (Years 5–6)
    6. Analyses images, film and multimodal texts using their codes and conventionsBuilds on: Explains why an author structured a text the way they did (Years 5–6); Understands texts as acts of representation and describes them with metalanguage
  3. Understanding and responding to texts B

    1. Analyses how arguments are constructed and evidencedBuilds on: Judges argument, objectivity and the authority of texts (Years 5–6)
    2. Explains how texts position readers to accept a point of viewBuilds on: Explains how perspective is shaped by context and authorial choice (Years 5–6); Distinguishes fact from opinion, identifies bias and questions the author (Years 5–6)
    3. Explains how cultural context shapes a text and its languageBuilds on: Explains how texts position readers to accept a point of view; Explores how culture and time shape language in texts
    4. Describes the stylistic and aesthetic qualities of a textBuilds on: Weighs modality and shades of meaning between synonyms (Years 5–6); Understands texts as acts of representation and describes them with metalanguage
    5. Identifies themes and explains how they develop across a textBuilds on: Identifies the recurring messages in literature (Years 5–6); Re-reads closely to uncover main ideas and layers of meaning
    6. Analyses personal voice and how a text builds authorityBuilds on: Analyses how arguments are constructed and evidenced
  4. Understanding and responding to texts C

    1. Analyses genre conventions and how texts exhibit or challenge themBuilds on: Explains genre codes and the texts that break them (Years 5–6); Analyses narrative conventions and the identities they depict
    2. Analyses connections between texts, including adaptations and appropriationsBuilds on: Analyses genre conventions and how texts exhibit or challenge them; Compares and synthesises texts on the same topic (Years 5–6)
    3. Explains why texts are valued differently in different contextsBuilds on: Describes the stylistic and aesthetic qualities of a text; Analyses connections between texts, including adaptations and appropriations
  5. Essay craft and composing written texts

    1. Controls the structural and grammatical conventions of imaginative, informative and persuasive writingBuilds on: Controls tense, referencing, substitution and paragraph transitions across a whole text (Years 5–6); Varies sentence type and length for clarity and effect suited to text purpose (Years 5–6)
    2. Discusses a central idea from personal and objective positionsBuilds on: Writes objective arguments, blends them with personal ones, and presents multiple viewpoints (Years 5–6)
    3. Uses imagery, figurative language and modality to create tone, atmosphere and moodBuilds on: Uses metaphor, hyperbole, oxymoron and allusion for effect (Years 5–6); Targets rhetorical devices and modality to qualify or strengthen arguments (Years 5–6)
    4. Composes persuasive texts with a defining thesis, elaboration paragraphs and a synthesising conclusionBuilds on: Builds a statement of position and logical lines of argument to a rhetorical conclusion (Years 5–6); Writes objective arguments, blends them with personal ones, and presents multiple viewpoints (Years 5–6)
    5. Uses rhetorical language to shape ideas and express a perspectiveBuilds on: Targets rhetorical devices and modality to qualify or strengthen arguments (Years 5–6)
    6. Structures and sequences texts cohesively and orients the reader in the openingBuilds on: Controls tense, referencing, substitution and paragraph transitions across a whole text (Years 5–6)
    7. Writes a structured analytical text with introduction, supporting points and conclusionBuilds on: Chooses informative formats and organises ideas into logically sequenced paragraphs (Years 5–6); Structures and sequences texts cohesively and orients the reader in the opening
    8. Supports arguments with subjective and objective evidence, and refutes counterargumentsBuilds on: Composes persuasive texts with a defining thesis, elaboration paragraphs and a synthesising conclusion
    9. Embeds textual evidence within sentences to support a personal perspectiveBuilds on: Writes a structured analytical text with introduction, supporting points and conclusion
    10. Composes informative texts that summarise conceptual informationBuilds on: Writes a structured analytical text with introduction, supporting points and conclusion
  6. Imaginative and poetic composition

