App Library
Menu
Shop
Learn More
Overview
Features & Benefits
Lesson Content
Adaptive Learning
View Pricing
Other Articles
Help for School Users
Help for Home Users
Contact Us
Register
Login
NSW Syllabus
Australian Curriculum
Common Core State Standards
EdAlive Curriculum
NAPLAN
National Curriculum 2014 (UK)
New Zealand Curriculum
NSW Syllabus
Victorian Curriculum
Show Curriculum Tree
English
Early Stage One
Objective A
Speaking and Listening 1
ENe-1A
Respond to simple questions either verbally or non-verbally
Writing and Representing 1
ENe-2A
Know that spoken sounds and words can be written down using letters of the alphabet and how to write some high-frequency sight words and known words (ACELA1758)
Handwriting and Using Digital Technologies
ENe-3A
Begin to understand the sequence of letters through structured and guided activities
Write from left to right and leave spaces between words
Reading and Viewing 1
ENe-4A
Recognise the letters of the alphabet and know there are lower and upper case letters (ACELA1440)
Understand that spoken words are made up of sounds
Recognise rhymes, syllables and sounds (phonemes) in spoken words (ACELA1439)
Consistently identify words that start with the same initial sound
segment words into onset and rime
Identify the beginning and end sounds of words
Segment simple spoken words into separate sounds
recognise high-frequency words, including own name
Use phonological strategies when reading, including letter-sound relationships
Use knowledge of letters and sounds to decode words, including those in initial, final and medial positions
Use comprehension strategies to understand and discuss texts listened to, viewed or read independently (ACELY1650)
Spelling
ENe-5A
Know how to use onset and rime to spell words (ACELA1438)
Identify patterns in words leading to the identification of word families
Use and write beginning and ending sounds of spoken words
Know that letters are used to represent sounds when writing words
Use plural form when spelling some words
Objective B
Reading and Viewing 2
ENe-8B
Recognise that words and pictures have meaning and that words can be read aloud
Grammar, Punctuation and Vocabulary
ENe-9B
Recognise that sentences are key units for expressing ideas (ACELA1435)
Demonstrate an awareness of nouns, pronouns and conjunctions
Stage One
Objective A
Speaking and Listening 1
EN1-1A
Identify, reproduce and experiment with rhythmic, sound and word patterns in poems, chants, rhymes and songs (ACELT1592)
Carry out complex instructions involving more than one step
Writing and Representing 1
EN1-2A
Compose texts supported by visual information (eg diagrams and maps) on familiar topics
Reread and edit text for spelling, sentence-boundary punctuation and text structure (ACELY1662, ACELY1672)
Reading and Viewing 1
EN1-4A
Recognise grammatical patterns to enhance comprehension, eg action verbs, words or groups of words that tell who, what, when, where and how
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)
Identify the parts of a simple sentence that represent 'What's happening?', 'Who or what is involved?' and the surrounding circumstances (ACELA1451)
Understand how sentence punctuation is used to enhance meaning and fluency
Identify word families and word origins to understand the meaning of unfamiliar words, eg base words, rhyming words and synonyms
Recognise sound-letter matches including common vowel and consonant digraphs and consonant blends (ACELA1458)
Understand the variability of sound-letter matches (ACELA1459)
Recognise most sound-letter matches including silent letters, vowel/consonant digraphs and many less common sound-letter combinations (ACELA1474)
Automatically recognise irregular high-frequency words, eg 'come' and 'are'
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
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)
Use background knowledge of a topic to make inferences about the ideas in a text
Predict author intent, series of events and possible endings in an imaginative, informative and persuasive text
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)
Spelling
EN1-5A
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)
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)
Recognise common prefixes and suffixes and how they change a word's meaning (ACELA1455, ACELA1472)
Isolate and write the initial, medial and final sound of a word
Exchange one letter in a written word with a different letter to make a new word
Use double consonants where appropriate, eg 'hopping'
Recognise when a word is spelt incorrectly
Use morphemic and phonological knowledge when spelling
Objective B
Speaking and Listening 2
EN1-6B
Identify language that can be used for appreciating texts and the qualities of people and things (ACELA1462)
Writing and Representing 2
EN1-7B
Understand that different types of texts have identifiable text structures and language features that help the text serve its purpose (ACELA1447, ACELA1463)
Grammar, Punctuation and Vocabulary
EN1-9B
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)
Recognise that a preposition placed in front of a noun group can show where, when, eg 'on the box' (where), 'before my birthday' (when)
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)
Recognise that capital letters signal proper nouns and commas are used to separate items in lists (ACELA1465)
Understand how texts are made cohesive through resources, for example word associations, synonyms, and antonyms (ACELA1464)
Recognise, discuss and use creative word play, eg alliteration and onomatopoeia
Compose sentences effectively using basic grammatical features and punctuation conventions
Stage Two
Objective A
Speaking and Listening 1
EN2-1A
Interpret ideas and information in spoken texts and listen for key points in order to carry out tasks and use information to share and extend ideas and information (ACELY1687)
Writing and Representing 1
EN2-2A
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)
Experiment with visual, multimodal and digital processes to represent ideas encountered in texts
Reread and edit texts for meaning, appropriate structure, grammatical choices and punctuation (ACELY1683)
Reread and edit for meaning by adding, deleting or moving words or word groups to improve content and structure (ACELY1695)
Reading and Viewing 1
EN2-4A
Know that word contractions are a feature of informal language and that apostrophes of contraction are used to signal missing letters (ACELA1480)
Skim a text for overall message and scan for particular information, eg headings, key words
Use graphological, phonological, syntactic and semantic strategies to respond to texts, eg knowledge of homophones, contractions, syllables, word families and common prefixes
Identify syllables in multisyllabic words in order to support decoding of longer words in context to make meaning
Recognise high frequency sight words (ACELA1486)
Use comprehension strategies to build literal and inferred meaning to expand content knowledge, integrating and linking ideas and analysing and evaluating texts (ACELY1680, ACELY1692)
Use strategies to confirm predictions about author intent in imaginative, informative and persuasive texts
Summarise a paragraph and indicate the main idea, key points or key arguments in imaginative, informative and persuasive texts
Spelling
EN2-5A
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)
Recognise homophones and know how to use context to identify correct spelling (ACELA1780)
Understand how knowledge of word origins supports spelling
Use a variety of spelling strategies to spell high-frequency words correctly when composing imaginative and other texts
Use morphemic, visual, syntactic, semantic and phonological knowledge when attempting to spell unknown words
Use knowledge of alphabetical order to locate information in texts, eg dictionaries, glossaries
Identify spelling errors in own writing and unknown texts and provide correct spelling
Objective B
Writing and Representing 2
EN2-7B
Identify and analyse the purpose and audience of imaginative, informative and persuasive texts
Reading and Viewing 2
EN2-8B
Interpret how imaginative, informative and persuasive texts vary in purpose, structure and topic
Identify organisational patterns and language features of print and visual texts appropriate to a range of purposes
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)
Recognise the use of figurative language in texts, eg similes, metaphors, idioms and personification, and discuss their effects
Recognise how quotation marks are used in texts to signal dialogue, titles and quoted (direct) speech (ACELA1492)
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)
Identify and interpret the different forms of visual information, including maps, tables, charts, diagrams, animations and images
Grammar, Punctuation and Vocabulary
EN2-9B
Understand that paragraphs are a key organisational feature of written texts (ACELA1479)
Understand how adverb groups/phrases and prepositional phrases work in different ways to provide circumstantial details about an activity (ACELA1495)
Identify and use grammatical features, eg pronouns, conjunctions and connectives, to accurately link ideas and information
Understand that verbs represent different processes (doing, thinking, saying, and relating) and that these processes are anchored in time through tense (ACELA1482)
Investigate how quoted (direct) and reported (indirect) speech work in different types of text (ACELA1494)
Use apostrophes for contractions
Learn extended and technical vocabulary and ways of expressing opinion including modal verbs and adverbs (ACELA1484)
Objective C
Thinking Imaginatively, Creatively and Interpretively
EN2-10C
Identify creative language features in imaginative, informative and persuasive texts that contribute to engagement
Objective D
Expressing Themselves
EN2-11D
