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• 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

• VCLVU193

  Reflect on how ways of using language are shaped by communities’ ways of thinking, behaving and viewing the world, and the role of language in passing on knowledge

  Elaborations

  • explaining the role of Aboriginal languages and cultures in passing on knowledge such as sustainable care of the environment, rules for living, ways of behaving, spiritual and cultural functions and History
  • reflecting on Indigenous taxonomies and the ways they divide the natural and cultural world and comparing these to other systems of classification
  • analysing concepts related to cultural values in Aboriginal languages, including naming systems, for example, the use of kinship terms, nicknames, substitute words and pronoun systems, comparing to ways of referencing relationships in their own language(s) and culture(s)
  • exploring how aspects of traditional culture and society have been preserved through language, and discussing the importance of maintaining Australian Aboriginal and Torres Strait Islander languages, for their speakers and for all Australians
  • analysing and discussing core cultural concepts reflected in Aboriginal languages, such as respect, avoidance, reciprocity, obligation, responsibility
  • understanding that culturally significant attitudes and beliefs conveyed through Aboriginal languages are related to the past, to land, plants and animals and to celebrations
  • identifying and comparing how emotions or attitudes, such as respect, affection or embarrassment, are shown/displayed across different languages and cultures
  • comparing elements of communication such as the role of silence or use/avoidance of eye contact in different cultural contexts and exchanges
  • recognising that there are multiple views on and partial explanations for events and issues
  • reflecting on the ways culture is interpreted by others, for example, by identifying how stereotypes influence perceptions of other groups or individuals
  • understanding that each Aboriginal or Torres Strait Islander person inherits language as part of their birthright, along with membership of a particular group and attachment to Country or Place, and that they become custodians and owners of land, water or sea and of language

  VCLVU193 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Role of language and culture

• VCLVU194

  Explore language building processes and protocols in communities

  Elaborations

  • investigating language revival efforts in their own community and neighbouring regions, for example, who and what is involved, successes, challenges and protocols, and what these efforts mean to local communities
  • understanding what lexical and grammatical resources and processes are available to build language, for example, linguistic resources and analogies from neighbouring languages, speakers, archival material
  • investigating/understanding protocols for filling gaps and extending semantic domains in the language, including protocols for borrowing from other languages, for creating words by analogy and drawing from within the resources of the language, and discussing associated ethical issues
  • investigating/researching the protocols for receiving, transferring and publishing linguistic resources
  • understanding the importance of intergenerational collaboration in reviving languages, and discussing some of the associated challenges
  • discussing the importance of reviving languages for the individual, the language community and the wider Australian society
  • identifying potential avenues/domains for expansion of the language and gaps to be filled, with the support of community language teams and respected community members
  • appreciating the role of languages advocacy, education and research in building languages
  • understanding how the process of language-building expands existing linguistic and cultural resources in the Australian community

  VCLVU194 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Role of language building

• VCLVU186

  Expand vocabulary and understand and use a range of vocabulary sets and grammatical structures that are available in the language

  Elaborations

  • understanding case and case marking on nouns, pronouns and adjectives
  • explaining how verbs can be derived from nouns and vice versa, comparing with similar processes in English and other known languages
  • composing and varying messages according to the available resources of the language, such as:
    • suffixes, including ‘having’, ‘for want of’, ‘similar to’, ‘like’
    • verbless sentences, for example, equative, descriptive, possessive
    • verb categories, including intransitive, transitive, causative, inchoative, reflexive–reciprocal
    • verb aspect, including continuous, transitory, perfective, imperfective
    • verb-stem morphology, including compound verbs, reduplicated verbs, habitual/characteristic, derivation (nouns into verbs)
  • expressing time, manner, attitude and place, according to the available language resources, such as:
    • elaborations of past tense
    • temporal expressions, for example, ‘beforehand’, ‘afterwards’, ‘too late’, ‘originally’
    • expressions of frequency, immediacy and duration, for example, ‘persistently’, ‘at once’, ‘a few times’, ‘for a while’
    • attitudinal words, particles and interjections, for example, terms expressing endearment, embarrassment, shame or pity
    • locational cases as used in locative phrases, and extensions of these, for example, expressing origin or causation
  • structuring and linking clauses, focusing on issues of agreement with transitive and intransitive verbs, using verb-linking devices, for example, serialisation and embedding
  • discussing lexical and grammatical relationships between the language and other languages of the region, for example, common words and structures
  • discussing grammatical and lexical contrasts between the language and English/ other known languages, for example, the figurative use of language, vocabulary associated with specialised domains

