NSW Syllabus
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English
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Early Stage One
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Objective A
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Speaking and Listening 1
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ENe-1A
Communicates with peers and known adults in informal and guided activities demonstrating emerging skills of group interaction
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ENe-1A
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Writing and Representing 1
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ENe-2A
Composes simple texts to convey an idea or message
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ENe-2A
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Handwriting and Using Digital Technologies
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ENe-3A
Produces most lower case and upper case letters and uses digital technologies to construct texts
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ENe-3A
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Reading and Viewing 1
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ENe-4A
Demonstrates developing skills and strategies to read, view and comprehend short, predictable texts on familiar topics in different media and technologies
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Recognise the letters of the alphabet and know there are lower and upper case letters (ACELA1440)
Examples
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Understand that spoken words are made up of sounds
Examples
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Recognise rhymes, syllables and sounds (phonemes) in spoken words (ACELA1439)
Examples
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Consistently identify words that start with the same initial sound
Examples
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segment words into onset and rime
Examples
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Identify the beginning and end sounds of words
Examples
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Segment simple spoken words into separate sounds
Examples
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recognise high-frequency words, including own name
Examples
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Use phonological strategies when reading, including letter-sound relationships
Play Activities 144Examples
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Use knowledge of letters and sounds to decode words, including those in initial, final and medial positions
Play Activities 194Examples
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Use comprehension strategies to understand and discuss texts listened to, viewed or read independently (ACELY1650)
Play Activities 178Examples
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Recognise the letters of the alphabet and know there are lower and upper case letters (ACELA1440)
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ENe-4A
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Spelling
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ENe-5A
Demonstrates developing skills in using letters, simple sound blends and some sight words to represent known words when spelling
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Know how to use onset and rime to spell words (ACELA1438)
Examples
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Identify patterns in words leading to the identification of word families
Examples
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Use and write beginning and ending sounds of spoken words
Examples
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Know that letters are used to represent sounds when writing words
Examples
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Use plural form when spelling some words
Examples
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Know how to use onset and rime to spell words (ACELA1438)
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ENe-5A
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Speaking and Listening 1
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Objective B
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Reading and Viewing 2
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ENe-8B
Demonstrates emerging skills and knowledge of texts to read and view, and shows developing awareness of purpose, audience and subject matter
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ENe-8B
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Grammar, Punctuation and Vocabulary
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ENe-9B
Demonstrates developing skills and knowledge in grammar, punctuation and vocabulary when responding to and composing texts
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ENe-9B
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Reading and Viewing 2
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Objective A
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Stage One
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Objective A
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Speaking and Listening 1
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EN1-1A
Communicates with a range of people in informal and guided activities demonstrating interaction skills and considers how own communication is adjusted in different situations
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EN1-1A
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Writing and Representing 1
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EN1-2A
Plans, composes and reviews a small range of simple texts for a variety of purposes on familiar topics for known readers and viewers
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EN1-2A
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Reading and Viewing 1
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EN1-4A
Draws on an increasing range of skills and strategies to fluently read, view and comprehend a range of texts on less familiar topics in different media and technologies
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Recognise grammatical patterns to enhance comprehension, eg action verbs, words or groups of words that tell who, what, when, where and how
Examples
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Understand that nouns represent people, places, things and ideas and can be, for example, common, proper, concrete or abstract, and that noun groups/phrases can be expanded using articles and adjectives (ACELA1468)
Examples
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Identify the parts of a simple sentence that represent 'What's happening?', 'Who or what is involved?' and the surrounding circumstances (ACELA1451)
Examples
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Understand how sentence punctuation is used to enhance meaning and fluency
Examples
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Identify word families and word origins to understand the meaning of unfamiliar words, eg base words, rhyming words and synonyms
Examples
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Recognise sound-letter matches including common vowel and consonant digraphs and consonant blends (ACELA1458)
Play Activities 338Examples
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Understand the variability of sound-letter matches (ACELA1459)
Play Activities 110Examples
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Recognise most sound-letter matches including silent letters, vowel/consonant digraphs and many less common sound-letter combinations (ACELA1474)
Play Activities 303Examples
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Automatically recognise irregular high-frequency words, eg 'come' and 'are'
Examples
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Use phonological, graphological, syntactic and semantic cues to decode and make meaning from written texts, eg using an increasing repertoire of high-frequency and sight words, segmenting words into syllables
Play Activities 227Examples
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Use comprehension strategies to build literal and inferred meaning and begin to analyse texts by drawing on growing knowledge of context, language and visual features and print and multimodal text structures (ACELY1660, ACELY1670)
Examples
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Use background knowledge of a topic to make inferences about the ideas in a text
Examples
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Predict author intent, series of events and possible endings in an imaginative, informative and persuasive text
Examples
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Identify visual representations of characters' actions, reactions, speech and thought processes in narratives, and consider how these images add to or contradict or multiply the meaning of accompanying words (ACELA1469)
Examples
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Recognise grammatical patterns to enhance comprehension, eg action verbs, words or groups of words that tell who, what, when, where and how
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EN1-4A
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Spelling
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EN1-5A
Uses a variety of strategies, including knowledge of sight words and letter-sound correspondences, to spell familiar words
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Know that regular one-syllable words are made up of letters and common letter clusters that correspond to the sounds heard, and how to use visual memory to write high-frequency words (ACELA1778)
Examples
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Understand how to use digraphs, long vowels, blends and silent letters to spell words, and use morphemes and syllabification to break up simple words and use visual memory to write irregular words (ACELA1471)
Examples
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Recognise common prefixes and suffixes and how they change a word's meaning (ACELA1455, ACELA1472)
Examples
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Isolate and write the initial, medial and final sound of a word
Examples
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Exchange one letter in a written word with a different letter to make a new word
Examples
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Use double consonants where appropriate, eg 'hopping'
Examples
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Recognise when a word is spelt incorrectly
Examples
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Use morphemic and phonological knowledge when spelling
Examples
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Know that regular one-syllable words are made up of letters and common letter clusters that correspond to the sounds heard, and how to use visual memory to write high-frequency words (ACELA1778)
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EN1-5A
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Speaking and Listening 1
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Objective B
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Speaking and Listening 2
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EN1-6B
Recognises a range of purposes and audiences for spoken language and recognises organisational patterns and features of predictable spoken texts
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EN1-6B
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Writing and Representing 2
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EN1-7B
Identifies how language use in their own writing differs according to their purpose, audience and subject matter
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EN1-7B
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Grammar, Punctuation and Vocabulary
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EN1-9B
Uses basic grammatical features, punctuation conventions and vocabulary appropriate to the type of text when responding to and composing texts
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Explore differences in words that represent people, places and things (nouns, including pronouns), happenings and states (verbs), qualities (adjectives) and details such as when, where and how (adverbs) (ACELA1452)
Examples
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Recognise that a preposition placed in front of a noun group can show where, when, eg 'on the box' (where), 'before my birthday' (when)
Examples
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Recognise that different types of punctuation, including full stops, question marks and exclamation marks, signal sentences that make statements, ask questions, express emotion or give commands (ACELA1449)
Examples
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Recognise that capital letters signal proper nouns and commas are used to separate items in lists (ACELA1465)
Examples
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Understand how texts are made cohesive through resources, for example word associations, synonyms, and antonyms (ACELA1464)
Examples
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Recognise, discuss and use creative word play, eg alliteration and onomatopoeia
Examples
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Compose sentences effectively using basic grammatical features and punctuation conventions
Examples
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Explore differences in words that represent people, places and things (nouns, including pronouns), happenings and states (verbs), qualities (adjectives) and details such as when, where and how (adverbs) (ACELA1452)
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EN1-9B
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Speaking and Listening 2
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Objective A
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Stage Two
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Objective A
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Speaking and Listening 1
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EN2-1A
Communicates in a range of informal and formal contexts by adopting a range of roles in group, classroom, school and community contexts
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EN2-1A
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Writing and Representing 1
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EN2-2A
Plans, composes and reviews a range of texts that are more demanding in terms of topic, audience and language
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Understand, interpret and experiment with a range of devices and deliberate word play in poetry and other literary texts, for example nonsense words, spoonerisms, neologisms and puns (ACELT1606)
Examples
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Experiment with visual, multimodal and digital processes to represent ideas encountered in texts
Examples
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Reread and edit texts for meaning, appropriate structure, grammatical choices and punctuation (ACELY1683)
Examples
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Reread and edit for meaning by adding, deleting or moving words or word groups to improve content and structure (ACELY1695)
Examples
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Understand, interpret and experiment with a range of devices and deliberate word play in poetry and other literary texts, for example nonsense words, spoonerisms, neologisms and puns (ACELT1606)
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EN2-2A
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Reading and Viewing 1
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EN2-4A
Uses an increasing range of skills, strategies and knowledge to fluently read, view and comprehend a range of texts on increasingly challenging topics in different media and technologies
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Know that word contractions are a feature of informal language and that apostrophes of contraction are used to signal missing letters (ACELA1480)