Understand differences between the language of opinion and feeling and the language of factual reporting or recording (ACELA1489)
Stage Three
Objective A
Writing and Representing
EN3-2A
Identify and explore underlying themes and central storylines in imaginative texts
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
Reread and edit students' own and others' work using agreed criteria and explaining editing choices (ACELY1705, ACELY1715)
Reading and Viewing
EN3-3A
Understand how texts vary in purpose, structure and topic as well as the degree of formality (ACELA1504)
Understand, interpret and experiment with sound devices and imagery, including simile, metaphor and personification, in narratives, shape poetry, songs, anthems and odes (ACELT1611)
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)
Navigate and read texts for specific purposes applying appropriate text processing strategies, for example predicting and confirming, monitoring meaning, skimming and scanning (ACELY1702)
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)
Summarise a text and evaluate the intended message or theme
Spelling
EN3-4A
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
Understand that the pronunciation, spelling and meanings of words have histories and change over time (ACELA1500)
Integrate a range of spelling strategies and conventions to accurately spell most words, including words of many syllables, when composing imaginative and other texts
Objective B
Responding and Composing
EN3-5B
Analyse strategies authors use to influence readers (ACELY1801)
Grammar, Punctuation and Vocabulary
EN3-6B
Understand that choices in grammar, punctuation and vocabulary contribute to the effectiveness of texts
Experiment using a range of language features, eg connectives, topic sentences, active and passive voice and nominalisation
Understand the use of vocabulary to express greater precision of meaning, and know that words can have different meanings in different contexts (ACELA1512)
Investigate how vocabulary choices, including evaluative language can express shades of meaning, feeling and opinion (ACELA1525)
Use grammatical features, eg pronouns, conjunctions and connectives, to accurately link ideas and information to ensure meaning when composing texts
Objective C
Thinking Imaginatively, Creatively, Interpretively and Critically
EN3-7C
Think imaginatively when engaging with texts, using prediction, for example, to imagine what happens to characters after the text
Identify the relationship between words, sounds, imagery and language patterns in narratives and poetry such as ballads, limericks and free verse (ACELT1617)
Stage Four
Objective A
Outcome 1
EN4-1A
Interpret the stated and implied meanings in spoken texts, and use evidence to support or challenge different perspectives (ACELY1730)
Apply increasing knowledge of vocabulary, text structures and language features to understand the content of texts (ACELY1733)
Recognise that vocabulary choices contribute to the specificity, abstraction and style of texts (ACELA1547)
Identify and evaluate devices that create tone, for example humour, wordplay, innuendo and parody in poetry, humorous prose, drama or visual texts (ACELT1630)
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)
Outcome 2
EN4-2A
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
Edit for meaning by removing repetition, refining ideas, reordering sentences and adding or substituting words for impact (ACELY1726)
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
Objective B
Outcome 3
EN4-3B
Engage with the language and structures of texts in meaningful, contextualised and authentic ways
Identify, discuss and reflect on the ideas and information in a range of texts
Understand how to apply learned knowledge consistently in order to spell accurately and to learn new words including nominalisations (ACELA1549)
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)
Understand the ways etymology can clarify choice of vocabulary
Interpret and analyse language choices, including sentence patterns, dialogue, imagery and other language features, in short stories, literary essays and plays (ACELT1767)
Understand how modality is achieved through discriminating choices in modal verbs, adverbs, adjectives and nouns (ACELA1536)
Understand how coherence is created in complex texts through devices like lexical cohesion, ellipsis, grammatical theme and text connectives (ACELA1809)
Understand the use of punctuation conventions, including colons, semicolons, dashes and brackets in formal and informal texts (ACELA1532, ACELA1544)
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)
Objective C
Outcome 5
EN4-5C
Critically consider the ways in which meaning is shaped by context, purpose, form, structure, style, content, language choices and their own personal perspective
Stage Five
Objective A
Outcome 1
EN5-1A
Analyse ideas, information, perspectives, contexts and ideologies and the ways they are presented in increasingly demanding, sustained imaginative, informative and persuasive texts
Identify how vocabulary choices contribute to specificity, abstraction and stylistic effectiveness (ACELA1561)
Outcome 2
EN5-2A
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
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)
Understand that authors innovate with text structures and language for specific purposes and effects (ACELA1553)
Apply an expanding vocabulary to read increasingly complex texts with fluency and comprehension (ACELY1743)
Objective B
Outcome 3
EN5-3B
Analyse and evaluate the effectiveness of a wide range of sentence and clause structures as authors design and craft texts (ACELA1557, ACELA1569)
Understand that Standard Australian English in its spoken and written forms has a history of evolution and change and continues to evolve (ACELA1550, ACELA1563)
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
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)
Understand how punctuation is used along with layout and font variations in constructing texts for different audiences and purposes (ACELA1556)
Outcome 4
EN5-4B
Appreciate and value the ways language concepts, ideas and information can be shaped and transformed for new and different contexts
Examine and evaluate the cohesion of syntax and content in familiar and unfamiliar texts
Use prediction, speculation, hypothesis and paraphrasing as strategies for accessing complex types of texts with unfamiliar ideas or structures
Objective C
Outcome 6
EN5-6C
Investigate and describe the recurring features of particular genres, eg westerns or science fiction, focusing on their storylines, iconography, value systems and techniques
Maths
Early Stage 1
Numbers and Algebra
Whole Numbers
MAe-4NA
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)
Count forwards to 30 from a given number
Count backwards from a given number in the range 0 to 20
Identify the number before and after a given number
Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
Read numbers to at least 20, including zero, and represent these using objects (such as fingers), pictures, words and numerals
Subitise small collections of objects (ACMNA003)
Recognise the number of objects or dots in a pattern of objects or dots instantly
Instantly recognise (subitise) different arrangements for the same number, eg different representations of five
Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
Count with one-to-one correspondence
Compare and order numbers and groups of objects
Addition and Subtraction
MAe-5NA
Represent practical situations to model addition and sharing (ACMNA004)
Combine two or more groups of objects to model addition
Model subtraction by separating and taking away part of a group of objects
Use concrete materials or fingers to model and solve simple addition and subtraction problems
Compare two groups of objects to determine 'how many more'
Use visual representations of numbers to assist with addition and subtraction, eg ten frames
Count forwards by ones to add and backwards by ones to subtract
Multiplication and Division
MAe-6NA
Investigate and model equal groups
Use the term 'group' to describe a collection of objects
Model equal groups
Patterns and Algebra
MAe-8NA
Sort and classify familiar objects and explain the basis for these classifications (ACMNA005)
Sort and classify a group of familiar objects into smaller groups
Recognise that a group of objects can be sorted and classified in different ways
Copy, continue and create patterns with objects and drawings
Recognise, copy, continue and create repeating patterns using shapes, objects or pictures
Measurement and Geometry
Length
MAe-9MG
Use direct and indirect comparisons to decide which is longer, and explain their reasoning using everyday language (ACMMG006)
Use everyday language to describe length, eg long, short, high, tall, low
Use comparative language to describe length, eg longer, higher, taller than, shortest, lower than, longest, the same as
Area
MAe-10MG
Use direct comparison to decide which shape has a larger area and explain their reasoning using everyday language
Use comparative language to describe area, eg bigger than, smaller than, the same as
Volume and Capacity
MAe-11MG
Use direct and indirect comparisons to decide which holds more, and explain their reasoning using everyday language (ACMMG006)
Use the terms 'full', 'empty' and 'about half-full'
Use comparative language to describe volume and capacity, eg has more, has less, will hold more, will hold less, takes up more space
Mass
MAe-12MG
Use direct and indirect comparisons to decide which is heavier, and explain their reasoning using everyday language (ACMMG006)
Use everyday language to describe objects in terms of their mass, eg heavy, light, hard to push, hard to pull
Use comparative language to describe mass, eg heavier, lighter, heaviest, lightest
Time
MAe-13MG