  VCLVU186 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Systems of language

• VCLVU188

  Investigate how the kinship system functions to integrate personal and community histories and relationships

  Elaborations

  • understanding and discussing kinship as a system, and explaining its importance in maintaining and regulating social relationships in Aboriginal communities
  • investigating how the language community addresses gaps in knowledge about the kinship system
  • exploring how language is involved in the patterning of ownership and management of land and associated stories
  • understanding that different roles and responsibilities in community and public life can be determined by kinship and traditional social groupings
  • explaining how art forms, songs and dances identify people and places

  VCLVU188 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Systems of language

• VCLVU190

  Describe and reflect on how languages change over time and influence one another

  Elaborations

  • exploring form, usage, history and impact of contact languages, including creoles, pidgins and Aboriginal Englishes
  • investigating and describing how the language has changed over time
  • observing changes to language that reflect changing lifestyles, cultural trends and emerging needs, for example, youth language, the language of new technologies, the impact of music, media and technology on communication
  • reflecting on changes in their own use of their first language(s) over time, noticing how and when new ways are adopted or existing ways adapted
  • exploring changes in language over time, for example, by reviewing old films from state archives or early television shows that include Aboriginal actors

  VCLVU190 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Language variation and change

• VCLVU192

  Understand and apply cultural norms, skills and protocols associated with learning, using and researching Aboriginal languages

  Elaborations

  • using culturally appropriate protocols when engaging with and learning from Aboriginal peoples and communities
  • acknowledging cultural and intellectual property rights and copyright over language work, including song holders, story keepers, language informers, composers and choreographers

  VCLVU192 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Language awareness

• VCLVU191

  Investigate and compare the ecology of Aboriginal and Torres Strait Islander languages to Indigenous languages in other countries, and consider issues such as language policy, language rights, language loss, advocacy, reform and multilingualism

  Elaborations

  • investigating the social, cultural and linguistic effects of language change and/or language loss in the region
  • understanding terms used in the discussion of language revival, for example, revitalisation, reclamation, renewal
  • investigating the geographical extent of use of the language in earlier times
  • considering the future prospects of the language in the context of its current linguistic ecology
  • exploring Indigenous multilingualism in various communities, including regional varieties, Aboriginal Englishes and creoles
  • researching the impact on Aboriginal and Torres Strait Islander languages in general, and on the target language in particular, of historical events, government policies, legislation and judicial processes, such as stolen generations, mission schools and advocacy
  • identifying social and government policies and practices that have impacted positively on language acquisition, for example, the performing of Welcome to Country and the Acknowledgement of Country at events, on television programs, in films, and efforts to raise the profile of Aboriginal and Torres Strait Islander languages in the wider Australian community and in particular geographical regions
  • investigating the situation of indigenous languages in other countries, for example, New Zealand, Hawaii, North America, Japan, Latin America, considering issues such as language rights, language endangerment, revival and reclamation, drawing comparisons with the situation of Aboriginal languages and Torres Strait Islander languages in Australia
  • researching current media debates in relation to Aboriginal languages
  • comparing word lists of languages and dialects of the region, to understand similarities and differences and identify potential opportunities for reconstruction

  VCLVU191 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Language awareness

• VCLVU187

  Discuss the purpose and roles of various spoken, written and visual texts in the language

  Elaborations

  • understanding the purpose and role of different types of text in the language, for example, declaring identity, acknowledging parts of traditional belief systems, acknowledging ancestors, passing on knowledge and information, mapping resources on Country and managing natural phenomena such as weather
  • understanding that Country/Place can be interpreted as text by the community
  • discussing ways that songs function to capture language and meaning in ways similar to literature in other cultures
  • linking and sequencing ideas to form cohesive texts, using appropriate grammatical forms and elements, for example, serialisation, connectives, embedding, headings and paragraphing

  VCLVU187 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Systems of language