Examples
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Skim a text for overall message and scan for particular information, eg headings, key words
Examples
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Use graphological, phonological, syntactic and semantic strategies to respond to texts, eg knowledge of homophones, contractions, syllables, word families and common prefixes
Examples
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Identify syllables in multisyllabic words in order to support decoding of longer words in context to make meaning
Examples
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Recognise high frequency sight words (ACELA1486)
Examples
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Use comprehension strategies to build literal and inferred meaning to expand content knowledge, integrating and linking ideas and analysing and evaluating texts (ACELY1680, ACELY1692)
Play Activities 226Examples
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Use strategies to confirm predictions about author intent in imaginative, informative and persuasive texts
Examples
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Summarise a paragraph and indicate the main idea, key points or key arguments in imaginative, informative and persuasive texts
Examples
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Know that word contractions are a feature of informal language and that apostrophes of contraction are used to signal missing letters (ACELA1480)
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EN2-4A
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Spelling
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EN2-5A
Uses a range of strategies, including knowledge of letter-sound correspondences and common letter patterns, to spell familiar and some unfamiliar words
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Understand how to use strategies for spelling words, including spelling rules, knowledge of morphemic word families, spelling generalisations, and letter combinations including double letters (ACELA1485, ACELA1779)
Examples
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Recognise homophones and know how to use context to identify correct spelling (ACELA1780)
Examples
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Understand how knowledge of word origins supports spelling
Examples
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Use a variety of spelling strategies to spell high-frequency words correctly when composing imaginative and other texts
Examples
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Use morphemic, visual, syntactic, semantic and phonological knowledge when attempting to spell unknown words
Examples
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Use knowledge of alphabetical order to locate information in texts, eg dictionaries, glossaries
Examples
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Identify spelling errors in own writing and unknown texts and provide correct spelling
Examples
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Understand how to use strategies for spelling words, including spelling rules, knowledge of morphemic word families, spelling generalisations, and letter combinations including double letters (ACELA1485, ACELA1779)
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EN2-5A
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Speaking and Listening 1
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Objective B
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Writing and Representing 2
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EN2-7B
Identifies and uses language forms and features in their own writing appropriate to a range of purposes, audiences and contexts
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EN2-7B
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Reading and Viewing 2
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EN2-8B
Identifies and compares different kinds of texts when reading and viewing and shows an understanding of purpose, audience and subject matter
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Interpret how imaginative, informative and persuasive texts vary in purpose, structure and topic
Examples
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Identify organisational patterns and language features of print and visual texts appropriate to a range of purposes
Examples
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Understand how different types of texts vary in use of language choices, depending on their purpose and context (for example, tense and types of sentences) (ACELA1478)
Examples
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Recognise the use of figurative language in texts, eg similes, metaphors, idioms and personification, and discuss their effects
Examples
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Recognise how quotation marks are used in texts to signal dialogue, titles and quoted (direct) speech (ACELA1492)
Examples
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Discuss the nature and effects of some language devices used to enhance meaning and shape the reader's reaction, including rhythm and onomatopoeia in poetry and prose (ACELT1600)
Examples
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Identify and interpret the different forms of visual information, including maps, tables, charts, diagrams, animations and images
Examples
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Interpret how imaginative, informative and persuasive texts vary in purpose, structure and topic
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EN2-8B
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Grammar, Punctuation and Vocabulary
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EN2-9B
Uses effective and accurate sentence structure, grammatical features, punctuation conventions and vocabulary relevant to the type of text when responding to and composing texts
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Understand that paragraphs are a key organisational feature of written texts (ACELA1479)
Examples
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Understand how adverb groups/phrases and prepositional phrases work in different ways to provide circumstantial details about an activity (ACELA1495)
Examples
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Identify and use grammatical features, eg pronouns, conjunctions and connectives, to accurately link ideas and information
Examples
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Understand that verbs represent different processes (doing, thinking, saying, and relating) and that these processes are anchored in time through tense (ACELA1482)
Examples
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Investigate how quoted (direct) and reported (indirect) speech work in different types of text (ACELA1494)
Examples
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Use apostrophes for contractions
Examples
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Learn extended and technical vocabulary and ways of expressing opinion including modal verbs and adverbs (ACELA1484)
Examples
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Understand that paragraphs are a key organisational feature of written texts (ACELA1479)
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EN2-9B
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Writing and Representing 2
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Objective C
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Thinking Imaginatively, Creatively and Interpretively
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EN2-10C
Thinks imaginatively, creatively and interpretively about information, ideas and texts when responding to and composing texts
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EN2-10C
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Thinking Imaginatively, Creatively and Interpretively
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Objective D
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Expressing Themselves
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EN2-11D
Responds to and composes a range of texts that express viewpoints of the world similar to and different from their own
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EN2-11D
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Expressing Themselves
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Objective A
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Stage Three
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Objective A
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Writing and Representing
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EN3-2A
Composes, edits and presents well-structured and coherent texts
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Identify and explore underlying themes and central storylines in imaginative texts
Examples
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Understand, interpret and experiment with the use of imagery in imaginative texts, poetry and songs, eg similes, metaphors, personification and sound devices such as alliteration
Examples
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Reread and edit students' own and others' work using agreed criteria and explaining editing choices (ACELY1705, ACELY1715)
Examples
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Identify and explore underlying themes and central storylines in imaginative texts
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EN3-2A
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Reading and Viewing
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EN3-3A
Uses an integrated range of skills, strategies and knowledge to read, view and comprehend a wide range of texts in different media and technologies
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Understand how texts vary in purpose, structure and topic as well as the degree of formality (ACELA1504)
Examples
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Understand, interpret and experiment with sound devices and imagery, including simile, metaphor and personification, in narratives, shape poetry, songs, anthems and odes (ACELT1611)
Examples
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Select, navigate and read texts for a range of purposes, applying appropriate text processing strategies and interpreting structural features, for example table of contents, glossary, chapters, headings and subheadings (ACELY1712)
Examples
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Navigate and read texts for specific purposes applying appropriate text processing strategies, for example predicting and confirming, monitoring meaning, skimming and scanning (ACELY1702)
Examples
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Use comprehension strategies to interpret and analyse information and ideas, comparing content from a variety of textual sources including media and digital texts (ACELY1703, ACELY1713)
Examples
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Summarise a text and evaluate the intended message or theme
Examples
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Understand how texts vary in purpose, structure and topic as well as the degree of formality (ACELA1504)
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EN3-3A
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Spelling
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EN3-4A
Draws on appropriate strategies to accurately spell familiar and unfamiliar words when composing texts
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Understand how to use banks of known words, word origins, base words, suffixes and prefixes, morphemes, spelling patterns and generalisations to learn and spell new words, for example technical words and words adopted from other languages (ACELA1513, ACEL
Play Activities 139Examples
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Understand that the pronunciation, spelling and meanings of words have histories and change over time (ACELA1500)
Examples
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Integrate a range of spelling strategies and conventions to accurately spell most words, including words of many syllables, when composing imaginative and other texts
Play Activities 118Examples
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Understand how to use banks of known words, word origins, base words, suffixes and prefixes, morphemes, spelling patterns and generalisations to learn and spell new words, for example technical words and words adopted from other languages (ACELA1513, ACEL
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EN3-4A
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Writing and Representing
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Objective B
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Responding and Composing
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EN3-5B
Discusses how language is used to achieve a widening range of purposes for a widening range of audiences and contexts
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EN3-5B
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Grammar, Punctuation and Vocabulary
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EN3-6B
Uses knowledge of sentence structure, grammar, punctuation and vocabulary to respond to and compose clear and cohesive texts in different media and technologies
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Understand that choices in grammar, punctuation and vocabulary contribute to the effectiveness of texts
Examples
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Experiment using a range of language features, eg connectives, topic sentences, active and passive voice and nominalisation
Examples
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Understand the use of vocabulary to express greater precision of meaning, and know that words can have different meanings in different contexts (ACELA1512)
Examples
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Investigate how vocabulary choices, including evaluative language can express shades of meaning, feeling and opinion (ACELA1525)
Examples
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Use grammatical features, eg pronouns, conjunctions and connectives, to accurately link ideas and information to ensure meaning when composing texts
Examples
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Understand that choices in grammar, punctuation and vocabulary contribute to the effectiveness of texts
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EN3-6B
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Responding and Composing
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Objective C
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Thinking Imaginatively, Creatively, Interpretively and Critically
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EN3-7C
Thinks imaginatively, creatively, interpretively and critically about information and ideas and identifies connections between texts when responding to and composing texts
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Think imaginatively when engaging with texts, using prediction, for example, to imagine what happens to characters after the text
Examples
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Identify the relationship between words, sounds, imagery and language patterns in narratives and poetry such as ballads, limericks and free verse (ACELT1617)
Examples
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Think imaginatively when engaging with texts, using prediction, for example, to imagine what happens to characters after the text
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EN3-7C
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Thinking Imaginatively, Creatively, Interpretively and Critically
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Objective A
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Stage Four
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Objective A
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Outcome 1