Compare and order the duration of events using the everyday language of time (ACMMG007)
Sequence events in time
Compare the duration of two events using everyday language, eg 'It takes me longer to eat my lunch than it does to clean my teeth'
Connect days of the week to familiar events and actions (ACMMG008)
Recall that there are seven days in a week
Name and order the days of the week
Classify weekdays and weekend days
Relate events to a particular day or time of day, eg 'Assembly is on Tuesday', 'We come to school in the morning'
Tell time on the hour on analog and digital clocks
Read analog and digital clocks to the hour using the term 'o'clock'
Three-Dimensional Space
MAe-14MG
Sort, describe and name familiar three-dimensional objects in the environment (ACMMG009)
Sort three-dimensional objects and explain the attributes used to sort them, eg colour, size, shape, function
Two-Dimensional Space
MAe-15MG
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
Sort two-dimensional shapes according to features such as size and shape
Identify and draw straight and curved lines
Compare and describe closed shapes and open lines
Position
MAe-16MG
Describe position and movement (ACMMG010)
Give and follow simple directions to position an object or themselves, eg 'Put the blue teddy in the circle'
Stage One
Numbers and Algebra
Whole Numbers
MA1-4NA
Whole Numbers 1
Develop confidence with number sequences to 100 by ones from any starting point (ACMNA012)
Count forwards and backwards by ones from a given two-digit number
Identify the number before and after a given two-digit number
Count collections to 100 by partitioning numbers using place value (ACMNA014)
Count and represent large sets of objects by systematically grouping in tens
Use place value to partition two-digit numbers, eg 32 as 3 groups of ten and 2 ones
State the place value of digits in two-digit numbers, eg 'In the number 32, the "3" represents 30 or 3 tens'
Recognise, model, read, write and order numbers to at least 100; locate these numbers on a number line (ACMNA013)
Represent two-digit numbers using objects, pictures, words and numerals
Apply an understanding of place value and the role of zero to read, write and order two-digit numbers
Round numbers to the nearest ten
Whole Numbers 2
Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
Use the terms 'more than' and 'less than' to compare numbers
Arrange numbers of up to three digits in ascending order
Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026)
Count forwards and backwards by twos, threes and fives from any starting point
Count forwards and backwards by tens, on and off the decade, with two- and three-digit numbers, eg 40, 30, 20, ... (on the decade); 427, 437, 447, ... (off the decade)
Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
Count and represent large sets of objects by systematically grouping in tens and hundreds
Addition and Subtraction
MA1-5NA
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
Use concrete materials and a number line to model and determine the difference between two numbers
Create, record and recognise combinations of two numbers that add to numbers up to and including 9
Create, record and recognise combinations of two numbers that add to numbers from 11 up to and including 20
Investigate and generalise the effect of adding zero to a number, eg 'Adding zero to a number does not change the number'
Relate addition and subtraction facts for numbers to at least 20, eg 5 + 3 = 8, so 8 - 3 = 5 and 8 - 5 = 3
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
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
Addition and Subtraction 2
Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)
Use and record a range of mental strategies to solve addition and subtraction problems involving two-digit numbers, including:the jump strategy on an empty number line, the split strategy, eg record how the answer to 37 + 45 was obtained using the split s
Multiplication and Division
MA1-6NA
Multiplication and Division 1
Model and use equal groups of objects as a strategy for multiplication
Model and describe collections of objects as 'groups of'
Find the total number of objects using skip counting
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'
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
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
Recognise when items have been arranged into groups, eg 'I can see two groups of three pencils'
Use concrete materials to model multiplication as equal 'groups' and by forming an array of equal 'rows' or equal 'columns'
Model the commutative property of multiplication, eg '3 groups of 2 is the same as 2 groups of 3'
Represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)
Solve multiplication and division problems using objects, diagrams, imagery and actions
Record answers to multiplication and division problems using drawings, words and numerals, eg 'two rows of five make ten', '2 rows of 5 is 10'
Fractions and Decimals
MA1-7NA
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
Recognise that halves refer to two equal parts of a whole
Describe parts of a whole object as 'about a half', 'more than a half' or 'less than a half'
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
Use concrete materials to model half of a collection
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
Recognise when objects and shapes have been shared into halves, quarters or eighths
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
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
Patterns and Algebra
MA1-8NA
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
Represent number patterns on number lines and number charts
Recognise, copy and continue given number patterns that increase or decrease, eg 1, 2, 3, 4, 20, 18, 16, 14,
Recognise, copy and continue patterns with objects or symbols
Describe a repeating pattern of objects or symbols in terms of a 'number' pattern
Patterns and Algebra 2
Describe patterns with numbers and identify missing elements (ACMNA035)
Determine a missing number in a number pattern, eg 3, 7, 11, __, 19, 23, 27
Solve problems by using number sentences for addition or subtraction (ACMNA036)
Complete number sentences involving one operation of addition or subtraction by calculating the missing number, eg find x so that 5+x=13 or 15?x=9
Measurement and Geometry
Length
MA1-9MG
Length 1
Measure and compare the lengths of pairs of objects using uniform informal units (ACMMG019)
Record lengths and distances by referring to the number and type of uniform informal unit used
Compare the lengths of two or more objects using appropriate uniform informal units and check by placing the objects side-by-side and aligning the ends
Length 2
Compare and order several shapes and objects based on length, using appropriate uniform informal units (ACMMG037)
Compare and order two or more shapes or objects according to their lengths using an appropriate uniform informal unit
Recognise and use formal units to measure the lengths of objects
Use the metre as a unit to measure lengths and distances to the nearest metre or half-metre
Estimate lengths and distances to the nearest metre and check by measuring
Estimate lengths and distances to the nearest centimetre and check by measuring
Area
MA1-10MG
Area 2
Compare and order several shapes and objects based on area using appropriate uniform informal units (ACMMG037)
Compare and order the areas of two or more surfaces that cannot be moved, or superimposed, by measuring in uniform informal units
Volume and Capacity
MA1-11MG
Volume and Capacity 1
Measure and compare the capacities of pairs of objects using uniform informal units (ACMMG019)
Compare the capacities of two or more containers using appropriate uniform informal units
Mass
MA1-12MG
Mass 1
Investigate mass using a pan balance
Sort objects on the basis of their mass
Use a pan balance to find two collections of objects that have the same mass, eg a collection of blocks and a collection of counters
Mass 2
Compare the masses of objects using balance scales (ACMMG038)
Compare two or more objects according to their masses using appropriate uniform informal units
Time
MA1-13MG
Time 1
Name and order months and seasons (ACMMG040)
Name and order the months of the year
Name and order the seasons, and name the months for each season
Tell time to the half-hour (ACMMG020)
Read analog and digital clocks to the half-hour using the terms 'o'clock' and 'half past'
Record hour and half-hour time on analog and digital clocks
Time 2
Describe duration using months, weeks, days and hours (ACMMG021)
Experience and recognise activities that have a duration of one hour, half an hour or a quarter of an hour, one minute, and a few seconds
Three-Dimensional Space
MA1-14MG
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
Sort familiar three-dimensional objects according to obvious features, eg 'All these objects have curved surfaces'
Select and name a familiar three-dimensional object from a description of its features, eg find an object with six square faces
Identify cones, cubes, cylinders and prisms when drawn in different orientations
Three-Dimensional Space 2
Describe the features of three-dimensional objects (ACMMG043)
Recognise that flat surfaces of three-dimensional objects are two-dimensional shapes and name the shapes of these surfaces
Sort three-dimensional objects according to particular attributes, eg the shape of the surfaces
Two-Dimensional Space
MA1-15MG
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
Identify parallel lines in pictures and the environment and use the term 'parallel' to describe such lines
Manipulate, compare and describe features of two-dimensional shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons
Sort two-dimensional shapes by a given attribute, eg by the number of sides or vertices