• VCLVU185

  Understand and explain the sound patterns in spoken language and use developing phonemic awareness to represent these patterns in written form

  Elaborations

  • reading aloud for meaning to demonstrate comprehension of sound–symbol correspondences
  • developing metalanguage to describe and talk about sounds and phonology, for example, place and manner of articulation, uncertain or missing sounds
  • investigating sound patterns, for example, consonant and vowel sequences, and word-level patterns, for example, allowable word-final sounds, allowable consonant clusters, word stress
  • understanding the major categories of place of articulation in Aboriginal languages, for example, peripheral, laminal, apical, and their realisation across different languages and regions in Australia
  • establishing similarities in the sound systems of related languages otherwise masked by differing spelling systems
  • using their knowledge of alphabetic conventions for Aboriginal languages to transcribe spoken texts from a range of languages, for example, those related to the target language or those from neighbouring regions
  • comparing and explaining the relative consistency of Aboriginal languages and English in spelling words
  • understanding the phonemic basis of alphabetic spelling systems and the fact that different sounds can be covered within a single phoneme or letter
  • exploring different writing systems that are based on different principles, for example, syllabic or ideographic

  VCLVU185 | Languages | Victorian Aboriginal Languages | Levels 7 to 10 | Understanding | Systems of language

• VC2M9A02

  simplify algebraic expressions, apply the distributive law to expand algebraic expressions including binomial products, and factorise monic quadratic expressions

  Elaborations

  • expanding combinations of binomials such as x+7x+8, x+7x-8,  x-7x+8,  (x-7)(x-8) to identify expansion and factorisation patterns related to x+ax+b=x2+a+bx+ab, where a and b are integers
  • using manipulatives such as algebra tiles or area models to expand or factorise algebraic expressions with readily identifiable binomial factors; for example, x+1x+3=x2+4x+3, (x-5)2=x2-10x+25 or (x-3)2+4=x2-6x+9+4=x2-6x+13
  • recognising the relationship between expansion and factorisation, and using digital tools to systematically explore the factorisation of x2+mx+n where m and n are integers

  VC2M9A02 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A03

  sketch linear graphs of equations in various algebraic forms, using the coordinates of 2 points, and solve linear equations

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs, and describing them using both words and algebra

  VC2M9A03 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A06

  use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and...

  Elaborations

  • modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically
  • modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w; for example, l=w,  l=w+5,  l=3w,  l=2w+7
  • modelling practical contexts (for example, area, paths of projectiles, parabolic mirrors, satellite dishes) using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and, algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes
  • modelling and solving problems involving financial contexts using linear functions, for example, combinations of purchases of different items when they have a set amount of money to spend, profit/loss situations and trade quotes involving call-out fees
  • modelling situations involving change, for example, change in daily temperature during the ski season, fluctuation of speed above and below the speed limit, and acceleration and deceleration of a car coming to and moving off from a set of traffic lights
  • modelling the hunting techniques of Aboriginal and Torres Strait Islander Peoples using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey 

  VC2M9A06 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A04

  find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

  Elaborations

  • recognising that the gradient of a line is calculated using the gradient of a line segment on that line and is independent of which 2 distinct points on the line are used for this calculation
  • using digital tools and transformations to illustrate that parallel lines in the Cartesian plane have the same gradient and that the relationship between the gradients of pairs of perpendicular lines is that their product is (−1)
  • using Pythagoras’ theorem to establish the distance between 2 points in the Cartesian plane and applying this using horizontal and vertical distances and coordinates
  • investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between 2 points
  • using dynamic graphing software and superimposed images (for example, playground equipment, ramps and escalators) to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts

  VC2M9A04 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A07

  experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns 

  Elaborations

  • investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpreting the effects of these transformations using digital tools; for example,
    y=x→y=2x (vertical enlargement as a>1) →y=2x-1 (vertical translation) and
     y=x→y=12x (vertical compression as 0<a<1) →y=-12x (reflection in the horizontal axis) →y=-12x+3 (vertical translation)
  • investigating transformations of the parabola y=x2 to the graph of y=ax-h2+b in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example,
    y=x2→y=13x2 (vertical compression as 0<a<1) →y=13(x-5)2 (horizontal translation) →y=13(x-5)2+7 (vertical translation) or
    y=x2→y=2x2 (vertical enlargement as a>1) →y=-2x2 (reflection in the horizontal axis) →y=-2(x+6)2 (horizontal translation) →y=-2x+62+10 (vertical translation)
  • experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=1x, square root y=x, cubic y=x3 and exponential functions y=2x, y=(12)x, identifying patterns

