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• VC2M3M05

  identify angles as measures of turn and use right angles as a reference to compare angles in everyday situations

  Elaborations

  • using quarter, half and three-quarter turns and comparing them to a right angle, for example, a quarter turn is the same as a right angle; a half a turn is greater than a right angle and is the same as 2 right angles; a three-quarter turn is greater than a right angle and is the same as 3 right angles
  • recognising that right angles occur at the corners of many everyday objects, for example, books, windows, tabletops and whiteboards
  • identifying angles that are bigger than, smaller than and the same as a right angle in the environment; for example, opening doors partially and fully and comparing the angles created to a right angle
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games to investigate angles as measures of turn, for example, in the game Waayin from the Datiwuy People in the northern part of the Northern Territory

  VC2M3M05 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M10M03

  solve practical problems by applying Pythagoras’ theorem and trigonometry to right-angled triangles, including problems involving direction and angles of elevation and depression

  Elaborations

  • applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
  • applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
  • using a clinometer to measure angles of inclination, and applying trigonometry and proportional reasoning to determine the height of buildings in practical contexts
  • applying Pythagoras’ theorem and trigonometry and using dynamic geometry software to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
  • exploring navigation, design of technologies or surveying by Aboriginal and Torres Strait Islander Peoples, investigating geometric and spatial reasoning and how these connect to trigonometry 

  VC2M10M03 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M3M03

  recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events

  Elaborations

  • estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
  • planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
  • reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock
  • using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
  • exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars

  VC2M3M03 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M9M05

  use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

  Elaborations

  • modelling situations that involve direct proportion (such as pro rata pay rates, exchange rates, multiple quotes for a job, conversion between scales or other appropriate science contexts); for example, situations that involve Hooke’s law and other science contexts involving wavelengths and frequencies
  • modelling situations that impact on image editing used in social media and how proportion may not be maintained and can result in distorted images
  • modelling situations involving compliance with building and construction standards in design and construction, such as the rise and tread of staircases, and vertical and horizontal components of escalators
  • modelling situations involving the application of rates in practical contexts, for example, density, birth, flow or heartbeats
  • exploring fire techniques in land management practices used by Aboriginal and Torres Strait Islander Peoples that use proportion relationships, including the rate of fire spread in different fuel types to wind speed, temperature and relative humidity

  VC2M9M05 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M10M02

  interpret and use logarithmic scales in applied contexts involving small and large quantities and change 

  Elaborations

  • understanding that the logarithmic scale is calibrated in terms of order of magnitude, for example, doubling or powers of 10
  • identifying and interpreting data representations (charts and graphs) that use logarithmic scales (for example, graphs representing percentage change, a wide range of values or exponential growth) and discussing when it is appropriate to use this type of scale and when it is not appropriate
  • investigating and interpreting logarithmic scales used in real-world contexts (for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of microorganisms and disease) and describing reasons for choosing to use a logarithmic scale rather than a linear scale
  • investigating dating methods of geological sites to provide evidence of Aboriginal and Torres Strait Islander Peoples’ presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales, scientific notation and measurement accuracy in the dating

  VC2M10M02 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M3N05

  multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

  Elaborations

  • applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem
  • using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems
  • matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve
  • formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences

  VC2M3N05 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M6P01

  describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–‍1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals

  Elaborations

  • recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen
  • using a scale of zero to one or 0% to 100% to estimate chances of events
  • listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4
  • recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

  VC2M6P01 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability

• VC2M8SP03

  describe in different ways the position and location of three-dimensional objects in 3 dimensions, including using a three-dimensional Cartesian coordinate system with the use of dynamic geometry software or other digital tools

  Elaborations

  • locating aircraft or drones using latitude, longitude and altitude as a three-dimensional coordinate system
  • constructing three-dimensional objects using 3D printers or designing software that uses a three-dimensional coordinate system
  • comparing and contrasting two-dimensional and three-dimensional coordinate systems by highlighting what is the same and what is different, including virtual maps versus street views
  • using dynamic geometry software to construct shapes and objects within the first quadrant of a three-dimensional coordinate system
  • interpreting three-dimensional coordinate locations for objects in multistorey car parks, or playing games based on three-dimensional coordinate systems such as three-dimensional noughts-and-crosses
  • exploring position and transformation through geospatial technologies used by Aboriginal and/or Torres Strait Islander communities