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'
Identify and name shapes embedded in pictures, designs and the environment, eg in Aboriginal art
Two-Dimensional Space 2
Investigate the effect of one-step slides and flips, with and without the use of digital technologies (ACMMG045)
Identify a one-step slide or flip of a single shape and use the terms 'slide' and 'flip' to describe the movement of the shape
Make designs with line symmetry using paper-folding, pattern blocks, drawings and paintings
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
Record the result of performing full-, half- and quarter-turns of a shape, with and without the use of digital technologies
Position
MA1-16MG
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
Give and follow instructions to position objects in models and drawings, eg 'Draw the bird between the two trees'
Describe the path from one location to another on drawings
Position 2
Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044)
Interpret simple maps by identifying objects in different locations, eg find a classroom on a school plan map
Describe the positions of objects in models, photographs and drawings
Statistics and Probability
Data
MA1-17SP
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
Interpret information presented in data displays where one object, picture or drawing represents one data value, eg weather charts
Data 2
Create displays of data using lists, tables and picture graphs and interpret them (ACMSP050)
Interpret information presented in lists, tables and picture graphs
Stage 2
Numbers and Algebra
Whole Numbers
MA2-4NA
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
Identify the number before and after a given two-, three- or four-digit number
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)
Arrange numbers of up to four digits in ascending and descending order
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
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
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'
Partition numbers of up to four digits in non-standard forms, eg 3265 as 32 hundreds and 65 ones
Round numbers to the nearest ten, hundred or thousand
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
Arrange numbers of up to five digits in ascending and descending order
State the place value of digits in numbers of up to five digits
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
Partition numbers of up to five digits in non-standard forms, eg 67 000 as 50 000 + 17 000
Round numbers to the nearest ten, hundred, thousand or ten thousand
Addition and Subtraction
MA2-5NA
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
Model and apply the associative property of addition to aid mental computation, eg 2 + 3 + 8 = 2 + 8 + 3 = 10 + 3 = 13
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
Use concrete materials to model the addition and subtraction of two or more numbers, with and without trading, and record the method used
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
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
Recognise and explain the connection between addition and subtraction (ACMNA054)
Demonstrate how addition and subtraction are inverse operations
Explain and check solutions to problems, including by using the inverse operation
Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)
Perform simple calculations with money, including finding change, and round to the nearest five cents
Addition and Subtraction 2
Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)
Use a formal written algorithm to record addition and subtraction calculations involving two-, three-, four- and five-digit numbers
Solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080)
Solve addition and subtraction problems involving money, with and without the use of digital technologies
Multiplication and Division
MA2-6NA
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
Use mental strategies to recall multiplication facts for multiples of two, three, five and ten
Link multiplication and division facts using groups or arrays
Model and apply the commutative property of multiplication, eg 5 x 8 = 8 x 5
Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)
Use mental strategies to multiply a one-digit number by a multiple of 10, including: repeated addition, using place value concepts, factorising the multiples of 10
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
Use the term 'product' to describe the result of multiplying two or more numbers, eg 'The product of 5 and 6 is 30'
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,
Recall multiplication facts up to 10 x 10, including zero facts, with automaticity
Find 'multiples' for a given whole number, eg the multiples of 4 are 4, 8, 12, 16, ...
Relate multiplication facts to their inverse division facts, eg 6 x 4 = 24, so 24 / 6 = 4 and 24 / 4 = 6
Determine 'factors' for a given whole number, eg the factors of 12 are 1, 2, 3, 4, 6, 12
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
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
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
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
Select and use a variety of mental and informal written strategies to solve multiplication and division problems
Use mental strategies and informal recording methods for division with remainders
Model division, including where the answer involves a remainder, using concrete materials
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
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
Fractions and Decimals
MA2-7NA
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
Name fractions up to one whole, eg 1/5, 2/5, 3/5, 4/5, 5/5
Interpret the denominator as the number of equal parts a whole has been divided into
Interpret the numerator as the number of equal fractional parts, eg 3/8 means 3 equal parts of 8
Count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line (ACMNA078)
Identify and describe 'mixed numerals' as having a whole-number part and a fractional part
Fractions and Decimals 2
Investigate equivalent fractions used in contexts (ACMNA077)
Model, compare and represent the equivalence of fractions with related denominators by redividing the whole, using concrete materials, diagrams and number lines
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
State the place value of digits in decimal numbers of up to two decimal places
Round a number with one or two decimal places to the nearest whole number
Patterns and Algebra
MA2-8NA
Patterns and Algebra 1
Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060)
Identify and describe patterns when counting forwards or backwards by threes, fours, sixes, sevens, eights and nines from any starting point
Create and continue a variety of number patterns that increase or decrease, and describe them in more than one way
Investigate the conditions required for a number to be even or odd and identify even and odd numbers (ACMNA051)
Identify even or odd numbers of up to four digits
Patterns and Algebra 2
Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)
Complete number sentences involving addition and subtraction by calculating missing numbers, eg find the missing numbers: ( ) + 55 = 88, ( ) - 15 = 19
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
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 = ( )
Measurement and Geometry
Length
MA2-9MG
Length 1
Measure, order and compare objects using familiar metric units of length (ACMMG061)
Compare and order lengths and distances using metres and centimetres
Estimate lengths and distances using metres and centimetres and check by measuring
Length 2
Use scaled instruments to measure and compare lengths (ACMMG084)
Use a tape measure, ruler and trundle wheel to measure lengths and distances
Select and use an appropriate unit to estimate, measure and compare lengths and distances
Estimate and measure the perimeters of two-dimensional shapes
Convert between metres and centimetres, and between centimetres and millimetres
Area
MA2-10MG
Area 1
Recognise and use formal units to measure and estimate the areas of rectangles
Recognise the need for the square centimetre as a formal unit to measure area
Estimate the areas of rectangles (including squares) in square centimetres
Estimate the areas of rectangles (including squares) in square metres
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
Measure the areas of irregular shapes using a square-centimetre grid overlay
Compare two or more areas by informal means, eg using tiles or a square-centimetre grid overlay
Volume and Capacity
MA2-11MG
Volume and Capacity 1
Measure, order and compare objects using familiar metric units of capacity (ACMMG061)
Compare and order two or more containers by capacity measured in litres
Compare objects using familiar metric units of volume (ACMMG290)
Construct three-dimensional objects using cubic-centimetre blocks and count the blocks to determine the volumes of the objects
Compare the volumes of two or more objects made from cubic-centimetre blocks by counting blocks
Volume and Capacity 2
Use scaled instruments to measure and compare capacities (ACMMG084)
Convert between millilitres and litres, eg 1250 mL = 1 litre 250 millilitres
Compare and order the capacities of two or more containers measured in millilitres
Mass
MA2-12MG
Mass 1
Measure, order and compare objects using familiar metric units of mass (ACMMG061)
Use the kilogram as a unit to measure mass, using a pan balance
Record masses using the abbreviation for kilograms (kg)
Mass 2
Use scaled instruments to measure and compare masses (ACMMG084)
Record masses using the abbreviation for grams (g)
Record masses using kilograms and grams, eg 1 kg 200 g
Time
MA2-13MG
Time 1
Tell time to the minute and investigate the relationship between units of time (ACMMG062)