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EN4-1A
Responds to and composes texts for understanding, interpretation, critical analysis, imaginative expression and pleasure
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Interpret the stated and implied meanings in spoken texts, and use evidence to support or challenge different perspectives (ACELY1730)
Examples
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Apply increasing knowledge of vocabulary, text structures and language features to understand the content of texts (ACELY1733)
Examples
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Recognise that vocabulary choices contribute to the specificity, abstraction and style of texts (ACELA1547)
Examples
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Identify and evaluate devices that create tone, for example humour, wordplay, innuendo and parody in poetry, humorous prose, drama or visual texts (ACELT1630)
Examples
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Understand, interpret and discuss how language is compressed to produce a dramatic effect in film or drama, and to create layers of meaning in poetry, for example haiku, tankas, couplets, free verse and verse novels (ACELT1623)
Examples
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Interpret the stated and implied meanings in spoken texts, and use evidence to support or challenge different perspectives (ACELY1730)
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EN4-1A
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Outcome 2
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EN4-2A
Effectively uses a widening range of processes, skills, strategies and knowledge for responding to and composing texts in different media and technologies
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Consider and apply a range of strategies to improve their texts, including editing by rereading and peer editing, checking accuracy of paragraphing, grammar, spelling and punctuation, and considering relevance for purpose, audience and context
Examples
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Edit for meaning by removing repetition, refining ideas, reordering sentences and adding or substituting words for impact (ACELY1726)
Examples
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Use a range of effective strategies for organising information, ideas and arguments, eg clustering, listing, compare and contrast, semantic chains, graphic and diagram outlines, and mind maps WE
Examples
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Consider and apply a range of strategies to improve their texts, including editing by rereading and peer editing, checking accuracy of paragraphing, grammar, spelling and punctuation, and considering relevance for purpose, audience and context
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EN4-2A
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Outcome 1
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Objective B
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Outcome 3
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EN4-3B
Uses and describes language forms, features and structures of texts appropriate to a range of purposes, audiences and contexts
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Engage with the language and structures of texts in meaningful, contextualised and authentic ways
Examples
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Identify, discuss and reflect on the ideas and information in a range of texts
Examples
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Understand how to apply learned knowledge consistently in order to spell accurately and to learn new words including nominalisations (ACELA1549)
Examples
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Understand how rhetorical devices are used to persuade and how different layers of meaning are developed through the use of metaphor, irony and parody (ACELA1542)
Examples
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Understand the ways etymology can clarify choice of vocabulary
Examples
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Interpret and analyse language choices, including sentence patterns, dialogue, imagery and other language features, in short stories, literary essays and plays (ACELT1767)
Examples
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Understand how modality is achieved through discriminating choices in modal verbs, adverbs, adjectives and nouns (ACELA1536)
Examples
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Understand how coherence is created in complex texts through devices like lexical cohesion, ellipsis, grammatical theme and text connectives (ACELA1809)
Examples
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Understand the use of punctuation conventions, including colons, semicolons, dashes and brackets in formal and informal texts (ACELA1532, ACELA1544)
Examples
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Understand how to use spelling rules and word origins, for example Greek and Latin roots, base words, suffixes, prefixes, spelling patterns and generalisations to learn new words and how to spell them (ACELA1539)
Examples
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Engage with the language and structures of texts in meaningful, contextualised and authentic ways
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EN4-3B
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Outcome 3
- Objective C
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Objective A
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Stage Five
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Objective A
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Outcome 1
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EN5-1A
Responds to and composes increasingly sophisticated and sustained texts for understanding, interpretation, critical analysis, imaginative expression and pleasure
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Analyse ideas, information, perspectives, contexts and ideologies and the ways they are presented in increasingly demanding, sustained imaginative, informative and persuasive texts
Examples
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Identify how vocabulary choices contribute to specificity, abstraction and stylistic effectiveness (ACELA1561)
Examples
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Analyse ideas, information, perspectives, contexts and ideologies and the ways they are presented in increasingly demanding, sustained imaginative, informative and persuasive texts
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EN5-1A
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Outcome 2
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EN5-2A
Effectively uses and critically assesses a wide range of processes, skills, strategies and knowledge for responding to and composing a wide range of texts in different media and technologies
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Consider how aspects of texts, including characterisation, setting, situations, issues, ideas, tone and point of view, can evoke a range of responses, including empathy, sympathy, antipathy and indifference
Examples
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Review, edit and refine students' own and others' texts for control of content, organisation, sentence structure, vocabulary, and/or visual features to achieve particular purposes and effects (ACELY1747, ACELY1757)
Play Activities 159Examples
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Understand that authors innovate with text structures and language for specific purposes and effects (ACELA1553)
Examples
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Apply an expanding vocabulary to read increasingly complex texts with fluency and comprehension (ACELY1743)
Examples
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Consider how aspects of texts, including characterisation, setting, situations, issues, ideas, tone and point of view, can evoke a range of responses, including empathy, sympathy, antipathy and indifference
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EN5-2A
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Outcome 1
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Objective B
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Outcome 3
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EN5-3B
Selects and uses language forms, features and structures of texts appropriate to a range of purposes, audiences and contexts, describing and explaining their effects on meaning
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Analyse and evaluate the effectiveness of a wide range of sentence and clause structures as authors design and craft texts (ACELA1557, ACELA1569)
Examples
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Understand that Standard Australian English in its spoken and written forms has a history of evolution and change and continues to evolve (ACELA1550, ACELA1563)
Examples
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Evaluate techniques (eg contrast, exaggeration, juxtaposition or changing chronological order) used in spoken, written and visual texts to, for example, construct plot and create emotional responses
Examples
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Understand how to use knowledge of the spelling system to spell unusual and technical words accurately, for example those based on uncommon Greek and Latin roots (ACELA1573)
Play Activities 266Examples
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Understand how punctuation is used along with layout and font variations in constructing texts for different audiences and purposes (ACELA1556)
Examples
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Analyse and evaluate the effectiveness of a wide range of sentence and clause structures as authors design and craft texts (ACELA1557, ACELA1569)
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EN5-3B
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Outcome 4
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EN5-4B
Effectively transfers knowledge, skills and understanding of language concepts into new and different contexts
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Appreciate and value the ways language concepts, ideas and information can be shaped and transformed for new and different contexts
Examples
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Examine and evaluate the cohesion of syntax and content in familiar and unfamiliar texts
Examples
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Use prediction, speculation, hypothesis and paraphrasing as strategies for accessing complex types of texts with unfamiliar ideas or structures
Examples
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Appreciate and value the ways language concepts, ideas and information can be shaped and transformed for new and different contexts
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EN5-4B
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Outcome 3
- Objective C
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Objective A
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Early Stage One
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Maths
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Early Stage 1
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Numbers and Algebra
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Whole Numbers
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MAe-4NA
Counts to 30, and orders, reads and represents numbers in the range 0 to 20
- Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)
- Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
- Subitise small collections of objects (ACMNA003)
- Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
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MAe-4NA
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Addition and Subtraction
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MAe-5NA
Combines, separates and compares collections of objects, describes using everyday language, and records using informal methods
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Represent practical situations to model addition and sharing (ACMNA004)
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Combine two or more groups of objects to model addition
Examples
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Model subtraction by separating and taking away part of a group of objects
Examples
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Use concrete materials or fingers to model and solve simple addition and subtraction problems
Examples
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Compare two groups of objects to determine 'how many more'
Examples
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Use visual representations of numbers to assist with addition and subtraction, eg ten frames
Play Activities 151Examples
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Count forwards by ones to add and backwards by ones to subtract
Examples
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Combine two or more groups of objects to model addition
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Represent practical situations to model addition and sharing (ACMNA004)
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MAe-5NA
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Multiplication and Division
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MAe-6NA
Groups, shares and counts collections of objects, describes using everyday language, and records using informal methods
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MAe-6NA
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Patterns and Algebra
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MAe-8NA
Recognises, describes and continues repeating patterns
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MAe-8NA
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Whole Numbers
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Measurement and Geometry
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Length
-
MAe-9MG
Describes and compares lengths and distances using everyday language
-
MAe-9MG
-
Area
-
MAe-10MG
Describes and compares areas using everyday language
-
MAe-10MG
-
Volume and Capacity
-
MAe-11MG
Describes and compares the capacities of containers and the volumes of objects or substances using everyday language
-
MAe-11MG
-
Mass
-
MAe-12MG
Describes and compares the masses of objects using everyday language
-
MAe-12MG
-
Time
-
MAe-13MG
Sequences events, uses everyday language to describe the durations of events, and reads hour time on clocks
-
MAe-13MG
-
Three-Dimensional Space
-
MAe-14MG
Manipulates, sorts and represents three-dimensional objects and describes them using everyday language
-
MAe-14MG
-
Two-Dimensional Space
-
MAe-15MG
Manipulates, sorts and describes representations of two-dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
-
Sort, describe and name familiar two-dimensional shapes in the environment (ACMMG009)
-
Identify, represent and name circles, triangles, squares and rectangles presented in different orientations
Examples
-
Sort two-dimensional shapes according to features such as size and shape
Examples
-
Identify and draw straight and curved lines
Examples
-
Compare and describe closed shapes and open lines
Examples
-
Identify, represent and name circles, triangles, squares and rectangles presented in different orientations
-
Sort, describe and name familiar two-dimensional shapes in the environment (ACMMG009)
-
MAe-15MG
-
Position
-
MAe-16MG
Describes position and gives and follows simple directions using everyday language
-
MAe-16MG
-
Length
-
Numbers and Algebra
-
Stage One
-
Numbers and Algebra
-
Whole Numbers
-
MA1-4NA
Applies place value, informally, to count, order, read and represent two- and three-digit numbers
- Whole Numbers 1
-
Whole Numbers 2
- Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
- Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026)
- Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
-
MA1-4NA
-
Addition and Subtraction
-
MA1-5NA
Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers
-