  VC2M8SP03 | Mathematics | Mathematics Version 2.0 | Level 8 | Space

• VC2M1SP01

  make, compare and classify familiar shapes; recognise familiar shapes and objects in the environment, identifying the similarities and differences between them

  Elaborations

  • classifying a collection of shapes including different circles, ovals, regular and irregular shapes, triangles and quadrilaterals, saying what is the same about the shapes in a group and what is different between the shapes in a group
  • selecting a shape from a small collection of shapes inside a bag and describing the shape by feel, so that others can name the shape and give reasons for their choice
  • comparing the different objects that can be built out of the same number of blocks or centi-cubes and discussing the differences between them
  • exploring string games used in storytelling by Aboriginal and/or Torres Strait Islander Peoples (for example, in Karda from the Yandruwandha Peoples of north-eastern South Australia), recognising, comparing, describing and classifying the shapes made by the string and these shapes’ relationship to shapes and objects on Country/Place

  VC2M1SP01 | Mathematics | Mathematics Version 2.0 | Level 1 | Space

• VC2M3SP02

  interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other

  Elaborations

  • designing the layout of a space; for example, designing a proposed games room or a classroom using a blank sheet of paper as the boundary and cut-outs of shapes to represent furniture from a top-view perspective
  • locating themselves within a space, such as a basketball court, oval, stage or assembly hall, guided by a simple hand-held plan indicating the different positions of the participants in the activity
  • sketching a map indicating where they have hidden an object within the classroom, swapping maps with partners and then providing feedback about what was helpful and what was confusing on the map
  • identifying differences in the representation of a place on a map, in an aerial photograph, in a street view and in a satellite image, and discussing the different information the representations can give
  • exploring land maps or cultural maps used by Aboriginal and Torres Strait Islander Peoples to locate, identify and position important landmarks such as waterholes

  VC2M3SP02 | Mathematics | Mathematics Version 2.0 | Level 3 | Space

• VC2M5SP03

  describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries

  Elaborations

  • understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not its shape or size
  • using pattern blocks and paper, tracing around a shape and then conducting a series of one-step transformations and tracing each resulting image, and then finally copying the original position and end position on a new sheet of paper
  • demonstrating how different combinations of transformations can produce the same resulting image
  • challenging classmates to select a combination of transformations to move from an original image to the final image, noting the different combinations by using different colours to trace images
  • investigating how animal tracks can be interpreted by Aboriginal and Torres Strait Islander Peoples using the transformation of their shapes, to help determine and understand animal behaviour

  VC2M5SP03 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VC2M4ST01

  acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

  Elaborations

  • investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features
  • understanding that data can be represented with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements
  • constructing graphs of data collected through observation during science experiments, recording, interpreting and discussing the results in terms of the scientific study
  • acquiring samples of data using practical activities, observations or repeated chance experiments; recording data using tally charts, digital tables or spreadsheets; and graphing, discussing and comparing the results using a column graph
  • using secondary data of fire burns to construct data displays that assist Aboriginal and/or Torres Strait Islander ranger groups and other groups to care for Country/Place

  VC2M4ST01 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• VC2M5ST01

  acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data

  Elaborations

  • recognising that ordinal data is a form of categorical data even though the data being collected might be numbers, for example, a rating scale using numbers 1–5 to represent the categories people can choose from when asked, ‘What rating would you give this film out of 5?’
  • determining the mode for a set of data and discussing that there may be more than one mode
  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
  • acquiring data through chance experiments, discussing and reporting on the distribution of outcomes and how this relates to equal and unequal outcomes
  • using digital systems to validate data; for example, recognising the difference between numerical, text and date formats in spreadsheets, and setting data types in a spreadsheet to make sure a date is input correctly
  • investigating data relating to the reconciliation process between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, posing questions, discussing and reporting on findings