Read analog and digital clocks to the minute, including using the terms 'past' and 'to', eg 7:35 is read as 'seven thirty-five' or 'twenty-five to eight'
Record in words various times shown on analog and digital clocks
Time 2
Convert between units of time (ACMMG085)
Convert between units of time and recall time facts, eg 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day
Use am and pm notation and solve simple time problems (ACMMG086)
Record digital time using the correct notation, including am and pm, eg 9:15 am
Solve simple time problems using appropriate strategies, eg calculate the time spent on particular activities during the school day
Read and interpret simple timetables, timelines and calendars
Read and interpret calendars
Three-Dimensional Space
MA2-14MG
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
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
Deconstruct everyday packages that are prisms (including cubes) to create nets, eg cut up tissue boxes
Three-Dimensional Space 2
Investigate and represent three-dimensional objects using drawings
Identify prisms (including cubes), pyramids, cylinders, cones and spheres in the environment and from drawings, photographs and descriptions
Interpret given isometric drawings to make models of three-dimensional objects using connecting cubes
Two-Dimensional Space
MA2-15MG
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
Identify right angles in squares and rectangles
Group parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributes, eg quadrilaterals with parallel sides and right angles
Construct regular and irregular two-dimensional shapes from a variety of materials, eg cardboard, straws, pattern blocks
Identify symmetry in the environment (ACMMG066)
Identify and draw lines of symmetry on given shapes, including the special quadrilaterals and other regular and irregular shapes
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
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
Create symmetrical patterns, pictures and shapes, with and without the use of digital technologies (ACMMG091)
Create symmetrical patterns, designs, pictures and shapes by translating (sliding), reflecting (flipping) and rotating (turning) one or more common shapes
Create and record tessellating designs by reflecting, translating and rotating common shapes
Angles
MA2-16MG
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
Compare angles directly by placing one angle on top of another and aligning one arm
Identify 'perpendicular' lines in pictures, designs and the environment
Use the term 'right angle' to describe the angle formed when perpendicular lines meet
Angles 2
Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)
Recognise and describe angles as 'less than', 'equal to', 'about the same as' or 'greater than' a right angle
Classify angles as acute, right, obtuse, straight, reflex or a revolution
Position
MA2-17MG
Position 1
Create and interpret simple grid maps to show position and pathways (ACMMG065)
Use given directions to follow routes on simple maps
Identify and mark particular locations on maps and plans, given their grid references
Draw and describe routes or paths on grid-referenced maps and plans
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
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'
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'
Statistics and Probability
Data
MA2-18SP
Data 1
Collect data, organise it into categories, and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069)
Construct vertical and horizontal column graphs and picture graphs that represent data using one-to-one correspondence
Interpret and compare data displays (ACMSP070)
Describe and interpret information presented in simple tables, column graphs and picture graphs
Chance
MA2-19SP
Chance 2
Describe possible everyday events and order their chances of occurring (ACMSP092)
Compare the likelihood of obtaining particular outcomes in a simple chance experiment, eg for a collection of 7 red, 13 blue and 10 yellow marbles, name blue as being the colour most likely to be drawn out and recognise that it is impossible to draw out a
Stage 3
Numbers and Algebra
Whole Numbers
MA3-4NA
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
State the place value of digits in numbers of any size
Arrange numbers of any size in ascending and descending order
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
Use numbers of any size in real-life situations, including in money problems
Round numbers to a specified place value, eg round 5 461 883 to the nearest million
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
Determine the 'highest common factor' (HCF) of two whole numbers, eg the HCF of 16 and 24 is 8
Determine 'multiples' of a given whole number, eg multiples of 7 are 7, 14, 21, 28, ...
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?'
Whole Numbers 2
Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)
Determine whether a number is prime, composite or neither
Model square and triangular numbers and record each number group in numerical and diagrammatic form
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
Select and apply efficient mental, written and calculator strategies to solve addition and subtraction word problems, including problems involving money
Record the strategy used to solve addition and subtraction word problems
Check solutions to problems, including by using the inverse operation
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
Record the strategy used to solve addition and subtraction word problems
Multiplication and Division
MA3-6NA
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
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
Apply appropriate mental and written strategies, and digital technologies, to solve multiplication word problems
Record the strategy used to solve multiplication word problems
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'
Recognise and use different notations to indicate division
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
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
Apply appropriate mental and written strategies, and digital technologies, to solve division word problems
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?'
Record the strategy used to solve division word problems
Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)
Round numbers appropriately when obtaining estimates to numerical calculations
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
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
Use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples
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?'
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
Apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies
Fractions and Decimals
MA3-7NA
Fractions and Decimals 1
Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)
Compare and order unit fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100
Recognise that the place value system can be extended beyond hundredths (ACMNA104)
State the place value of digits in decimal numbers of up to three decimal places
Compare, order and represent decimals (ACMNA105)
Compare and order decimal numbers of up to three decimal places, eg 0.5, 0.125, 0.25
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
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
Find equivalent fractions by re-dividing the whole, using diagrams and number lines
Record equivalent fractions using diagrams and numerals
Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)
Add and subtract fractions, including mixed numerals, where one denominator is the same as, or a multiple of, the other, eg 2/3 + 1/6, 2 3/8 - 1 1/2, 2 3/8 - 3/4
Find a simple fraction of a quantity where the result is a whole number, with and without the use of digital technologies (ACMNA127)
Calculate a simple fraction of a collection/quantity, with and without the use of digital technologies, eg calculate 2/5 of 30
Solve word problems involving a fraction of a collection/quantity
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
Add and subtract decimals with a different number of decimal places, with and without the use of digital technologies
Round a number of up to three decimal places to the nearest whole number
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
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'
Divide decimals by a one-digit whole number where the result is a terminating decimal, eg 5.25 / 5 = 1.05
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
Multiply and divide decimals by powers of 10 (ACMNA130)
Recognise the number patterns formed when decimals are multiplied and divided by 10, 100 and 1000
Multiply and divide decimals by 10, 100 and 1000
Make connections between equivalent fractions, decimals and percentages (ACMNA131)
Recognise that the symbol % means 'percent'
Represent simple fractions as decimals and as percentages
Represent decimals as fractions and percentages, eg 1.37 = 137% = 137/100 = 1 37/100
Patterns and Algebra
MA3-8NA
Patterns and Algebra 1
Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)
Identify, continue and create simple number patterns involving addition and subtraction
Describe patterns using the terms 'increase' and 'decrease', eg for the pattern 48, 41, 34, 27, ..., 'The terms decrease by seven'
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
Complete number sentences involving multiplication and division, including those involving simple fractions or decimals, eg 7 x ( ) = 7.7
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?
Patterns and Algebra 2
Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)
Continue and create number patterns, with and without the use of digital technologies, using whole numbers, fractions and decimals, eg 1/4, 1/8, 1/16,... or 1.25, 2.5, 5, ...
Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)
Recognise that the number plane (Cartesian plane) is a visual way of describing location on a grid
Recognise that the number plane consists of a horizontal axis (x-axis) and a vertical axis (y-axis), creating four quadrants
Measurement and Geometry
Length
MA3-9MG
Length 1
Choose appropriate units of measurement for length (ACMMG108)
Select and use the appropriate unit and measuring device to measure lengths and distances
Calculate the perimeters of rectangles using familiar metric units (ACMMG109)
Calculate perimeters of common two-dimensional shapes, including squares, rectangles, triangles and regular polygons with more than four sides (ie regular polygons other than equilateral triangles and squares)
Length 2
Connect decimal representations to the metric system (ACMMG135)
Recognise the equivalence of whole-number and decimal representations of measurements of length, eg 165 cm is the same as 1.65 m
Interpret decimal notation for lengths and distances, eg 13.5 cm is 13 centimetres and 5 millimetres
Convert between common metric units of length (ACMMG136)
Convert between metres and kilometres
Convert between millimetres, centimetres and metres to compare lengths and distances
Solve problems involving the comparison of lengths using appropriate units (ACMMG137)
Solve a variety of problems involving length and perimeter, including problems involving different units of length, eg 'Find the total length of three items measuring 5 mm, 20 cm and 1.2 m'
Area
MA3-10MG
Area 1
Choose appropriate units of measurement for area (ACMMG108)
Identify situations where square kilometres are used for measuring area, eg a suburb
Recognise that there are 10 000 square metres in one hectare, ie 10 000 square metres = 1 hectare
Area 2
Solve problems involving the comparison of areas using appropriate units (ACMMG137)
Solve a variety of problems involving the areas of rectangles (including squares) and triangles
Volume and Capacity
MA3-11MG
Volume and Capacity 1
Choose appropriate units of measurement for volume and capacity (ACMMG108)
Select and use appropriate units to estimate the volumes of a variety of objects, eg cubic centimetres for a lolly jar, cubic metres for the classroom
Volume and capacity 2
Connect volume and capacity and their units of measurement (ACMMG138)
Select the appropriate unit to measure volume and capacity
Connect decimal representations to the metric system (ACMMG135)
Record volume and capacity using decimal notation to three decimal places, eg 1.275 L
Convert between common metric units of capacity (ACMMG136)
Convert between millilitres and litres
Calculate the volumes of rectangular prisms (ACMMG160)
Construct rectangular prisms using cubic-centimetre blocks and count the blocks to determine the volumes of the prisms
Mass
MA3-12MG
Mass 1
Choose appropriate units of measurement for mass (ACMMG108)
Select and use the appropriate unit and device to measure mass, eg electronic scales, kitchen scales
Mass 2
Connect decimal representations to the metric system (ACMMG135)
Recognise the equivalence of whole-number and decimal representations of measurements of mass, eg 3 kg 250 g is the same as 3.25 kg
Measure mass using scales and record using decimal notation of up to three decimal places, eg 0.875 kg
Convert between common metric units of mass (ACMMG136)
Convert between kilograms and grams and between kilograms and tonnes
Solve problems involving different units of mass, eg find the total mass of three items weighing 50 g, 750 g and 2.5 kg
Time
MA3-13MG
Time 1
Compare 12- and 24-hour time systems and convert between them (ACMMG110)
Convert between 24-hour time and time given using am or pm notation
Compare the local times in various time zones in Australia, including during daylight saving
Determine and compare the duration of events
Select an appropriate unit to measure a particular period of time
Order a series of events according to the time taken to complete each one
Use start and finish times to calculate the elapsed time of events, eg the time taken to travel from home to school
Time 2
Interpret and use timetables (ACMMG139)
Read, interpret and use timetables from real-life situations, including those involving 24-hour time
Three-Dimensional Space
MA3-14MG
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'
Recognise that prisms have a 'uniform cross-section' when the section is parallel to the base
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
Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)
Visualise and sketch three-dimensional objects from different views, including top, front and side views
Examine a diagram to determine whether it is or is not the net of a closed three-dimensional object
Visualise and sketch nets for given three-dimensional objects
Two-Dimensional Space
MA3-15MG
Two-Dimensional Space 1
Classify two-dimensional shapes and describe their features
Manipulate, identify and name right-angled, equilateral, isosceles and scalene triangles
Compare and describe features of the sides of equilateral, isosceles and scalene triangles
Select and classify a two-dimensional shape from a description of its features
Describe translations, reflections and rotations of two-dimensional shapes (ACMMG114)
Use the terms 'translate', 'reflect' and 'rotate' to describe the movement of two-dimensional shapes
Describe the effect when a two-dimensional shape is translated, reflected or rotated, eg when a vertical arrow is rotated 90 degrees, the resulting arrow is horizontal
Identify line and rotational symmetries (ACMMG114)
Identify and quantify the total number of lines (axes) of symmetry (if any exist) of two-dimensional shapes, including the special quadrilaterals and triangles
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'
Construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software
Angles
MA3-16MG
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
Identify and describe angle size in degrees for each of the classifications acute, obtuse and reflex
Compare the sizes of two or more angles in degrees, eg compare angles in different two-dimensional shapes
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'
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
Position
MA3-17MG
Use a grid-reference system to describe locations (ACMMG113)
Find locations on maps, including maps with legends, given their grid references
Describe particular locations on grid-referenced maps, including maps with a legend, eg 'The post office is at E4'
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
Describe the direction of one location relative to another, eg 'Darwin is north-west of Sydney'
Follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map
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'
Statistics and Probability
Data
MA3-18SP
Data 1
Describe and interpret different data sets in context (ACMSP120)
Interpret line graphs using the scales on the axes
Describe and interpret data presented in tables, dot plots, column graphs and line graphs, eg 'The graph shows that the heights of all children in the class are between 125 cm and 154 cm'
Data 2
Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)
Create a two-way table to organise data involving two categorical variables
Interpret and compare different displays of the same data set to determine the most appropriate display for the data set
Chance
MA3-19SP
Chance 1
List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)
Represent probabilities of outcomes of chance experiments using fractions, eg for one throw of a standard six-sided die or for one spin of an eight-sector spinner
Stage 4
Numbers and Algebra
Computing with Integers
MA4-4NA
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
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
Compare, order, add and subtract integers (ACMNA280)
Order integers
Add and subtract integers using mental and written strategies
Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)
Multiply and divide integers using mental and written strategies
Apply the order of operations to mentally evaluate expressions involving integers, including where an operator is contained within the numerator or denominator of a fraction
Fractions, Decimals and Percentages
MA4-5NA
Compare fractions using equivalence; locate and represent positive and negative fractions and mixed numerals on a number line (ACMNA152)
Determine the highest common factor (HCF) of numbers and the lowest common multiple (LCM) of numbers
Generate equivalent fractions
Write a fraction in its simplest form
Express improper fractions as mixed numerals and vice versa
Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)
Add and subtract fractions, including mixed numerals and fractions with unrelated denominators, using written and calculator methods
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
Multiply and divide decimals by powers of 10
Multiply and divide decimals using written methods, limiting operators to two digits
Multiply and divide fractions and mixed numerals using written methods
Multiply and divide fractions and decimals using a calculator
Calculate fractions and decimals of quantities using mental, written and calculator methods
Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)
Express one quantity as a fraction of another eg 15 minutes is of an hour
Round decimals to a specified number of decimal places (ACMNA156)
Round decimals to a given number of decimal places
Investigate terminating and recurring decimals (ACMNA184)
Convert fractions to terminating or recurring decimals as appropriate
Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)
Convert fractions to decimals (terminating and recurring) and percentages
Convert terminating decimals to fractions and percentages
Convert percentages to fractions and decimals (terminating and recurring)
Order fractions, decimals and percentages
Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies (ACMNA158)
Calculate percentages of quantities using mental, written and calculator methods
Express one quantity as a percentage of another, using mental, written and calculator methods, eg 45 minutes is 75% of an hour
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