Addition and Subtraction 1
-
Represent and solve simple addition and subtraction problems using a range of strategies, including counting on, partitioning and rearranging parts (ACMNA015)
-
Use concrete materials to model addition and subtraction problems involving one- and two-digit numbers
Examples
-
Use concrete materials and a number line to model and determine the difference between two numbers
Examples
-
Create, record and recognise combinations of two numbers that add to numbers up to and including 9
Examples
-
Create, record and recognise combinations of two numbers that add to numbers from 11 up to and including 20
Examples
-
Investigate and generalise the effect of adding zero to a number, eg 'Adding zero to a number does not change the number'
Examples
-
Relate addition and subtraction facts for numbers to at least 20, eg 5 + 3 = 8, so 8 - 3 = 5 and 8 - 5 = 3
Examples
-
Use and record a range of mental strategies to solve addition and subtraction problems involving one- and two-digit numbers, including:counting on from the larger number to find the total of two numbers, counting back from a number to find the number rema
Play Activities 317Examples
-
Use the equals sign to record equivalent number sentences involving addition, and to mean 'is the same as', rather than as an indication to perform an operation, eg 5 + 2 = 3 + 4
Examples
-
Use concrete materials to model addition and subtraction problems involving one- and two-digit numbers
-
Represent and solve simple addition and subtraction problems using a range of strategies, including counting on, partitioning and rearranging parts (ACMNA015)
- Addition and Subtraction 2
-
Addition and Subtraction 1
-
MA1-5NA
-
Multiplication and Division
-
MA1-6NA
Uses a range of mental strategies and concrete materials for multiplication and division
-
Multiplication and Division 1
- Model and use equal groups of objects as a strategy for multiplication
-
Recognise and represent division as grouping into equal sets (ACMNA032)
-
Recognise when there are equal numbers of items in groups, eg 'There are three pencils in each group'
Examples
-
Model division by sharing a collection of objects equally into a given number of groups to determine how many in each group, eg determine the number in each group when 10 objects are shared between two people
Examples
-
Recognise when there are equal numbers of items in groups, eg 'There are three pencils in each group'
-
Multiplication and Division 2
-
Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
-
Model multiplication as repeated addition, eg 3 groups of 4 is the same as 4 + 4 + 4
Examples
-
Recognise when items have been arranged into groups, eg 'I can see two groups of three pencils'
Examples
-
Use concrete materials to model multiplication as equal 'groups' and by forming an array of equal 'rows' or equal 'columns'
Examples
-
Model the commutative property of multiplication, eg '3 groups of 2 is the same as 2 groups of 3'
Examples
-
Model multiplication as repeated addition, eg 3 groups of 4 is the same as 4 + 4 + 4
- Represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)
-
Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
-
Multiplication and Division 1
-
MA1-6NA
-
Fractions and Decimals
-
MA1-7NA
Represents and models halves, quarters and eighths
-
Fractions and Decimals 1
-
Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
-
Use concrete materials to model half of a whole object
Examples
-
Recognise that halves refer to two equal parts of a whole
Examples
-
Describe parts of a whole object as 'about a half', 'more than a half' or 'less than a half'
Examples
-
Record two equal parts of whole objects and shapes, and the relationship of the parts to the whole, using pictures and the fraction notation for half 1/2
Examples
-
Use concrete materials to model half of a collection
Examples
-
Use concrete materials to model half of a whole object
-
Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
-
Fractions and Decimals 2
-
Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
-
Use concrete materials to model a half, a quarter or an eighth of a whole object, eg divide a piece of ribbon into quarters
Examples
-
Recognise when objects and shapes have been shared into halves, quarters or eighths
Examples
-
Record equal parts of whole objects and shapes, and the relationship of the parts to the whole, using pictures and the fraction notation for half 1/2, quarter 1/4 and eighth 1/8
Examples
-
Record equal parts of a collection, and the relationship of the parts to the whole, using pictures and the fraction notation for half 1/2, quarter 1/4 and eighth 1/8
Examples
-
Use concrete materials to model a half, a quarter or an eighth of a whole object, eg divide a piece of ribbon into quarters
-
Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
-
Fractions and Decimals 1
-
MA1-7NA
-
Patterns and Algebra
-
MA1-8NA
Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values
-
Patterns and Algebra 1
-
Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018)
-
Identify and describe patterns when skip counting forwards or backwards by ones, twos, fives and tens from any starting point
Examples
-
Represent number patterns on number lines and number charts
Examples
-
Recognise, copy and continue given number patterns that increase or decrease, eg 1, 2, 3, 4, 20, 18, 16, 14,
Examples
-
Recognise, copy and continue patterns with objects or symbols
Examples
-
Describe a repeating pattern of objects or symbols in terms of a 'number' pattern
Examples
-
Identify and describe patterns when skip counting forwards or backwards by ones, twos, fives and tens from any starting point
-
Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018)
- Patterns and Algebra 2
-
Patterns and Algebra 1
-
MA1-8NA
-
Whole Numbers
-
Measurement and Geometry
-
Length
-
MA1-9MG
Measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres
-
MA1-9MG
-
Area
-
MA1-10MG
Measures, records, compares and estimates areas using uniform informal units
-
MA1-10MG
-
Volume and Capacity
-
MA1-11MG
Measures, records, compares and estimates volumes and capacities using uniform informal units
-
MA1-11MG
- Mass
-
Time
-
MA1-13MG
Describes, compares and orders durations of events, and reads half- and quarter-hour time
-
MA1-13MG
-
Three-Dimensional Space
-
MA1-14MG
Sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms
-
Three-Dimensional Space 1
-
Recognise and classify familiar three-dimensional objects using obvious features (ACMMG022)
-
Identify and name familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms, from a collection of everyday objects
Examples
-
Sort familiar three-dimensional objects according to obvious features, eg 'All these objects have curved surfaces'
Examples
-
Select and name a familiar three-dimensional object from a description of its features, eg find an object with six square faces
Examples
-
Identify cones, cubes, cylinders and prisms when drawn in different orientations
Examples
-
Identify and name familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms, from a collection of everyday objects
-
Recognise and classify familiar three-dimensional objects using obvious features (ACMMG022)
- Three-Dimensional Space 2
-
Three-Dimensional Space 1
-
MA1-14MG
-
Two-Dimensional Space
-
MA1-15MG
Manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons
-
Two-Dimensional Space 1
-
Recognise and classify familiar two-dimensional shapes using obvious features (ACMMG022)
-
Identify vertical and horizontal lines in pictures and the environment and use the terms 'vertical' and 'horizontal' to describe such lines
Examples
-
Identify parallel lines in pictures and the environment and use the term 'parallel' to describe such lines
Examples
-
Manipulate, compare and describe features of two-dimensional shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons
Examples
-
Sort two-dimensional shapes by a given attribute, eg by the number of sides or vertices
Examples
-
Identify and name two-dimensional shapes presented in different orientations according to their number of sides, including using the terms 'triangle', 'quadrilateral', 'pentagon', 'hexagon' and 'octagon'
Examples
-
Identify and name shapes embedded in pictures, designs and the environment, eg in Aboriginal art
Examples
-
Identify vertical and horizontal lines in pictures and the environment and use the terms 'vertical' and 'horizontal' to describe such lines
-
Recognise and classify familiar two-dimensional shapes using obvious features (ACMMG022)
-
Two-Dimensional Space 2
- Investigate the effect of one-step slides and flips, with and without the use of digital technologies (ACMMG045)
-
Identify and describe half-turns and quarter-turns (ACMMG046)
-
Identify full-, half- and quarter-turns of a single shape and use the terms 'turn', 'full-turn', 'half-turn' and 'quarter-turn' to describe the movement of the shape
Examples
-
Record the result of performing full-, half- and quarter-turns of a shape, with and without the use of digital technologies
Examples
-
Identify full-, half- and quarter-turns of a single shape and use the terms 'turn', 'full-turn', 'half-turn' and 'quarter-turn' to describe the movement of the shape
-
Two-Dimensional Space 1
-
MA1-15MG
-
Position
-
MA1-16MG
Represents and describes the positions of objects in everyday situations and on maps
-
Position 1
-
Give and follow directions to familiar locations (ACMMG023)
-
Give and follow directions, including directions involving turns to the left and right, to move between familiar locations, eg within the classroom or school
Examples
-
Give and follow instructions to position objects in models and drawings, eg 'Draw the bird between the two trees'
Examples
-
Describe the path from one location to another on drawings
Examples
-
Give and follow directions, including directions involving turns to the left and right, to move between familiar locations, eg within the classroom or school
-
Give and follow directions to familiar locations (ACMMG023)
- Position 2
-
Position 1
-
MA1-16MG
-
Length
-
Statistics and Probability
-
Data
-
MA1-17SP
Gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results
-
Data 1
-
Represent data with objects and drawings where one object or drawing represents one data value and describe the displays (ACMSP263)
-
Use concrete materials or pictures of objects as symbols to create data displays where one object or picture represents one data value (one-to-one correspondence), eg use different-coloured blocks to represent different-coloured cars
Examples
-
Interpret information presented in data displays where one object, picture or drawing represents one data value, eg weather charts
Examples
-
Use concrete materials or pictures of objects as symbols to create data displays where one object or picture represents one data value (one-to-one correspondence), eg use different-coloured blocks to represent different-coloured cars
-
Represent data with objects and drawings where one object or drawing represents one data value and describe the displays (ACMSP263)
- Data 2
-
Data 1
-
MA1-17SP
-
Data
-
Numbers and Algebra
-
Stage 2
-
Numbers and Algebra
-
Whole Numbers
-
MA2-4NA
Applies place value to order, read and represent numbers of up to five digits
-
Whole Numbers 1
-
Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
-
Represent numbers of up to four digits using objects, words, numerals and digital displays
Examples
-
Identify the number before and after a given two-, three- or four-digit number
Examples
-
Count forwards and backwards by tens and hundreds on and off the decade, eg 1220, 1230, 1240, ... (on the decade); 423, 323, 223, ... (off the decade)
Examples
-
Arrange numbers of up to four digits in ascending and descending order
Examples
-
Represent numbers of up to four digits using objects, words, numerals and digital displays
-
Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)
-
Apply an understanding of place value and the role of zero to read, write and order numbers of up to four digits
Examples
-
Use place value to partition numbers of up to four digits, eg 3265 as 3 groups of one thousand, 2 groups of one hundred, 6 groups of ten and 5 ones
Examples
-
State the 'place value' of digits in numbers of up to four digits, eg 'In the number 3426, the place value of the "4" is 400 or 4 hundreds'
Examples
-
Partition numbers of up to four digits in non-standard forms, eg 3265 as 32 hundreds and 65 ones
Examples
-
Round numbers to the nearest ten, hundred or thousand
Examples
-
Apply an understanding of place value and the role of zero to read, write and order numbers of up to four digits
-
Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
-
Whole Numbers 2
-
Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
-
Apply an understanding of place value to read and write numbers of up to five digits
Examples
-
Arrange numbers of up to five digits in ascending and descending order
Examples
-
State the place value of digits in numbers of up to five digits
Examples
-
Use place value to partition numbers of up to five digits and recognise this as 'expanded notation', eg 67 012 is 60 000 + 7000 + 10 + 2
Examples
-
Partition numbers of up to five digits in non-standard forms, eg 67 000 as 50 000 + 17 000
Examples
-
Round numbers to the nearest ten, hundred, thousand or ten thousand
Examples
-
Apply an understanding of place value to read and write numbers of up to five digits
-
Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
-
Whole Numbers 1
-
MA2-4NA
-
Addition and Subtraction
-
MA2-5NA
Uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers
-
Addition and Subtraction 1
-
Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
-
Add three or more single-digit numbers
Examples
-
Model and apply the associative property of addition to aid mental computation, eg 2 + 3 + 8 = 2 + 8 + 3 = 10 + 3 = 13
Examples
-
Apply known single-digit addition and subtraction facts to mental strategies for addition and subtraction of two-, three- and four-digit numbers, including:the jump strategy on an empty number line, the split strategy, the compensation strategy, using pat
Play Activities 301Examples
-
Use concrete materials to model the addition and subtraction of two or more numbers, with and without trading, and record the method used
Examples
-
Select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to four digits
Examples
-
Use the equals sign to record equivalent number sentences involving addition and subtraction and so to mean 'is the same as', rather than to mean to perform an operation, eg 32 - 13 = 30 - 11
Examples
-
Add three or more single-digit numbers
- Recognise and explain the connection between addition and subtraction (ACMNA054)
- Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)
-
Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
- Addition and Subtraction 2
-
Addition and Subtraction 1
-
MA2-5NA
-
Multiplication and Division
-
MA2-6NA
Uses mental and informal written strategies for multiplication and division
-
Multiplication and Division 1
-
Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)
-
Count by twos, threes, fives or tens using skip counting
Examples
-
Use mental strategies to recall multiplication facts for multiples of two, three, five and ten
Examples
-
Link multiplication and division facts using groups or arrays
Examples
-
Model and apply the commutative property of multiplication, eg 5 x 8 = 8 x 5
Examples
-
Count by twos, threes, fives or tens using skip counting
- Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)
-
Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)
-
Multiplication and Division 2
-
Recall multiplication facts up to 10 x 10 and related division facts (ACMNA075)
-
Count by fours, sixes, sevens, eights and nines using skip counting
Examples
-
Use the term 'product' to describe the result of multiplying two or more numbers, eg 'The product of 5 and 6 is 30'
Examples
-
Use mental strategies to build multiplication facts to at least 10 x 10, including:using the commutative property of multiplication, using known facts to work out unknown facts, using doubling and repeated doubling as a strategy to multiply by 2, 4 and 8,
Examples
-
Recall multiplication facts up to 10 x 10, including zero facts, with automaticity
Examples
-
Find 'multiples' for a given whole number, eg the multiples of 4 are 4, 8, 12, 16, ...