    1. Creates imaginative texts that drive plot, develop character and build place and atmosphereBuilds on: Crafts imaginative texts with deliberate choices of setting, character, voice and theme (Years 5–6)
    2. Selects poetic forms and features to express ideas and personal perspectivesBuilds on: Selects poetic forms to express ideas descriptively (Years 5–6)
    3. Experiments with unpredictable structural features to engage a readerBuilds on: Creates imaginative texts that drive plot, develop character and build place and atmosphere
    4. Develops thematic elements around a central complication or conflictBuilds on: Creates imaginative texts that drive plot, develop character and build place and atmosphere
    5. Reshapes aspects of texts to create new meaningBuilds on: Creates imaginative texts that drive plot, develop character and build place and atmosphere
  7. Representing and multimodal composition

    1. Composes visual and multimodal texts that create tone, atmosphere and moodBuilds on: Chooses multimodal features for an audience and acknowledges sources (Years 5–6)
  8. Sentence-level grammar and punctuation

    1. Embeds adjectival clauses and positions adverbial phrases and clauses to clarify meaningBuilds on: Embeds adjectival clauses and repositions adverbial clauses for effect (Years 5–6)
    2. Selects noun groups and verb forms to control clarity and express modalityBuilds on: Uses appositives and nominalisation to write succinctly and authoritatively (Years 5–6)
    3. Applies a wide range of punctuation to control clarity, pace and reader responseBuilds on: Uses parentheses, dashes and hyphens, and experiments with punctuation for effect (Years 5–6)
    4. Constructs varied sentence structures and controls the four sentence types for purposeBuilds on: Varies sentence type and length for clarity and effect suited to text purpose (Years 5–6)
    5. Controls agreement, prepositions, articles, conjunctions, linking devices and pronouns for cohesionBuilds on: Controls tense, referencing, substitution and paragraph transitions across a whole text (Years 5–6)
    6. Controls active and passive voice and tense for particular purposesBuilds on: Controls tense, referencing, substitution and paragraph transitions across a whole text (Years 5–6)
    7. Applies punctuation conventions for quotations and citing sourcesBuilds on: Uses capitals, commas and quotation marks consistently across a text (Years 5–6); Embeds textual evidence within sentences to support a personal perspective
  9. Word-level language and spelling

    1. Spells unfamiliar, complex and technical words using phonological, orthographic and morphological knowledgeBuilds on: Segments unfamiliar multisyllabic words and applies infrequent graphemes (Years 5–6); Adds derivational suffixes and assimilated prefixes to base words and roots (Years 5–6)
    2. Selects topic-specific vocabulary that contributes to the stylistic features of writingBuilds on: Uses Tier 2 and Tier 3 vocabulary, synonyms and modality with control (Years 5–6)
  10. Planning, monitoring, revising and reflecting

    1. Uses model texts to plan and to shape compositional choicesBuilds on: Plans hybrid texts and researches from several sources using print or digital tools (Years 5–6)
    2. Monitors accuracy and responds to verbal and written feedbackBuilds on: Justifies authorial decisions and edits own and others' writing against criteria (Years 5–6)
    3. Integrates information and perspectives from different sources into informed textsBuilds on: Assesses the reliability and authority of sources when researching (Years 5–6)
    4. Reflects on own composition using technical vocabularyBuilds on: Monitors accuracy and responds to verbal and written feedback
    5. Develops a coherent thesis for extended analytical and persuasive textsBuilds on: Composes persuasive texts with a defining thesis, elaboration paragraphs and a synthesising conclusion; Writes a structured analytical text with introduction, supporting points and conclusion
    6. Plans a logical sequence of arguments and sets goals at conceptual, text and paragraph levelBuilds on: Develops a coherent thesis for extended analytical and persuasive texts
    7. Produces co-constructed texts that represent different ideas and valuesBuilds on: Plans a logical sequence of arguments and sets goals at conceptual, text and paragraph level
  11. Speaking

    1. Participates in informal, speculative and exploratory discussion about texts and ideasBuilds on: Initiates and sustains a discussion by questioning, building on and evaluating ideas (Years 5–6); Applies interactive and active listening strategies and gives feedback to a speaker (Years 5–6)
    2. Delivers a spoken text with control of intonation, emphasis, volume, pace and timingBuilds on: Delivers a presentation suited to purpose and audience, moderating length, content and style (Years 5–6); Experiments with volume, pace and intonation and recognises the effect on the audience (Years 5–6)
    3. Creates spoken, signed or communicated texts that convey ideas and viewpoints to an audienceBuilds on: Delivers a spoken text with control of intonation, emphasis, volume, pace and timing; Identifies imagery, simile, metaphor and personification and analyses their effect
    4. Uses rhetorical strategies to engage an audience and evoke an emotional responseBuilds on: Delivers a spoken text with control of intonation, emphasis, volume, pace and timing; Presents a researched multimodal argument with references and persuasive techniques (Years 5–6); Writes a persuasive text with a stated position, sequenced arguments and a conclusion (Years 3–4)
  • From an earlier year — optional

Sequence: NSW syllabus, as used on the learning platform for English K–10; detailed outcome alignment for NSW is not verified.