  VC2M5ST01 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M8ST03

  compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation

  Elaborations

  • comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
  • using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
  • using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
  • investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
  • investigating Aboriginal and/or Torres Strait Islander ranger groups and other groups’ use of sampling techniques to track biodiversity of species

  VC2M8ST03 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M9ST05

  plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

  Elaborations

  • planning and conducting an investigation using questions together with analysis of a secondary data set collected from online databases such as the Australian Bureau of Statistics
  • planning and conducting an investigation relating to consumer spending habits; and modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias
  • investigating where would be the best location for a tropical fruit plantation, by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
  • posing statistical questions; collecting, representing and interpreting data from different sources in relation to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians; and considering the relationships between variables

  VC2M9ST05 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VCLVC161

  Explore their own sense of identity, including elements such as family, friends, interests, membership of groups, and consider markers of identity that may be important across all cultures

  Elaborations

  • creating a class wall chart or family tree, labelling with appropriate kinship terms (Aboriginal and Torres Strait Islander students may be able to source information about their totems/moieties and other affiliations from home, family and community sources)
  • investigating and discussing, as culturally appropriate, the meaning of personal, family and other names and their significance as markers of identity
  • working with respected community members to map community-wide links between families according to known kin links
  • designing visual representations, such as concept maps, posters or captioned slide presentations, of their group memberships, for example, friendship, family, sporting, interest and community groups, moieties, and discussing what such membership means to their sense of identity
  • creating a profile to capture their sense of personal identity, for example, through an avatar or montage, using key words and expressions and commenting on the significance of particular events, influences or interactions
  • considering how their individual upbringing and experiences impact on their assumptions/attitudes when participating in intercultural interactions, for example, in relation to notions of leisure/free time or family and community responsibilities
  • talking about ways local Aboriginal communities express elements of their shared identity, for example, through behaviours associated with sporting teams, distinctions between coastal versus inland communities, through community events and profiling of identities from their community
  • noticing and comparing their use of words or expressions from different languages when communicating in English and discussing how this relates to their sense of identity
  • monitoring their development as learners of the language, for example, by recording learning experiences, reflections in blogs, learning logs or journals
  • identifying markers of identity that may be important across all cultures, for example, family, community, location, language, age, gender
  • exploring the concept of collective identity by designing an item, such as a language flag or artefact, that incorporates elements of importance to the language/community

  VCLVC161 | Languages | Victorian Aboriginal Languages | Levels 3 to 6 | Communicating | Identity

• VCLVU195

  Investigate and explain techniques used to build language, considering challenges involved and understanding their role as contemporary documenters of language

  Elaborations

  • identifying and discussing the main areas of the language that could be served by language building
  • analysing the authenticity of historical sources used in language building and discuss the strengths and limitations of these
  • investigating different approaches that have historically been used to record language and what this means for language revival, for example, different spellings, different domains of use, lexical biases
  • understanding challenges in developing new words and structures for the language, and how these words might be developed within the existing resources of the language or by analogy from related languages
  • discussing techniques used to build language, such as analysing historical sources, interviewing/recording existing speakers
  • understanding the orthographic and grammatical choices of the contemporary community
  • considering domains of use where the language may grow in the future
  • trying out ways of making new words under the guidance of an Aboriginal languages specialist or a respected community member where appropriate
  • working with local Aboriginal communities in language-related projects, and contributing to local language records and resources through structured and research-based projects
  • understanding their role as contemporary documenters of the language, for example, listening and transcribing spoken texts, preserving language resources developed at school
  • developing a variety of resources for younger and future students of the language
  • investigating programs and initiatives that serve to maintain and strengthen language use, for example, school languages programs, bilingual education, research programs, recording and archiving material, websites, databases and documentaries
  • exploring the importance of advocacy in supporting the maintenance and development of language and culture

  VCLVU195 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Role of language building

• VC2M2M01

  measure and compare objects based on length, capacity and mass using appropriate uniform informal units and smaller units for accuracy when necessary