Examples
-
Relate multiplication facts to their inverse division facts, eg 6 x 4 = 24, so 24 / 6 = 4 and 24 / 4 = 6
Examples
-
Determine 'factors' for a given whole number, eg the factors of 12 are 1, 2, 3, 4, 6, 12
Examples
-
Use the equals sign to record equivalent number relationships involving multiplication, and to mean 'is the same as', rather than to mean to perform an operation, eg 4 x 3 = 6 x 2
Examples
-
Count by fours, sixes, sevens, eights and nines using skip counting
-
Develop efficient mental and written strategies, and use appropriate digital technologies, for multiplication and for division where there is no remainder (ACMNA076)
-
Model and apply the associative property of multiplication to aid mental computation, eg 2 x 3 x 5 = 2 x 5 x 3 = 10 x 3 = 30
Examples
-
Use mental and informal written strategies to multiply a two-digit number by a one-digit number, including: using known facts, multiplying the tens and the units, using an area model, using doubling and repeating, using the relationship between multiplica
Examples
-
Use mental strategies to divide a two-digit number by a one-digit number where there is no remainder, including: using the inverse relationship of multiplication and division eg 63 / 9 = 7 because 7 x 9 = 63, recalling known division facts, using halving
Play Activities 123Examples
-
Select and use a variety of mental and informal written strategies to solve multiplication and division problems
Examples
-
Model and apply the associative property of multiplication to aid mental computation, eg 2 x 3 x 5 = 2 x 5 x 3 = 10 x 3 = 30
-
Use mental strategies and informal recording methods for division with remainders
-
Model division, including where the answer involves a remainder, using concrete materials
Examples
-
Use mental strategies to divide a two-digit number by a one-digit number in problems for which answers include a remainder, eg 27 / 6: if 4 x 6 = 24 and 5 x 6 = 30, the answer is 4 remainder 3
Examples
-
Interpret the remainder in the context of a word problem, eg 'If a car can safely hold 5 people, how many cars are needed to carry 41 people?'; the answer of 8 remainder 1 means that 9 cars will be needed
Examples
-
Model division, including where the answer involves a remainder, using concrete materials
-
Recall multiplication facts up to 10 x 10 and related division facts (ACMNA075)
-
Multiplication and Division 1
-
MA2-6NA
-
Fractions and Decimals
-
MA2-7NA
Represents, models and compares commonly used fractions and decimals
-
Fractions and Decimals 1
-
Model and represent unit fractions, including 1/2, 1/4, 1/3 and 1/5 and their multiples, to a complete whole (ACMNA058)
-
Model fractions with denominators of 2, 3, 4, 5 and 8 of whole objects, shapes and collections using concrete materials and diagrams
Examples
-
Name fractions up to one whole, eg 1/5, 2/5, 3/5, 4/5, 5/5
Examples
-
Interpret the denominator as the number of equal parts a whole has been divided into
Examples
-
Interpret the numerator as the number of equal fractional parts, eg 3/8 means 3 equal parts of 8
Examples
-
Model fractions with denominators of 2, 3, 4, 5 and 8 of whole objects, shapes and collections using concrete materials and diagrams
- Count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line (ACMNA078)
-
Model and represent unit fractions, including 1/2, 1/4, 1/3 and 1/5 and their multiples, to a complete whole (ACMNA058)
-
Fractions and Decimals 2
- Investigate equivalent fractions used in contexts (ACMNA077)
-
Recognise that the place value system can be extended to tenths and hundredths, and make connections between fractions and decimal notation (ACMNA079)
-
Recognise and apply decimal notation to express whole numbers, tenths and hundredths as decimals, eg 0.1 is the same as 1/10
Examples
-
State the place value of digits in decimal numbers of up to two decimal places
Examples
-
Round a number with one or two decimal places to the nearest whole number
Examples
-
Recognise and apply decimal notation to express whole numbers, tenths and hundredths as decimals, eg 0.1 is the same as 1/10
-
Fractions and Decimals 1
-
MA2-7NA
-
Patterns and Algebra
-
MA2-8NA
Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values
- Patterns and Algebra 1
-
Patterns and Algebra 2
- Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)
-
Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)
-
Complete number sentences involving multiplication and division by calculating missing numbers, eg find the missing numbers: 28 = ( ) x 7
Examples
-
Represent and solve multiplication and division word problems using number sentences, eg 'I buy six pens and the total cost is $24. What is the cost of each pen?' can be represented as 6 x ( ) = 24 or 24 / 6 = ( )
Examples
-
Complete number sentences involving multiplication and division by calculating missing numbers, eg find the missing numbers: 28 = ( ) x 7
-
MA2-8NA
-
Whole Numbers
-
Measurement and Geometry
-
Length
-
MA2-9MG
Measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures
- Length 1
-
Length 2
-
Use scaled instruments to measure and compare lengths (ACMMG084)
-
Use a tape measure, ruler and trundle wheel to measure lengths and distances
Examples
-
Select and use an appropriate unit to estimate, measure and compare lengths and distances
Examples
-
Estimate and measure the perimeters of two-dimensional shapes
Examples
-
Convert between metres and centimetres, and between centimetres and millimetres
Examples
-
Use a tape measure, ruler and trundle wheel to measure lengths and distances
-
Use scaled instruments to measure and compare lengths (ACMMG084)
-
MA2-9MG
-
Area
-
MA2-10MG
Measures, records, compares and estimates areas using square centimetres and square metres
- Area 1
-
Area 2
-
Compare the areas of regular and irregular shapes by informal means (ACMMG087)
-
Measure the areas of common two-dimensional shapes using a square-centimetre grid overlay, eg measure the area of a regular hexagon
Examples
-
Measure the areas of irregular shapes using a square-centimetre grid overlay
Examples
-
Compare two or more areas by informal means, eg using tiles or a square-centimetre grid overlay
Examples
-
Measure the areas of common two-dimensional shapes using a square-centimetre grid overlay, eg measure the area of a regular hexagon
-
Compare the areas of regular and irregular shapes by informal means (ACMMG087)
-
MA2-10MG
-
Volume and Capacity
-
MA2-11MG
Measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres
-
MA2-11MG
- Mass
-
Time
-
MA2-13MG
Reads and records time in one-minute intervals and converts between hours, minutes and seconds
- Time 1
- Time 2
-
MA2-13MG
-
Three-Dimensional Space
-
MA2-14MG
Makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features
-
Three-Dimensional Space 1
-
Make models of three-dimensional objects and describe key features (ACMMG063)
-
Identify and name three-dimensional objects as prisms (including cubes), pyramids, cylinders, cones and spheres
Examples
-
Use a variety of materials to make models of prisms (including cubes), pyramids, cylinders, cones and spheres, given a three-dimensional object, picture or photograph to view
Examples
-
Deconstruct everyday packages that are prisms (including cubes) to create nets, eg cut up tissue boxes
Examples
-
Identify and name three-dimensional objects as prisms (including cubes), pyramids, cylinders, cones and spheres
-
Make models of three-dimensional objects and describe key features (ACMMG063)
- Three-Dimensional Space 2
-
Three-Dimensional Space 1
-
MA2-14MG
-
Two-Dimensional Space
-
MA2-15MG
Manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
-
Two-Dimensional Space 1
-
Compare and describe features of two-dimensional shapes, including the special quadrilaterals
-
Manipulate, compare and describe features of two-dimensional shapes, including the special quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapeziums and kites
Examples
-
Identify right angles in squares and rectangles
Examples
-
Group parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributes, eg quadrilaterals with parallel sides and right angles
Examples
-
Construct regular and irregular two-dimensional shapes from a variety of materials, eg cardboard, straws, pattern blocks
Examples
-
Manipulate, compare and describe features of two-dimensional shapes, including the special quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapeziums and kites
- Identify symmetry in the environment (ACMMG066)
-
Compare and describe features of two-dimensional shapes, including the special quadrilaterals
-
Two-Dimensional Space 2
-
Compare and describe two-dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)
-
Combine common two-dimensional shapes, including special quadrilaterals, to form other common shapes or designs, eg combine a rhombus and a triangle to form a trapezium
Examples
-
Record the arrangements of common shapes used to create other shapes, and the arrangement of shapes formed after splitting a shape, in diagrammatic form, with and without the use of digital technologies
Examples
-
Combine common two-dimensional shapes, including special quadrilaterals, to form other common shapes or designs, eg combine a rhombus and a triangle to form a trapezium
- Create symmetrical patterns, pictures and shapes, with and without the use of digital technologies (ACMMG091)
-
Compare and describe two-dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)
-
Two-Dimensional Space 1
-
MA2-15MG
-
Angles
-
MA2-16MG
Identifies, describes, compares and classifies angles
-
Angles 1
-
Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)
-
Describe informally an angle as the 'amount of turning' between two arms
Examples
-
Compare angles directly by placing one angle on top of another and aligning one arm
Examples
-
Identify 'perpendicular' lines in pictures, designs and the environment
Examples
-
Use the term 'right angle' to describe the angle formed when perpendicular lines meet
Examples
-
Describe informally an angle as the 'amount of turning' between two arms
-
Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)
- Angles 2
-
Angles 1
-
MA2-16MG
-
Position
-
MA2-17MG
Uses simple maps and grids to represent position and follow routes, including using compass directions
- Position 1
-
Position 2
-
Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)
-
Determine the directions north, east, south and west when given one of the directions
Examples
-
Use north, east, south and west to describe the location of a particular object in relation to another object on a simple map, given an arrow that represents north, eg 'The treasure is east of the cave'
Examples
-
Use north-east, south-east, south-west and north-west to describe the location of an object on simple maps, given a compass rose, eg 'The tree is south-west of the sign'
Examples
-
Determine the directions north, east, south and west when given one of the directions
-
Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)
-
MA2-17MG
-
Length
-
Statistics and Probability
-
Data
-
MA2-18SP
Selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs
-
MA2-18SP
-
Chance
-
MA2-19SP
Describes and compares chance events in social and experimental contexts
-
MA2-19SP
-
Data
-
Numbers and Algebra
-
Stage 3
-
Numbers and Algebra
-
Whole Numbers
-
MA3-4NA
Orders, reads and represents integers of any size and describes properties of whole numbers
-
Whole Numbers 1
-
Recognise, represent and order numbers to at least tens of millions
-
Apply an understanding of place value and the role of zero to read and write numbers of any size
Play Activities 104Examples
-
State the place value of digits in numbers of any size
Examples
-
Arrange numbers of any size in ascending and descending order
Examples
-
Partition numbers of any size in non-standard forms to aid mental calculation, eg when adding 163 480 and 150 000, 163 480 could be partitioned as 150 000 + 13 480, so that 150 000 could then be doubled and added to 13 480
Examples
-
Use numbers of any size in real-life situations, including in money problems
Examples
-
Round numbers to a specified place value, eg round 5 461 883 to the nearest million
Examples
-
Apply an understanding of place value and the role of zero to read and write numbers of any size
-
Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)
-
Determine all 'factors' of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36
Examples
-
Determine the 'highest common factor' (HCF) of two whole numbers, eg the HCF of 16 and 24 is 8
Examples
-
Determine 'multiples' of a given whole number, eg multiples of 7 are 7, 14, 21, 28, ...