Reading and viewingReading, viewing and listening to texts

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Re-reads closely to uncover main ideas and layers of meaningStructure
  1. Introduction
  2. Prerequisite review
  3. The idea
  4. Worked examples
  5. Practice set
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Explores how culture and time shape language in textsStructure
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Explains a personal response and where it comes fromStructure
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Reads strategically: pathways, context cues and reading aloudStructure
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Reflects on what reading has taught youStructure
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Sustains wide reading across diverse perspectivesStructure
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Reading and viewingUnderstanding and responding to texts A

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Analyses how characters are constructed and what they representStructure
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Identifies imagery, simile, metaphor and personification and analyses their effectStructure
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Analyses narrative conventions and the identities they depictStructure
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Analyses narrative voice, focaliser and personStructure
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Understands texts as acts of representation and describes them with metalanguageStructure
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Analyses images, film and multimodal texts using their codes and conventionsStructure
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Reading and viewingUnderstanding and responding to texts B

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Analyses how arguments are constructed and evidencedStructure
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Explains how cultural context shapes a text and its languageStructure
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Explains how texts position readers to accept a point of viewStructure
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Describes the stylistic and aesthetic qualities of a textStructure
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Identifies themes and explains how they develop across a textStructure
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Analyses personal voice and how a text builds authorityStructure
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Reading and viewingUnderstanding and responding to texts C

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Analyses genre conventions and how texts exhibit or challenge themStructure
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Analyses connections between texts, including adaptations and appropriationsStructure
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Explains why texts are valued differently in different contextsStructure
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Writing and representingEssay craft and composing written texts

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Controls the structural and grammatical conventions of imaginative, informative and persuasive writingStructure
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Discusses a central idea from personal and objective positionsStructure
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Writes a structured analytical text with introduction, supporting points and conclusionStructure
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Supports arguments with subjective and objective evidence, and refutes counterargumentsStructure
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Uses imagery, figurative language and modality to create tone, atmosphere and moodStructure
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Embeds textual evidence within sentences to support a personal perspectiveStructure
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Composes persuasive texts with a defining thesis, elaboration paragraphs and a synthesising conclusionStructure
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Uses rhetorical language to shape ideas and express a perspectiveStructure
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Structures and sequences texts cohesively and orients the reader in the openingStructure
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Composes informative texts that summarise conceptual informationStructure
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Writing and representingImaginative and poetic composition

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Experiments with unpredictable structural features to engage a readerStructure
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Creates imaginative texts that drive plot, develop character and build place and atmosphereStructure
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Selects poetic forms and features to express ideas and personal perspectivesStructure
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Develops thematic elements around a central complication or conflictStructure
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Reshapes aspects of texts to create new meaningStructure
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Writing and representingRepresenting and multimodal composition

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Composes visual and multimodal texts that create tone, atmosphere and moodStructure
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Writing and representingSentence-level grammar and punctuation

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Embeds adjectival clauses and positions adverbial phrases and clauses to clarify meaningStructure
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Selects noun groups and verb forms to control clarity and express modalityStructure
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Applies a wide range of punctuation to control clarity, pace and reader responseStructure
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Applies punctuation conventions for quotations and citing sourcesStructure
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Constructs varied sentence structures and controls the four sentence types for purposeStructure
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Controls agreement, prepositions, articles, conjunctions, linking devices and pronouns for cohesionStructure
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Controls active and passive voice and tense for particular purposesStructure
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Writing and representingWord-level language and spelling

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Spells unfamiliar, complex and technical words using phonological, orthographic and morphological knowledgeStructure
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Selects topic-specific vocabulary that contributes to the stylistic features of writingStructure
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Writing and representingPlanning, monitoring, revising and reflecting