  Elaborations

  • choosing suitable informal units to measure the length of a range of objects, and justifying their choice of a longer unit to measure things that are long (such as the width of a room) and a shorter unit to measure shorter things or when more accuracy is needed
  • comparing the capacity of several containers using sand and units such as a spoon or cup, to say which container will hold the most and how much more it will hold; recording the results; writing an explanation of their measurement process, including using smaller units to be more accurate; and justifying the result
  • using balance scales to compare the mass of several objects, selecting an appropriate informal unit; counting the number of informal units to determine which object is heavier and how much heavier; and explaining why the informal units chosen need to be the same mass
  • recognising that the same informal unit needs to be used when measuring (for example, demonstrating and discussing why using different shoe lengths to measure the same distance could result in the measures being different) and discussing why a smaller-sized informal unit may result in a larger number of units compared to a larger-sized informal unit
  • investigating Aboriginal and/or Torres Strait Islander Peoples’ use of body parts, such as hands, as uniform informal units of measurement used to measure and compare objects, for example, in the manufacturing of nets for a particular purpose
  • investigating and comparing measurable attributes that are interpreted by Aboriginal and/or Torres Strait Islander Peoples to understand animal behaviour, such as the length, width and depth of animal tracks

  VC2M2M01 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VCASFC116

  Translate and interpret different types of familiar short texts, demonstrating awareness of individual interpretations of meaning

  Elaborations

  • translating the school song into Auslan with support, identifying words or phrases that do not easily translate and finding suitable equivalents in Auslan that match the English concept
  • shadowing online Auslan translations and captioning, such as the Catching Fire series of safety videos or the emergency disaster preparedness videos
  • comparing their own translations of short familiar texts with those of their classmates, noting discrepancies or variations and discussing possible reasons for these
  • observing and interacting with deaf guests to the classroom who use different signed languages, such as ASL or a traditional signed language used by deaf Aboriginal and Torres Strait Islander elders, identifying differences between the languages and acting as interpreter with support
  • creating basic translations of song lyrics or simple poems from English to Auslan
  • translating and explaining the meaning of words or expressions associated with figurative language use in Auslan, such as train gone, sorry and comparing these to some common English idioms
  • conducting sight translations of plain, high-interest, low-readability English texts such as short news articles that are written for their age group
  • comparing existing translations in Auslan of narratives, such as fairytales or short stories, to their own ideas of how they would translate specific segments of these texts
  • explaining the role of accredited Auslan–English interpreters and that of Deaf interpreters, demonstrating through role-play correct protocols for working with interpreters

  VCASFC116 | Languages | Auslan | First Language Learner | 7–10 Sequence | Levels 9 and 10 | Communicating | Translating

• VCASFU125

  Understand the range of factors that influence the profile, diversity and distribution of Auslan use in the wider Australian society, and consider the concept of Auslan vitality in comparison with that of other languages

  Elaborations

  • understanding that strong and healthy languages are those used by many people across generations in most domains to communicate about most topics
  • mapping the distribution of Auslan users across Australian states and demographics, using data from censuses and other sources to present findings in graph/visual representation forms
  • exploring the vitality of different languages by obtaining information from the UNESCO interactive online atlas and/or Ethnologue to compare numbers of speakers/signers of different languages
  • recognising that some languages have no written form and have historically been passed on face to face/orally, making them less well recorded and documented
  • understanding that some languages used in Australia, such as English, have large numbers of users, while others, such as many Aboriginal and Torres Strait Islander languages, are endangered or in the process of being revived or reclaimed
  • describing the role religion has played in influencing the usage and spread of Auslan, for example, through religious orders, early Deaf Societies and Bible translation projects
  • reflecting on the role of Auslan interpreters in raising awareness and understanding of Auslan in the wider community, and considering ways in which they influence the function and nature of Auslan, for example by the introduction of neologisms
  • identifying language documentation tools, such as ELAN, as important ways of recording, transmitting and maintaining the vitality of a language
  • recognising that languages may be perceived as ‘weak’ or ‘strong’ based on community values and the existence of documentation and literature in the language

  VCASFU125 | Languages | Auslan | First Language Learner | 7–10 Sequence | Levels 9 and 10 | Understanding | Language awareness