Examples
-
Solve problems using knowledge of factors and multiples, eg 'There are 48 people at a party. In how many ways can you set up the tables and chairs, so that each table seats the same number of people and there are no empty chairs?'
Examples
-
Determine all 'factors' of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36
-
Recognise, represent and order numbers to at least tens of millions
- Whole Numbers 2
-
Whole Numbers 1
-
MA3-4NA
-
Addition and Subtraction
-
MA3-5NA
-
Addition and Subtraction 1
-
Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
-
Add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246
Examples
-
Select and apply efficient mental, written and calculator strategies to solve addition and subtraction word problems, including problems involving money
Play Activities 193Examples
-
Record the strategy used to solve addition and subtraction word problems
Examples
-
Check solutions to problems, including by using the inverse operation
Play Activities 165Examples
-
Add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246
-
Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
-
Addition and Subtraction 2
-
Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)
-
Solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluet
Examples
-
Record the strategy used to solve addition and subtraction word problems
Examples
-
Solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluet
-
Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)
-
Addition and Subtraction 1
-
MA3-5NA
-
Multiplication and Division
-
MA3-6NA
Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation
-
Multiplication and Division 1
-
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)
-
Use mental and written strategies to multiply three- and four-digit numbers by one-digit numbers, including:multiplying the thousands, then the hundreds, then the tens and then the ones, using an area model, using the formal algorithm
Examples
-
Use mental and written strategies to multiply two- and three-digit numbers by two-digit numbers, including: using an area model for two-digit by two-digit multiplication, factorising the numbers, using the extended form (long multiplication) of the formal
Examples
-
Apply appropriate mental and written strategies, and digital technologies, to solve multiplication word problems
Examples
-
Record the strategy used to solve multiplication word problems
Examples
-
Use mental and written strategies to multiply three- and four-digit numbers by one-digit numbers, including:multiplying the thousands, then the hundreds, then the tens and then the ones, using an area model, using the formal algorithm
-
Solve problems involving division by a one-digit number, including those that result in a remainder (ACMNA101)
-
Use the term 'quotient' to describe the result of a division calculation, eg 'The quotient when 30 is divided by 6 is 5'
Examples
-
Recognise and use different notations to indicate division
Examples
-
Use mental and written strategies to divide a number with three or more digits by a one-digit divisor where there is no remainder, including: dividing the hundreds, then the tens, and then the ones, using the formal algorithm
Examples
-
Use mental and written strategies to divide a number with three or more digits by a one-digit divisor where there is a remainder, including: dividing the tens and then the ones, using the formal algorithm
Examples
-
Apply appropriate mental and written strategies, and digital technologies, to solve division word problems
Examples
-
Use and interpret remainders in solutions to division problems, eg recognise when it is appropriate to round up an answer, such as 'How many 5-seater cars are required to take 47 people to the beach?'
Examples
-
Record the strategy used to solve division word problems
Examples
-
Use the term 'quotient' to describe the result of a division calculation, eg 'The quotient when 30 is divided by 6 is 5'
- Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)
-
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)
-
Multiplication and Division 2
-
Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)
-
Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers
Examples
-
Select and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainder
Examples
-
Use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples
Examples
-
Solve word problems involving multiplication and division, eg 'A recipe requires 3 cups of flour for 10 people. How many cups of flour are required for 40 people?'
Examples
-
Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers
-
Explore the use of brackets and the order of operations to write number sentences (ACMNA134)
-
Investigate and establish the order of operations using real-life contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 x 10 + 2 x 4 but, to obtai
Examples
-
Apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies
Examples
-
Investigate and establish the order of operations using real-life contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 x 10 + 2 x 4 but, to obtai
-
Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)
-
Multiplication and Division 1
-
MA3-6NA
-
Fractions and Decimals
-
MA3-7NA
Compares, orders and calculates with fractions, decimals and percentages
- Fractions and Decimals 1
-
Fractions and Decimals 2
-
Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)
-
Model, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objects
Examples
-
Compare and order simple fractions with related denominators using strategies such as diagrams, the number line, or equivalent fractions, eg write 3/5, 3/10, 1 1/10, 4/5 and 7/10 in ascending order
Examples
-
Find equivalent fractions by re-dividing the whole, using diagrams and number lines
Examples
-
Record equivalent fractions using diagrams and numerals
Examples
-
Model, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objects
- Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)
- Find a simple fraction of a quantity where the result is a whole number, with and without the use of digital technologies (ACMNA127)
-
Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)
-
Add and subtract decimals with the same number of decimal places, with and without the use of digital technologies
Play Activities 159Examples
-
Add and subtract decimals with a different number of decimal places, with and without the use of digital technologies
Examples
-
Round a number of up to three decimal places to the nearest whole number
Examples
-
Add and subtract decimals with the same number of decimal places, with and without the use of digital technologies
-
Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)
-
Use mental strategies to multiply simple decimals by single-digit numbers, eg 3.5 x 2
Examples
-
Multiply decimals of up to three decimal places by whole numbers of up to two digits, with and without the use of digital technologies, eg 'I measured three desks. Each desk was 1.25 m in length, so the total length is 3 x 1.25 = 3.75 m'
Examples
-
Divide decimals by a one-digit whole number where the result is a terminating decimal, eg 5.25 / 5 = 1.05
Examples
-
Solve word problems involving the multiplication and division of decimals, including those involving money, eg determine the 'best buy' for different-sized cartons of cans of soft drink
Examples
-
Use mental strategies to multiply simple decimals by single-digit numbers, eg 3.5 x 2
- Multiply and divide decimals by powers of 10 (ACMNA130)
- Make connections between equivalent fractions, decimals and percentages (ACMNA131)
-
Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)
-
MA3-7NA
-
Patterns and Algebra
-
MA3-8NA
Analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
-
Patterns and Algebra 1
- Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)
-
Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)
-
Identify and use inverse operations to assist with the solution of number sentences, eg 125 / 5 = ( ) becomes ( ) x 5 = 125
Play Activities 141Examples
-
Complete number sentences involving multiplication and division, including those involving simple fractions or decimals, eg 7 x ( ) = 7.7
Examples
-
Write number sentences to match word problems that require finding a missing number, eg 'I am thinking of a number that when I double it and add 5, the answer is 13. What is the number?