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Produces co-constructed texts that represent different ideas and valuesStructure
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Uses model texts to plan and to shape compositional choicesStructure
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Monitors accuracy and responds to verbal and written feedbackStructure
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Plans a logical sequence of arguments and sets goals at conceptual, text and paragraph levelStructure
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Reflects on own composition using technical vocabularyStructure
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Integrates information and perspectives from different sources into informed textsStructure
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Develops a coherent thesis for extended analytical and persuasive textsStructure
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Speaking and listeningSpeaking

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Creates spoken, signed or communicated texts that convey ideas and viewpoints to an audienceStructure
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Participates in informal, speculative and exploratory discussion about texts and ideasStructure
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Uses rhetorical strategies to engage an audience and evoke an emotional responseStructure
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Delivers a spoken text with control of intonation, emphasis, volume, pace and timingStructure
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Curriculum details for English K–10

NSW school sequence.

Stage 4 in the NSW source sequence · Years 7–8.

The English K–10 collection follows its named source sequence; detailed outcome alignment for New South Wales is not verified.

In English K–10, some source stages span two years and share lessons; choose a topic within the selected year level and revisit its foundation explanations when needed.

Mathematics K–10 · Year 8

46 lessons in this selection

Learning tree for Mathematics K–10 · Year 8 46 skills · 10 topics · builds on 18 skills from earlier years
Learning tree for Mathematics K–10 · Year 846 skills in lanes by topic, in sequence from left to right. Each arrow runs from a skill to one that builds on it. The list that follows names every skill and what it builds on.Integers, ratios and percentagesAlgebraic techniques and linear equationsFractions, decimals and percentages (Stage 4)Primes and indicesAngle relationships and circlesLength, area and volume (Stage 4)Geometrical figures and parallel linesRight-angled triangles (Pythagoras)Probability experimentsData classification and analysisFrom earlier yearsStep 1Step 2Step 3Step 4Step 5Step 6Subtracts two-digitnumbers with andwithout regroupingDivides two- andthree-digit numbersby a one-digitnumber, withremaindersMultiplies two- andthree-digit numbersby a one-digit numberPlaces numbers up to100 on a number lineFinds equivalentfractions usingmodels andmultiplicationAdds, subtracts andmultiplies decimalsConverts betweenfractions, decimalsand percentagesPlots and readspoints in all fourquadrants of theCartesian planeOrders, adds andsubtracts positiveand negative integersApplies the order ofoperations towhole-numbercalculationsSimplifies ratios anddivides a quantity ina given ratioCalculates apercentage of aquantity, includingdiscountsMultiplies anddivides integers,including with theorder of operationsUses rates to comparequantities, includingbest buys and speedInterpretsdistance–time graphsRecallsmultiplication factsto 10 × 10Describes numberpatterns and writesthe ruleUses algebraicnotation withpronumeralsSimplifies algebraicexpressions bycollecting like termsSolves one-steplinear equationsPlots straight-linegraphs from a tableof valuesSubstitutes valuesinto algebraicexpressions andformulasExpands expressionswith brackets usingthe distributive lawSolves quadraticequations of the formax² = cFinds the gradientand y-intercept andwrites the equationof a lineFactorises algebraicexpressions using thehighest common factorSolves two-steplinear equations,including withbracketsSolves linearequations graphicallyusing the point ofintersectionMultiplies anddivides fractions andmixed numeralsDivides decimals bywhole numbers and bydecimalsExpresses onequantity as afraction orpercentage of anotherCalculates percentageincrease anddecrease, includingGSTExpresses wholenumbers as productsof their primefactorsCalculates squares,cubes, square rootsand cube rootsUses index notationand applies the indexlaws with numericalbasesUses formulas to findthe area ofrectangles andtrianglesCalculates the volumeof rectangular prismsCalculates thecircumference andarea of circlesFinds the area ofcomposite shapesCalculates the volumeof prisms andcylindersFinds unknown anglesusing angles at apoint, on a line andin trianglesCalculates theperimeter ofrectangles and simpleshapesCalculates perimetersof plane shapes,including compositefiguresUses formulas to findthe area ofparallelograms,trapeziums, rhombusesand kitesCalculates the volumeand capacity of rightprisms with variouscross-sectionsMeasures and drawsangles with aprotractorClassifies trianglesand quadrilateralsusing their side,angle and symmetrypropertiesUses the angle sum ofa quadrilateral tofind unknown anglesFinds unknown anglesformed when parallellines are cut by atransversalApplies Pythagoras'theorem to findunknown sides inright-angledtrianglesAssigns probabilitiesto simple events asfractionsCalculatestheoreticalprobabilities forsingle-stepexperimentsRuns experiments andcompares relativefrequency withtheoreticalprobabilityUses tables and treediagrams for two-stepexperimentsUses complementaryevents to calculateprobabilitiesCollects data andsorts objects intocategoriesRecords data intables using tallymarksDraws and interpretscolumn graphsCalculates the mean,median, mode andrange of a data setClassifies data ascategorical ornumerical, discreteor continuousChooses appropriatemeasures of centreand spread, includingthe effect ofoutliersConstructs frequencytables and histogramsfor numerical dataConstructs andinterprets dot plotsand stem-and-leafplotsDescribes the shapeof datadistributions,including symmetry,clusters and outliers
  1. Integers, ratios and percentages