Interpret and calculate percentages greater than 100, eg an increase from $2 to $5 is an increase of 150%
Solve a variety of real-life problems involving percentages, including percentage composition problems and problems involving money
Financial Mathematics
MA4-6NA
Investigate and calculate 'best buys', with and without the use of digital technologies (ACMNA174)
Solve problems involving discounts, including calculating the percentage discount
Calculate 'best buys' by comparing price per unit, or quantity per monetary unit, eg 500 grams for $4.50 compared with 300 grams for $2.75
Solve problems involving profit and loss, with and without the use of digital technologies (ACMNA189)
Calculate the selling price, given the percentage profit/loss on the cost price
Calculate the cost price, given the selling price and percentage profit/loss
Ratios and Rates
MA4-7NA
Recognise and solve problems involving simple ratios (ACMNA173)
Use ratios to compare quantities measured in the same units
Write ratios using the symbol, eg 4:7
Simplify ratios, eg 4:6 = 2:3, 1/2:2 = 1:4, 0.3:1 = 3:10
Apply the unitary method to ratio problems
Divide a quantity in a given ratio
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
Solve a variety of real-life problems involving ratios, eg scales on maps, mixes for fuels or concrete
Use rates to compare quantities measured in different units
Solve a variety of real-life problems involving rates, including problems involving rate of travel (speed)
Investigate, interpret and analyse graphs from authentic data (ACMNA180)
Interpret distance/time graphs (travel graphs) made up of straight-line segments
Algebraic Techniques
MA4-8NA
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
Recognise and use equivalent algebraic expressions, eg y + y + y + y = 4y
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
Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)
Recognise like terms and add and subtract them to simplify algebraic expressions, eg 2n + 4m + n = 4m + 3n
Simplify algebraic expressions that involve multiplication and division, eg 2ab x 3a
Translate from everyday language to algebraic language and vice versa
Simplify algebraic expressions involving the four operations (ACMNA192)
Simplify a range of algebraic expressions, including those involving mixed operations
Algebraic Techniques 2
Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176)
Substitute into algebraic expressions and evaluate the result
Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190)
Expand algebraic expressions by removing grouping symbols, eg 3 (a + 2) = 3a + 6
Indices
MA4-9NA
Investigate and use square roots of perfect square numbers (ACMNA150)
Use the notations for square root and cube root
Recognise the link between squares and square roots and between cubes and cube roots
Apply the order of operations to evaluate expressions involving square roots and cube roots, with and without using a calculator
Equations
MA4-10NA
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
Solve linear equations that may have non-integer solutions, using algebraic techniques that involve up to two steps in the solution process
Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194)
Solve linear equations that may have non-integer solutions, using algebraic techniques that involve up to three steps in the solution process
Linear Relationships
MA4-11NA
Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)
Plot and label points on the Cartesian plane, given coordinates, including those with coordinates that are not whole numbers
Identify and record the coordinates of given points on the Cartesian plane, including those with coordinates that are not whole numbers
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
Plot and determine the coordinates for P' resulting from translating P one or more times
Plot and determine the coordinates for P' resulting from reflecting P in either the x- or y-axis
Plot and determine the coordinates for P' resulting from rotating P by a multiple of 90 degrees about the origin
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
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
Use a rule generated from a pattern to calculate the corresponding value for a larger number
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
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
Derive a rule for a set of points that has been graphed on the Cartesian plane
Solve linear equations using graphical techniques (ACMNA194)
Graph two intersecting lines on the same set of axes and read off the point of intersection
Measurement and Geometry
Length
MA4-12MG
Find perimeters of parallelograms, trapeziums, rhombuses and kites (ACMMG196)
Find the perimeters of a range of plane shapes, including parallelograms, trapeziums, rhombuses, kites and simple composite figures
Solve problems involving the perimeters of plane shapes, eg find the dimensions of a rectangle, given its perimeter and the length of one side
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
Find the perimeters of simple composite figures consisting of two shapes, including quadrants and semicircles
Area
MA4-13MG
Choose appropriate units of measurement for area and convert from one unit to another (ACMMG195)
Convert between metric units of area using 1 cm2 = 100 mm2, 1 m2 = 1 000 000 mm2, 1 ha = 10 000 m2, 1 km2 = 1 000 000 m2 = 100 ha
Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159)
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
Find the areas of simple composite figures that may be dissected into rectangles, squares, parallelograms and triangles
Find areas of trapeziums, rhombuses and kites (ACMMG196)
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
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
Select and use the appropriate formula to find the area of any of the special quadrilaterals
Solve a variety of practical problems relating to the areas of triangles and quadrilaterals
Investigate the relationship between features of circles, such as the area and the radius; use formulas to solve problems involving area (ACMMG197)
Develop, with or without the use of digital technologies, and use the formula to find the areas of circles: Area of circle = pi x r squared where r is the length of the radius
Find the areas of quadrants, semicircles and sectors
Volume
MA4-14MG
Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)
Draw (in two dimensions) prisms, and solids formed from combinations of prisms, from different views, including top, side, front and back views
Choose appropriate units of measurement for volume and convert from one unit to another (ACMMG195)
Convert between metric units of volume and capacity, using 1 cm3 = 1000 mm3, 1 L = 1000 mL = 1000 cm3, 1 m3 = 1000 L = 1 kL, 1000 kL = 1 ML
Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general; use formulas to solve problems involving volume (ACMMG198)
Develop the formula for the volume of prisms by considering the number and volume of 'layers' of identical shape: Volume of a prism = base area x height leading to V = Ah
Solve a variety of practical problems involving the volumes and capacities of right prisms
Calculate the volumes of cylinders and solve related problems (ACMMG217)
Develop and use the formula to find the volumes of cylinders: Volume of a cylinder = pi x r squared x h where r is the length of the radius of the base and h is the perpendicular height
Time
MA4-15MG
Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone (ACMMG199)
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 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)
Solve problems involving international time zones
Compare times in, and calculate time differences between, major cities of the world, eg 'Given that London is 10 hours behind Sydney, what time is it in London when it is 6:00 pm in Sydney?'
Right-Angled Triangles (Pythagoras)
MA4-16MG
Investigate Pythagoras' theorem and its application to solving simple problems involving right-angled triangles (ACMMG222)
Use Pythagoras' theorem to find the length of an unknown side in a right-angled triangle
Properties of Geometrical Figures
MA4-17MG
Properties of Geometrical Figures 1
Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)
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)
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
Identify line and rotational symmetries (ACMMG181)
Investigate and determine lines (axes) of symmetry and the order of rotational symmetry of polygons, including the special quadrilaterals
Identify line and rotational symmetries in pictures and diagrams, eg artistic and cultural designs
Demonstrate that the angle sum of a triangle is 180 degrees and use this to find the angle sum of a quadrilateral (ACMMG166)
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 angle sum results for triangles and quadrilaterals to determine unknown angles in triangles and quadrilaterals, giving reasons
Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning
Find unknown sides and angles embedded in diagrams, using the properties of special triangles and quadrilaterals, giving reasons
Angle Relationships
MA4-18MG
Use the language, notation and conventions of geometry
Label and name angles using the symbole for angle P or the symbol for angle QPR notation
Recognise the geometrical properties of angles at a point
Use the terms 'complementary' and 'supplementary' for angles adding to 90 degrees and 180 degrees, respectively, and the associated terms 'complement' and 'supplement'
Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)
Identify and name pairs of parallel lines using the symbol for 'is parallel to'
Define and identify 'transversals', including transversals of parallel lines
Identify, name and measure alternate angle pairs, corresponding angle pairs and co-interior angle pairs for two lines cut by a transversal
Recognise the equal and supplementary angles formed when a pair of parallel lines is cut by a transversal
Solve simple numerical problems using reasoning (ACMMG164)
Find the sizes of unknown angles embedded in diagrams using angle relationships, including angles at a point and angles associated with parallel lines, giving reasons
Statistics and Probability
Data Collection and Representation
MA4-19SP