Examples
-
Identify and use inverse operations to assist with the solution of number sentences, eg 125 / 5 = ( ) becomes ( ) x 5 = 125
- Patterns and Algebra 2
-
Patterns and Algebra 1
-
MA3-8NA
-
Whole Numbers
-
Measurement and Geometry
-
Length
-
MA3-9MG
Selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
- Length 1
- Length 2
-
MA3-9MG
- Area
-
Volume and Capacity
-
MA3-11MG
Selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity
-
MA3-11MG
-
Mass
-
MA3-12MG
Selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass
-
MA3-12MG
-
Time
-
MA3-13MG
Uses 24-hour time and am and pm notation in real-life situations, and constructs timelines
-
MA3-13MG
-
Three-Dimensional Space
-
MA3-14MG
Identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views
-
Three-Dimensional Space 1
-
Compare, describe and name prisms and pyramids
-
Identify and determine the number of pairs of parallel faces of three-dimensional objects, eg 'A rectangular prism has three pairs of parallel faces'
Examples
-
Recognise that prisms have a 'uniform cross-section' when the section is parallel to the base
Examples
-
Identify, describe and compare the properties of prisms and pyramids, including: number of faces, shape of faces, number and type of identical faces, number of vertices, number of edges
Examples
-
Identify and determine the number of pairs of parallel faces of three-dimensional objects, eg 'A rectangular prism has three pairs of parallel faces'
- Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)
-
Compare, describe and name prisms and pyramids
-
Three-Dimensional Space 1
-
MA3-14MG
-
Two-Dimensional Space
-
MA3-15MG
Manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties
- Two-Dimensional Space 1
-
Two-Dimensional Space 2
-
Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
-
Identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90 degrees once and then reflected once'
Examples
-
Construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software
Examples
-
Identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90 degrees once and then reflected once'
-
Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
-
MA3-15MG
-
Angles
-
MA3-16MG
Measures and constructs angles, and applies angle relationships to find unknown angles
-
Angles 1
-
Construct angles using a protractor (ACMMG112)
-
Identify that a right angle is 90 degrees, a straight angle is 180 degrees and an angle of revolution is 360 degrees
Examples
-
Identify and describe angle size in degrees for each of the classifications acute, obtuse and reflex
Examples
-
Compare the sizes of two or more angles in degrees, eg compare angles in different two-dimensional shapes
Examples
-
Identify that a right angle is 90 degrees, a straight angle is 180 degrees and an angle of revolution is 360 degrees
-
Construct angles using a protractor (ACMMG112)
-
Angles 2
-
Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)
-
Identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles'
Examples
-
Investigate, with and without the use of digital technologies, angles at a point and establish that they form an angle of revolution and add to 360 degrees
Examples
-
Identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles'
-
Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)
-
Angles 1
-
MA3-16MG
-
Position
-
MA3-17MG
Locates and describes position on maps using a grid-reference system
- Use a grid-reference system to describe locations (ACMMG113)
-
Describe routes using landmarks and directional language (ACMMG113)
-
Find a location on a map that is in a given direction from a town or landmark, eg locate a town that is north-east of Broken Hill
Examples
-
Describe the direction of one location relative to another, eg 'Darwin is north-west of Sydney'
Examples
-
Follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map
Examples
-
Describe a route taken on a map using landmarks and directional language, including compass directions, eg 'Start at the post office, go west to the supermarket and then go south-west to the park'
Examples
-
Find a location on a map that is in a given direction from a town or landmark, eg locate a town that is north-east of Broken Hill
-
MA3-17MG
-
Length
-
Statistics and Probability
-
Data
-
MA3-18SP
Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables
-
MA3-18SP
-
Chance
-
MA3-19SP
Conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes
-
MA3-19SP
-
Data
-
Numbers and Algebra
-
Stage 4
-
Numbers and Algebra
-
Computing with Integers
-
MA4-4NA
Compares, orders and calculates with integers, applying a range of strategies to aid computation
-
Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
-
Use an appropriate non-calculator method to divide two- and three-digit numbers by a two-digit number
Examples
-
Use factors of a number to aid mental computation involving multiplication and division, eg to multiply a number by 12, first multiply the number by 6 and then multiply the result by 2
Examples
-
Use an appropriate non-calculator method to divide two- and three-digit numbers by a two-digit number
-
Compare, order, add and subtract integers (ACMNA280)
-
Order integers
Examples
-
Add and subtract integers using mental and written strategies
Play Activities 446Examples
-
Order integers
- Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)
-
Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
-
MA4-4NA
-
Fractions, Decimals and Percentages
-
MA4-5NA
Operates with fractions, decimals and percentages
- Compare fractions using equivalence; locate and represent positive and negative fractions and mixed numerals on a number line (ACMNA152)
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)
-
Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)
-
Determine the effect of multiplying or dividing by a number with magnitude less than one
Examples
-
Multiply and divide decimals by powers of 10
Examples
-
Multiply and divide decimals using written methods, limiting operators to two digits
Play Activities 209Examples
-
Multiply and divide fractions and mixed numerals using written methods
Examples
-
Multiply and divide fractions and decimals using a calculator
Examples
-
Calculate fractions and decimals of quantities using mental, written and calculator methods
Examples
-
Determine the effect of multiplying or dividing by a number with magnitude less than one
- Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)
- Round decimals to a specified number of decimal places (ACMNA156)
- Investigate terminating and recurring decimals (ACMNA184)
- Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)
- Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies (ACMNA158)
-
Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologies (ACMNA187)
-
Increase and decrease a quantity by a given percentage, using mental, written and calculator methods
Examples
-
Interpret and calculate percentages greater than 100, eg an increase from $2 to $5 is an increase of 150%
Examples
-
Solve a variety of real-life problems involving percentages, including percentage composition problems and problems involving money
Examples
-
Increase and decrease a quantity by a given percentage, using mental, written and calculator methods
-
MA4-5NA
-
Financial Mathematics
-
MA4-6NA
Solves financial problems involving purchasing goods
-
MA4-6NA
-
Ratios and Rates
-
MA4-7NA
Operates with ratios and rates, and explores their graphical representation
- Recognise and solve problems involving simple ratios (ACMNA173)
-
Solve a range of problems involving ratios and rates, with and without the use of digital technologies (ACMNA188)
-
Interpret and calculate ratios that involve more than two numbers
Examples
-
Solve a variety of real-life problems involving ratios, eg scales on maps, mixes for fuels or concrete
Examples
-
Use rates to compare quantities measured in different units
Examples
-
Solve a variety of real-life problems involving rates, including problems involving rate of travel (speed)
Examples
-
Interpret and calculate ratios that involve more than two numbers
- Investigate, interpret and analyse graphs from authentic data (ACMNA180)
-
MA4-7NA
-
Algebraic Techniques
-
MA4-8NA
Generalises number properties to operate with algebraic expressions
-
Algebraic Techniques 1
-
Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)
-
Develop the concept that pronumerals (letters) can be used to represent numerical values
Examples
-
Recognise and use equivalent algebraic expressions, eg y + y + y + y = 4y
Examples
-
Use algebraic symbols to represent mathematical operations written in words and vice versa, eg the product of x and y is xy, x + y is the sum of x and y
Examples
-
Develop the concept that pronumerals (letters) can be used to represent numerical values
- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)
- Simplify algebraic expressions involving the four operations (ACMNA192)
-
Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)
- Algebraic Techniques 2
-
Algebraic Techniques 1
-
MA4-8NA
-
Indices
-
MA4-9NA
Operates with positive-integer and zero indices of numerical bases
-
MA4-9NA
-
Equations
-
MA4-10NA
Uses algebraic techniques to solve simple linear and quadratic equations
-
Solve simple linear equations (ACMNA179)
-
Solve simple linear equations using concrete materials, such as the balance model or cups and counters, stressing the notion of performing the same operation on both sides of an equation
Examples
-
Solve linear equations that may have non-integer solutions, using algebraic techniques that involve up to two steps in the solution process
Examples
-
Solve simple linear equations using concrete materials, such as the balance model or cups and counters, stressing the notion of performing the same operation on both sides of an equation
- Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194)
-
Solve simple linear equations (ACMNA179)
-
MA4-10NA
-
Linear Relationships
-
MA4-11NA
Creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane
- Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)
-
Describe translations, reflections in an axis, and rotations of multiples of 90 degrees on the Cartesian plane using coordinates (ACMMG181)
-
Use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
Examples
-
Plot and determine the coordinates for P' resulting from translating P one or more times
Examples
-
Plot and determine the coordinates for P' resulting from reflecting P in either the x- or y-axis
Examples
-
Plot and determine the coordinates for P' resulting from rotating P by a multiple of 90 degrees about the origin
Examples
-
Use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
-
Plot linear relationships on the Cartesian plane, with and without the use of digital technologies (ACMNA193)
-
Use objects to build a geometric pattern, record the results in a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
Examples
-
Recognise a given number pattern (including decreasing patterns), complete a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
Examples
-
Use a rule generated from a pattern to calculate the corresponding value for a larger number
Examples
-
Form a table of values for a linear relationship by substituting a set of appropriate values for either of the pronumerals and graph the number pairs on the Cartesian plane, eg given y = 3x + 1, form a table of values using x = 0, 1 and 2 and then graph t
Examples
-
Extend the line joining a set of points on the Cartesian plane to show that there is an infinite number of ordered pairs that satisfy a given linear relationship
Examples
-
Derive a rule for a set of points that has been graphed on the Cartesian plane
Examples
-
Use objects to build a geometric pattern, record the results in a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
- Solve linear equations using graphical techniques (ACMNA194)
-
MA4-11NA
-
Computing with Integers
-
Measurement and Geometry
-
Length
-
MA4-12MG
Calculates the perimeters of plane shapes and the circumferences of circles
- Find perimeters of parallelograms, trapeziums, rhombuses and kites (ACMMG196)
-
Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference (ACMMG197)
-
Develop and use the formulas to find the circumferences of circles in terms of the diameter d or radius r:
Circumference of a circle = pi x d
Circumference of a circle = 2 x pi x r
Examples
-
Find the perimeters of simple composite figures consisting of two shapes, including quadrants and semicircles
Examples
-
Develop and use the formulas to find the circumferences of circles in terms of the diameter d or radius r:
Circumference of a circle = pi x d
Circumference of a circle = 2 x pi x r
-
MA4-12MG
-
Area
-
MA4-13MG
Uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area
- Choose appropriate units of measurement for area and convert from one unit to another (ACMMG195)
-
Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159)
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Develop and use the formulas to find the areas of rectangles and squares:
Area of a rectangle = lb where l is the length and b is the breadth (or width) of the rectangle
Area of square = s squared where s is the side length of the square
Examples
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Find the areas of simple composite figures that may be dissected into rectangles, squares, parallelograms and triangles
Examples
-
Develop and use the formulas to find the areas of rectangles and squares:
Area of a rectangle = lb where l is the length and b is the breadth (or width) of the rectangle
Area of square = s squared where s is the side length of the square
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Find areas of trapeziums, rhombuses and kites (ACMMG196)
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Develop, with or without the use of digital technologies, and use the formula to find the areas of kites and rhombuses:
Area of rhombus/kite = 1/2xy where x and y are the lengths of the diagonals
Examples
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Develop and use the formula to find the areas of trapeziums:
Area of trapezium = 1/2h (a + b) where h is the perpendicular height and a and b are the lengths of the parallel sides
Examples
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Select and use the appropriate formula to find the area of any of the special quadrilaterals
Examples
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Solve a variety of practical problems relating to the areas of triangles and quadrilaterals
Examples
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Develop, with or without the use of digital technologies, and use the formula to find the areas of kites and rhombuses:
Area of rhombus/kite = 1/2xy where x and y are the lengths of the diagonals
- Investigate the relationship between features of circles, such as the area and the radius; use formulas to solve problems involving area (ACMMG197)
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MA4-13MG
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Volume
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MA4-14MG
Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume
- Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)
- Choose appropriate units of measurement for volume and convert from one unit to another (ACMMG195)
- Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general; use formulas to solve problems involving volume (ACMMG198)
- Calculate the volumes of cylinders and solve related problems (ACMMG217)
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MA4-14MG
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Time
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MA4-15MG
Performs calculations of time that involve mixed units, and interprets time zones
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Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone (ACMMG199)
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Add and subtract time mentally using bridging strategies, eg from 2:45 to 3:00 is 15 minutes and from 3:00 to 5:00 is 2 hours, so the time from 2:45 until 5:00 is 15 minutes + 2 hours = 2 hours 15 minutes
Examples
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Solve a variety of problems involving duration, including where times are expressed in 12-hour and 24-hour notation, that require the use of mixed units (years, months, days, hours and/or minutes)
Examples
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Add and subtract time mentally using bridging strategies, eg from 2:45 to 3:00 is 15 minutes and from 3:00 to 5:00 is 2 hours, so the time from 2:45 until 5:00 is 15 minutes + 2 hours = 2 hours 15 minutes
- Solve problems involving international time zones
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Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone (ACMMG199)
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MA4-15MG
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Right-Angled Triangles (Pythagoras)
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MA4-16MG
Applies Pythagoras' theorem to calculate side lengths in right-angled triangles, and solves related problems
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MA4-16MG
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Properties of Geometrical Figures
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MA4-17MG
Classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles
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Properties of Geometrical Figures 1
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Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)
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Recognise and classify types of triangles on the basis of their properties (acute-angled triangles, right-angled triangles, obtuse-angled triangles, equilateral triangles, isosceles triangles and scalene triangles)