    1. Orders, adds and subtracts positive and negative integersBuilds on: Places numbers up to 100 on a number line (Years 1–2); Subtracts two-digit numbers with and without regrouping (Years 1–2)
    2. Applies the order of operations to whole-number calculationsBuilds on: Multiplies two- and three-digit numbers by a one-digit number (Years 3–4); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
    3. Simplifies ratios and divides a quantity in a given ratioBuilds on: Finds equivalent fractions using models and multiplication (Years 5–6); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
    4. Calculates a percentage of a quantity, including discountsBuilds on: Converts between fractions, decimals and percentages (Years 5–6); Adds, subtracts and multiplies decimals (Years 5–6)
    5. Multiplies and divides integers, including with the order of operationsBuilds on: Orders, adds and subtracts positive and negative integers; Applies the order of operations to whole-number calculations
    6. Uses rates to compare quantities, including best buys and speedBuilds on: Simplifies ratios and divides a quantity in a given ratio; Divides decimals by whole numbers and by decimals
    7. Interprets distance–time graphsBuilds on: Uses rates to compare quantities, including best buys and speed; Plots and reads points in all four quadrants of the Cartesian plane (Years 5–6)
  2. Algebraic techniques and linear equations

    1. Describes number patterns and writes the ruleBuilds on: Recalls multiplication facts to 10 × 10 (Years 3–4)
    2. Uses algebraic notation with pronumeralsBuilds on: Describes number patterns and writes the rule; Applies the order of operations to whole-number calculations
    3. Simplifies algebraic expressions by collecting like termsBuilds on: Uses algebraic notation with pronumerals
    4. Solves one-step linear equationsBuilds on: Uses algebraic notation with pronumerals; Orders, adds and subtracts positive and negative integers
    5. Plots straight-line graphs from a table of valuesBuilds on: Uses algebraic notation with pronumerals; Plots and reads points in all four quadrants of the Cartesian plane (Years 5–6)
    6. Substitutes values into algebraic expressions and formulasBuilds on: Uses algebraic notation with pronumerals; Orders, adds and subtracts positive and negative integers
    7. Expands expressions with brackets using the distributive lawBuilds on: Simplifies algebraic expressions by collecting like terms
    8. Finds the gradient and y-intercept and writes the equation of a lineBuilds on: Plots straight-line graphs from a table of values
    9. Solves quadratic equations of the form ax² = cBuilds on: Solves one-step linear equations; Calculates squares, cubes, square roots and cube roots
    10. Solves two-step linear equations, including with bracketsBuilds on: Solves one-step linear equations; Expands expressions with brackets using the distributive law
    11. Factorises algebraic expressions using the highest common factorBuilds on: Expands expressions with brackets using the distributive law
    12. Solves linear equations graphically using the point of intersectionBuilds on: Plots straight-line graphs from a table of values; Solves two-step linear equations, including with brackets
  3. Fractions, decimals and percentages (Stage 4)