Construct and compare a range of data displays, including stem-and-leaf plots and dot plots (ACMSP170)
Construct and interpret frequency histograms and polygons
Interpret a variety of graphs, including dot plots, stem-and-leaf plots, divided bar graphs, sector graphs and line graphs
Single Variable Data Analysis
MA4-20SP
Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data (ACMSP171)
Calculate the mean of a set of data using the mean formula = sum of data values / number of data values
Determine the median, mode and range for sets of data
Describe and interpret data displays using mean, median and range (ACMSP172)
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
Draw conclusions based on the analysis of data displays using the mean, median and/or mode, and range
Probability
MA4-21SP
Probability 1
Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)
Distinguish between equally likely outcomes and outcomes that are not equally likely in single-step chance experiments
Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)
Assign a probability of 0 to events that are impossible and a probability of 1 to events that are certain to occur
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
Solve probability problems involving single-step experiments using cards, dice, spinners, etc
Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)
Establish that the sum of the probabilities of all of the possible outcomes of a single-step experiment is 1
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
Probability 2
Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292)
Interpret Venn diagrams involving two or three attributes
Construct Venn diagrams to represent all possible combinations of two attributes from given or collected data
Stage 5.1
Numbers and Algebra
Financial Mathematics
MA5.1-4NA
Solve problems involving earning money
Calculate earnings from wages for various time periods, given an hourly rate of pay, including penalty rates for overtime and special rates for Sundays and public holidays
Solve problems involving simple interest (ACMNA211)
Calculate simple interest using the formula I = PRM where I is the interest, P is the principal, R is the interest rate per time period (expressed as a fraction or decimal) and N is the number of time periods
Indices
MA5.1-5NA
Extend and apply the index laws to variables, using positive-integer indices and the zero index (ACMNA212)
Use the index laws previously established for numerical bases with positive-integer indices to develop the index laws in algebraic form
Simplify algebraic products and quotients using index laws (ACMNA231)
Simplify expressions that involve the product and quotient of simple algebraic terms containing positive-integer indices
Apply index laws to numerical expressions with integer indices (ACMNA209)
Write given numbers in index form (integer indices only) and vice versa
Linear Relationships
MA5.1-6NA
Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software (ACMNA214)
Use the interval between two points on the Cartesian plane as the hypotenuse of a right-angled triangle and apply Pythagoras' theorem to determine the length of the interval joining the two points (ie 'the distance between the two points')
Sketch linear graphs using the coordinates of two points (ACMNA215)
Identify the x- and y-intercepts of lines
Graph a variety of linear relationships on the Cartesian plane, with and without the use of digital technologies
Determine whether a point lies on a line by substitution
Measurement and Geometry
Area and Surface Area
MA5.1-8MG
Calculate the areas of composite shapes (ACMMG216)
Solve a variety of practical problems involving the areas of quadrilaterals and composite shapes
Solve problems involving the surface areas of right prisms (ACMMG218)
Identify the edge lengths and the areas making up the 'surface area' of rectangular and triangular prisms
Numbers of Any Magnitude
MA5.1-9MG
Investigate very small and very large time scales and intervals (ACMMG219)
Round numbers to a specified number of significant figures
Interpret the meaning of prefixes for very small and very large units of measurement, such as 'nano', 'micro', 'mega', 'giga' and 'tera'
Express numbers in scientific notation (ACMNA210)
Express numbers in scientific notation
Solve problems involving scientific notation
Statistics and Probability
Probability
MA5.1-13SP
Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226)
Predict the probability of an event from experimental data using relative frequencies
Calculate probabilities of events, including events involving 'and', 'or' and 'not', from data contained in two-way tables
Stage 5.2
Numbers and Algebra
Algebraic Techniques
MA5.26NA
Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)
Factorise algebraic expressions, including those involving indices, by determining common factors, eg factorise 3x to the power of 2 - 6x, 14ab + 12a to the power of 2, 21xy - 3x + 9x to the power of 2, 15p squared q cubed - 12pq to the power of 4
Equations
MA5.2-8NA
Substitute values into formulas to determine an unknown (ACMNA234)
Solve equations arising from substitution into formulas, eg given P = 2l + 2b and P = 20, l = 6, solve for b
Solve problems involving linear equations, including those derived from formulas (ACMNA235)
Translate word problems into equations, solve the equations and interpret the solutions
Solve linear simultaneous equations, using algebraic and graphical techniques, including with the use of digital technologies (ACMNA237)
Solve linear simultaneous equations by finding the point of intersection of their graphs, with and without the use of digital technologies
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}
Linear Relationships
MA5.2-9NA
Interpret and graph linear relationships using the gradient-intercept form of the equation of a straight line
Recognise equations of the form y = mx + b as representing straight lines and interpret the x-coefficient (m) as the gradient, and the constant (b) as the y-intercept, of a straight line
Non-Linear Relationships
MA5.2-10NA
Explore the connection between algebraic and graphical representations of relationships such as simple quadratics, circles and exponentials using digital technologies as appropriate (ACMNA239)
Identify graphs and equations of straight lines, parabolas, circles and exponentials
Measurement and Geometry
Area and Surface Area
MA5.2-11MG
Calculate the surface areas of cylinders and solve related problems (ACMMG217)
Develop and use the formula to find the surface areas of closed right cylinders: Surface area of (closed) cylinder=2 pi r squared + 2 pi r h where r is the length of the radius and h is the perpendicular height
Volume
MA5.2-12MG
Solve problems involving volume for a range of prisms, cylinders and composite solids (ACMMG242)
Solve a variety of practical problems related to the volumes and capacities of prisms, cylinders and related composite solids
Properties of Geometrical Figures
MA5.2-14MG
Formulate proofs involving congruent triangles and angle properties (ACMMG243)
Write formal proofs of the congruence of triangles, preserving matching order of vertices
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
Use the enlargement transformations to explain similarity and to develop the conditions for triangles to be similar (ACMMG220)
Investigate the minimum conditions needed, and establish the four tests, for two triangles to be similar: LCCT if the three sides of a triangle are proportional to the three sides of another triangle, then the two triangles are similar if two
Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)
Apply geometrical facts, properties and relationships to find the sizes of unknown sides and angles of plane shapes in diagrams, providing appropriate reasons
Statistics and Probability
Probability
MA5.2-17SP
List all outcomes for two-step chance experiments, with and without replacement, using tree diagrams or arrays; assign probabilities to outcomes and determine probabilities for events (ACMSP225)
Calculate probabilities of simple and compound events in two-step chance experiments, with and without replacement
Stage 5.3
Numbers and Algebra
Ratios and Rates
MA5.3-4NA
Solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
Interpret distance/time graphs when the speed is variable
Describe qualitatively the rate of change of a graph using terms such as 'increasing at a decreasing rate'
Linear Relationships
MA5.3-8NA
Find the midpoint and gradient of a line segment (interval) on the Cartesian plane (ACMNA294)
Use the concept of an average to establish the formula for the midpoint, M, of the interval joining two points (x1,y1) and (x2,y2) on the Cartesian plane: M(x,y) = (x1 + x2 / 2, y1 + y2 / 2)
Solve problems using various standard forms of the equation of a straight line
Find the equation of a line passing through two points
Non-Linear Relationships
MA5.3-9NA
Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)
Find x- and y-intercepts, where appropriate, for the graph of y = ax squared + bx + c, given a, b and c
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
Measurement and Geometry
Volume
MA5.3-14MG
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
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
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
Circle Geometry
MA5.3-17MG
Prove and apply angle and chord properties of circles (ACMMG272)
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 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
Apply chord and angle properties of circles to find unknown angles and lengths in diagrams
Prove and apply tangent and secant properties of circles
Apply tangent and secant properties of circles to find unknown angles and lengths in diagrams
Statistics and Probability
Single Variable Data Analysis
MA5.3-18SP
Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)
Investigate the meaning and calculation of standard deviation using a small set of data
NSW Syllabus
Maths
Stage 5.2
Measurement and Geometry
Volume
MA5.2-12MG
Solve problems involving volume for a range of prisms, cylinders and composite solids (ACMMG242)
Outcomes
Solve a variety of practical problems related to the volumes and capacities of prisms, cylinders and related composite solids
Play Activities
14
Examples