Examples
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Investigate the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapeziums and kites), including whether: the opposite sides are parallel, the opposite sides are equal, the adjacent sides are perpendicular, the opposi
Examples
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Recognise and classify types of triangles on the basis of their properties (acute-angled triangles, right-angled triangles, obtuse-angled triangles, equilateral triangles, isosceles triangles and scalene triangles)
- Identify line and rotational symmetries (ACMMG181)
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Demonstrate that the angle sum of a triangle is 180 degrees and use this to find the angle sum of a quadrilateral (ACMMG166)
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Justify informally that the interior angle sum of a triangle is 180 degrees, and that any exterior angle equals the sum of the two interior opposite angles
Examples
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Use the angle sum results for triangles and quadrilaterals to determine unknown angles in triangles and quadrilaterals, giving reasons
Examples
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Justify informally that the interior angle sum of a triangle is 180 degrees, and that any exterior angle equals the sum of the two interior opposite angles
- Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning
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Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)
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Properties of Geometrical Figures 1
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MA4-17MG
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Angle Relationships
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MA4-18MG
Identifies and uses angle relationships, including those related to transversals on sets of parallel lines
- Use the language, notation and conventions of geometry
- Recognise the geometrical properties of angles at a point
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Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)
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Identify and name pairs of parallel lines using the symbol for 'is parallel to'
Examples
-
Define and identify 'transversals', including transversals of parallel lines
Examples
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Identify, name and measure alternate angle pairs, corresponding angle pairs and co-interior angle pairs for two lines cut by a transversal
Examples
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Recognise the equal and supplementary angles formed when a pair of parallel lines is cut by a transversal
Examples
-
Identify and name pairs of parallel lines using the symbol for 'is parallel to'
- Solve simple numerical problems using reasoning (ACMMG164)
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MA4-18MG
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Length
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Statistics and Probability
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Data Collection and Representation
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MA4-19SP
Collects, represents and interprets single sets of data, using appropriate statistical displays
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MA4-19SP
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Single Variable Data Analysis
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MA4-20SP
Analyses single sets of data using measures of location, and range
- Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data (ACMSP171)
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Describe and interpret data displays using mean, median and range (ACMSP172)
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Calculate measures of location (mean, median and mode) and the range for data represented in a variety of statistical displays, including frequency distribution tables, frequency histograms, stem-and-leaf plots and dot plots
Examples
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Draw conclusions based on the analysis of data displays using the mean, median and/or mode, and range
Examples
-
Calculate measures of location (mean, median and mode) and the range for data represented in a variety of statistical displays, including frequency distribution tables, frequency histograms, stem-and-leaf plots and dot plots
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MA4-20SP
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Probability
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MA4-21SP
Represents probabilities of simple and compound events
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Probability 1
- Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)
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Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)
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Assign a probability of 0 to events that are impossible and a probability of 1 to events that are certain to occur
Examples
-
Assign probabilities to simple events by reasoning about equally likely outcomes, eg the probability of randomly drawing a card of the diamond suit from a standard pack of 52 playing cards is 13/25 = 1/4
Examples
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Solve probability problems involving single-step experiments using cards, dice, spinners, etc
Examples
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Assign a probability of 0 to events that are impossible and a probability of 1 to events that are certain to occur
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Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)
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Establish that the sum of the probabilities of all of the possible outcomes of a single-step experiment is 1
Examples
-
Calculate the probability of a complementary event using the fact that the sum of the probabilities of complementary events is 1, eg the probability of 'rolling a 6' when rolling a die is 1/6, therefore the probability of the complementary event, 'not rol
Examples
-
Establish that the sum of the probabilities of all of the possible outcomes of a single-step experiment is 1
- Probability 2
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Probability 1
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MA4-21SP
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Data Collection and Representation
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Numbers and Algebra
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Stage 5.1
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Numbers and Algebra
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Financial Mathematics
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MA5.1-4NA
Solves financial problems involving earning, spending and investing money
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MA5.1-4NA
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Indices
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MA5.1-5NA
Operates with algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases
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MA5.1-5NA
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Linear Relationships
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MA5.1-6NA
Determines the midpoint, gradient and length of an interval, and graphs linear relationships
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MA5.1-6NA
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Financial Mathematics
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Measurement and Geometry
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Area and Surface Area
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MA5.1-8MG
Calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms
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MA5.1-8MG
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Numbers of Any Magnitude
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MA5.1-9MG
Interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures
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MA5.1-9MG
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Area and Surface Area
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Statistics and Probability
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Probability
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MA5.1-13SP
Calculates relative frequencies to estimate probabilities of simple and compound events
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MA5.1-13SP
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Probability
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Numbers and Algebra
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Stage 5.2
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Numbers and Algebra
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Algebraic Techniques
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MA5.26NA
Simplifies algebraic fractions, and expands and factorises quadratic expressions
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MA5.26NA
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Equations
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MA5.2-8NA
Solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques
- Substitute values into formulas to determine an unknown (ACMNA234)
- Solve problems involving linear equations, including those derived from formulas (ACMNA235)
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Solve linear simultaneous equations, using algebraic and graphical techniques, including with the use of digital technologies (ACMNA237)
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Solve linear simultaneous equations by finding the point of intersection of their graphs, with and without the use of digital technologies
Examples
-
Solve linear simultaneous equations using appropriate algebraic techniques, including with the use of the 'substitution' and 'elimination' methods, eg solve {3a + b = 17; 2a - b = 8}
Examples
-
Solve linear simultaneous equations by finding the point of intersection of their graphs, with and without the use of digital technologies
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MA5.2-8NA
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Linear Relationships
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MA5.2-9NA
Uses the gradient-intercept form to interpret and graph linear relationships
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MA5.2-9NA
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Non-Linear Relationships
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MA5.2-10NA
Connects algebraic and graphical representations of simple non-linear relationships
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MA5.2-10NA
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Algebraic Techniques
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Measurement and Geometry
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Area and Surface Area
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MA5.2-11MG
Calculates the surface areas of right prisms, cylinders and related composite solids
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MA5.2-11MG
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Volume
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MA5.2-12MG
Applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders
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MA5.2-12MG
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Properties of Geometrical Figures
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MA5.2-14MG
Calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar
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Formulate proofs involving congruent triangles and angle properties (ACMMG243)
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Write formal proofs of the congruence of triangles, preserving matching order of vertices
Examples
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Use the congruence of triangles to prove properties of the special quadrilaterals, such as: CCT
the opposite angles of a parallelogram are equal
the diagonals of a parallelogram bisect each other
the diagonals of a rectangle are equal
Examples
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Write formal proofs of the congruence of triangles, preserving matching order of vertices
- Use the enlargement transformations to explain similarity and to develop the conditions for triangles to be similar (ACMMG220)
- Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)
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Formulate proofs involving congruent triangles and angle properties (ACMMG243)
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MA5.2-14MG
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Area and Surface Area
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Statistics and Probability
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Probability
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MA5.2-17SP
Describes and calculates probabilities in multi-step chance experiments
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MA5.2-17SP
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Probability
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Numbers and Algebra
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Stage 5.3
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Numbers and Algebra
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Ratios and Rates
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MA5.3-4NA
Draws, interprets and analyses graphs of physical phenomena
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MA5.3-4NA
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Linear Relationships
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MA5.3-8NA
Uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line
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MA5.3-8NA
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Non-Linear Relationships
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MA5.3-9NA
Sketches and interprets a variety of non-linear relationships
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Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)
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Find x- and y-intercepts, where appropriate, for the graph of y = ax squared + bx + c, given a, b and c
Examples
-
Determine the equation of the axis of symmetry of a parabola using: CCT
the midpoint of the interval joining the points at which the parabola cuts the x-axis
the formula x = -b/2a
Examples
-
Find x- and y-intercepts, where appropriate, for the graph of y = ax squared + bx + c, given a, b and c
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Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)
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MA5.3-9NA
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Ratios and Rates
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Measurement and Geometry
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Volume
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MA5.3-14MG
Applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids
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Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)
-
Develop and use the formula to find the volumes of right pyramids and right cones:
Volume of pyramid / cone = 1/3Ah where A is the base area and h is the perpendicular height CCT
Examples
-
Use the formula to find the volumes of spheres:
Volume of sphere = 4/3 pi r cubed where r is the length of the radius
Examples
-
Find the volumes of composite solids that include right pyramids, right cones and hemispheres,
eg find the volume of a cylinder with a cone on top
Examples
-
Develop and use the formula to find the volumes of right pyramids and right cones:
Volume of pyramid / cone = 1/3Ah where A is the base area and h is the perpendicular height CCT
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Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)
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MA5.3-14MG
-
Circle Geometry
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MA5.3-17MG
Applies deductive reasoning to prove circle theorems and to solve related problems
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Prove and apply angle and chord properties of circles (ACMMG272)
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prove the following chord properties of circles: CCT
chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre
the perpendicular from the centre of a circle to a chord bisects the chord; con
Examples
-
prove the following angle properties of circles: CCT
the angle at the centre of a circle is twice the angle at the circumference standing on the same arc
the angle in a semicircle is a right angle
angles at the circumference, standi
Examples
-
Apply chord and angle properties of circles to find unknown angles and lengths in diagrams
Examples
-
prove the following chord properties of circles: CCT
chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre
the perpendicular from the centre of a circle to a chord bisects the chord; con
- Prove and apply tangent and secant properties of circles
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Prove and apply angle and chord properties of circles (ACMMG272)
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MA5.3-17MG
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Volume
- Statistics and Probability
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Numbers and Algebra
-
Early Stage 1