    1. Multiplies and divides fractions and mixed numeralsBuilds on: Finds equivalent fractions using models and multiplication (Years 5–6); Multiplies two- and three-digit numbers by a one-digit number (Years 3–4)
    2. Divides decimals by whole numbers and by decimalsBuilds on: Adds, subtracts and multiplies decimals (Years 5–6); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
    3. Expresses one quantity as a fraction or percentage of anotherBuilds on: Converts between fractions, decimals and percentages (Years 5–6); Calculates a percentage of a quantity, including discounts
    4. Calculates percentage increase and decrease, including GSTBuilds on: Calculates a percentage of a quantity, including discounts
  4. Primes and indices

    1. Expresses whole numbers as products of their prime factorsBuilds on: Recalls multiplication facts to 10 × 10 (Years 3–4); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
    2. Calculates squares, cubes, square roots and cube rootsBuilds on: Recalls multiplication facts to 10 × 10 (Years 3–4); Expresses whole numbers as products of their prime factors
    3. Uses index notation and applies the index laws with numerical basesBuilds on: Expresses whole numbers as products of their prime factors; Calculates squares, cubes, square roots and cube roots
  5. Angle relationships and circles

    1. Calculates the circumference and area of circlesBuilds on: Uses formulas to find the area of rectangles and triangles (Years 5–6); Adds, subtracts and multiplies decimals (Years 5–6)
    2. Finds the area of composite shapesBuilds on: Uses formulas to find the area of rectangles and triangles (Years 5–6); Calculates the circumference and area of circles
    3. Calculates the volume of prisms and cylindersBuilds on: Calculates the volume of rectangular prisms (Years 5–6); Calculates the circumference and area of circles
    4. Finds unknown angles using angles at a point, on a line and in trianglesBuilds on: Measures and draws angles with a protractor (Years 5–6); Solves one-step linear equations
  6. Length, area and volume (Stage 4)

    1. Calculates perimeters of plane shapes, including composite figuresBuilds on: Calculates the perimeter of rectangles and simple shapes (Years 3–4); Adds, subtracts and multiplies decimals (Years 5–6)
    2. Uses formulas to find the area of parallelograms, trapeziums, rhombuses and kitesBuilds on: Uses formulas to find the area of rectangles and triangles (Years 5–6)
    3. Calculates the volume and capacity of right prisms with various cross-sectionsBuilds on: Calculates the volume of rectangular prisms (Years 5–6); Uses formulas to find the area of parallelograms, trapeziums, rhombuses and kites
  7. Geometrical figures and parallel lines

    1. Classifies triangles and quadrilaterals using their side, angle and symmetry propertiesBuilds on: Measures and draws angles with a protractor (Years 5–6)
    2. Uses the angle sum of a quadrilateral to find unknown anglesBuilds on: Finds unknown angles using angles at a point, on a line and in triangles; Classifies triangles and quadrilaterals using their side, angle and symmetry properties
    3. Finds unknown angles formed when parallel lines are cut by a transversalBuilds on: Finds unknown angles using angles at a point, on a line and in triangles
  8. Right-angled triangles (Pythagoras)

    1. Applies Pythagoras' theorem to find unknown sides in right-angled trianglesBuilds on: Finds unknown angles using angles at a point, on a line and in triangles; Calculates squares, cubes, square roots and cube roots
  9. Probability experiments

    1. Calculates theoretical probabilities for single-step experimentsBuilds on: Assigns probabilities to simple events as fractions (Years 5–6); Converts between fractions, decimals and percentages (Years 5–6)
    2. Runs experiments and compares relative frequency with theoretical probabilityBuilds on: Calculates theoretical probabilities for single-step experiments
    3. Uses tables and tree diagrams for two-step experimentsBuilds on: Calculates theoretical probabilities for single-step experiments
    4. Uses complementary events to calculate probabilitiesBuilds on: Calculates theoretical probabilities for single-step experiments
  10. Data classification and analysis

    1. Classifies data as categorical or numerical, discrete or continuousBuilds on: Collects data and sorts objects into categories (Years 1–2)
    2. Chooses appropriate measures of centre and spread, including the effect of outliersBuilds on: Calculates the mean, median, mode and range of a data set (Years 5–6)
    3. Constructs and interprets dot plots and stem-and-leaf plotsBuilds on: Classifies data as categorical or numerical, discrete or continuous; Draws and interprets column graphs (Years 3–4)
    4. Constructs frequency tables and histograms for numerical dataBuilds on: Classifies data as categorical or numerical, discrete or continuous; Records data in tables using tally marks (Years 3–4)
    5. Describes the shape of data distributions, including symmetry, clusters and outliersBuilds on: Constructs and interprets dot plots and stem-and-leaf plots; Chooses appropriate measures of centre and spread, including the effect of outliers
  • From an earlier year — optional

Sequence: NSW syllabus, as used on the learning platform for Mathematics K–10; detailed outcome alignment for NSW is not verified.

Number and algebraIntegers, ratios and percentages

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Orders, adds and subtracts positive and negative integersStructure
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Applies the order of operations to whole-number calculationsStructure
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Simplifies ratios and divides a quantity in a given ratioStructure
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Calculates a percentage of a quantity, including discountsStructure
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Multiplies and divides integers, including with the order of operationsStructure
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Uses rates to compare quantities, including best buys and speedStructure
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Interprets distance–time graphsStructure
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Number and algebraAlgebraic techniques and linear equations

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Describes number patterns and writes the ruleStructure
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Uses algebraic notation with pronumeralsStructure
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Simplifies algebraic expressions by collecting like termsStructure
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Expands expressions with brackets using the distributive lawStructure
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Solves one-step linear equationsStructure
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Solves two-step linear equations, including with bracketsStructure
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Plots straight-line graphs from a table of valuesStructure
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Finds the gradient and y-intercept and writes the equation of a lineStructure
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Substitutes values into algebraic expressions and formulasStructure
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Factorises algebraic expressions using the highest common factorStructure
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Solves quadratic equations of the form ax² = cStructure
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Solves linear equations graphically using the point of intersectionStructure
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Number and algebraFractions, decimals and percentages (Stage 4)

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Multiplies and divides fractions and mixed numeralsStructure
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Divides decimals by whole numbers and by decimalsStructure
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Expresses one quantity as a fraction or percentage of anotherStructure
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Calculates percentage increase and decrease, including GSTStructure
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Number and algebraPrimes and indices

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Expresses whole numbers as products of their prime factorsStructure
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Calculates squares, cubes, square roots and cube rootsStructure
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Uses index notation and applies the index laws with numerical basesStructure
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Measurement and spaceAngle relationships and circles

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Finds unknown angles using angles at a point, on a line and in trianglesStructure
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Calculates the circumference and area of circlesStructure
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Finds the area of composite shapesStructure
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Calculates the volume of prisms and cylindersStructure
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Measurement and spaceLength, area and volume (Stage 4)

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Calculates perimeters of plane shapes, including composite figuresStructure
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Uses formulas to find the area of parallelograms, trapeziums, rhombuses and kitesStructure
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Calculates the volume and capacity of right prisms with various cross-sectionsStructure
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Measurement and spaceGeometrical figures and parallel lines

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Classifies triangles and quadrilaterals using their side, angle and symmetry propertiesStructure
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Uses the angle sum of a quadrilateral to find unknown anglesStructure
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Finds unknown angles formed when parallel lines are cut by a transversalStructure
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Measurement and spaceRight-angled triangles (Pythagoras)

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Applies Pythagoras' theorem to find unknown sides in right-angled trianglesStructure
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Statistics and probabilityProbability experiments

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Calculates theoretical probabilities for single-step experimentsStructure
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Runs experiments and compares relative frequency with theoretical probabilityStructure
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Uses tables and tree diagrams for two-step experimentsStructure
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Uses complementary events to calculate probabilitiesStructure
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Statistics and probabilityData classification and analysis

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Classifies data as categorical or numerical, discrete or continuousStructure
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Constructs and interprets dot plots and stem-and-leaf plotsStructure
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Constructs frequency tables and histograms for numerical dataStructure
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Chooses appropriate measures of centre and spread, including the effect of outliersStructure
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Describes the shape of data distributions, including symmetry, clusters and outliersStructure
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Curriculum details for Mathematics K–10

NSW school sequence.

Stage 4 in the NSW source sequence · Years 7–8.

The Mathematics K–10 collection follows its named source sequence; detailed outcome alignment for New South Wales is not verified.

In Mathematics K–10, some source stages span two years and share lessons; choose a topic within the selected year level and revisit its foundation explanations when needed.

Lessons are written for Mathematics and English first. Register interest in any other area.