  VC2M9A07 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A01

  apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables

  Elaborations

  • representing decimals in exponential form; for example, 0.475 can be represented as 0.475=410+7100+51000=4×10-1+7×10-2+5×10-3 and 0.00023 as 23 × 10^-5
  • simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, 5-3=153=(15)3=1125 and connecting terms of the sequence 125, 25, 5, 1, 15, 125, 1125… to terms of the sequence 53, 52,51, 50, 5-1, 5-2, 5-3...
  • relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, 23÷25=2-2=122=14 and (3×5)2=32×52=9×25=225
  • recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number a, a0=1, x1=x,  r2=r×r,  h3=h×h×h,  y4=y×y×y×y, and 1w×1w=1w2=w-2
  • relating simplification of expressions from first principles and counting to the use of exponent laws; for example,
    (a2)3=a×a×a×a×a×a=a×a×a×a×a×a=a6;
    b2×b3=b×b×b×b×b=b×b×b×b×b=b5; y4y2=y×y×y×yy×y=y21=y2 and (5a)2=5×a×5×a=5 ×5×a×a=25×a2=25a2 
  • applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, (2xy)3xy4=8x3y3xy4=8x2y-1
  • relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10^-12 grams and one terabyte = 10¹² bytes

  VC2M9A01 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A05

  identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

  Elaborations

  • recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
  • graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values; and determining when values of the quadratic function lie within a given range
  • solving quadratic equations algebraically and comparing these to graphical solutions
  • using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the x-intercepts of its graph and that if the graph has no x-intercepts, then the corresponding equation has no real solutions
  • relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function y=x2-5x+6 can be represented as y=x-2x-3 with x-axis intercepts where either x-2=0 or x-3=0
  • recognising that the equation x2=a, where a>0, has 2 solutions, x=a and x=-a (for example, if x2=39 then x=39=6.245 correct to 3 decimal places, or x=-39=-6.245 correct to 3 decimal places) and representing these graphically
  • graphing percentages of illumination of moon phases in relation to Aboriginal and Torres Strait Islander Peoples’ understandings that describe the different phases of the moon

  VC2M9A05 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9M02

  solve problems involving very small and very large measurements, timescales and intervals expressed in scientific notation

  Elaborations

  • representing very large and very small real numbers in scientific notation, converting real numbers expressed in scientific notation into decimal form; for example, the approximate geological age of Earth is 4.6 × 10⁹ years, and the mass of a glucose molecule is 2.99 × 10⁻²² grams
  • using knowledge of place value and applying exponent laws to operate with numbers expressed in scientific notation in applied contexts; for example, performing calculations involving extremely small numbers in scientific and other contexts
  • examining the degree of accuracy that different measurement instruments provide in a science laboratory, such as a measuring cylinder compared with a pipette, and recording data values to the correct degree of accuracy using appropriate scientific notation

  VC2M9M02 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M9M01

  solve problems involving the volume and surface area of right prisms, cylinders and composite objects using appropriate units

  Elaborations

  • analysing nets of objects to generate short cuts and establish formulas for surface area 
  • determining the amount of material needed to make can-coolers for a class fundraising project and working out the most cost-efficient way to cut out the pieces
  • finding different prisms that have the same volume but different surface areas, making conjectures as to what type of prism would have the smallest or largest surface area
  • investigating objects and technologies of Aboriginal and Torres Strait Islander Peoples, analysing and connecting surface area and volume, and exploring their relationship to their capacity

  VC2M9M01 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M9M03

  solve spatial problems, applying angle properties, scale, similarity, ratio, Pythagoras’ theorem and trigonometry in right-angled triangles

  Elaborations

  • investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
  • applying the formula for calculation of distances between points on the Cartesian plane from their coordinates, emphasising the connection to vertical and horizontal displacements between the points 
  • understanding the relationship between the corresponding sides of similar right-angled triangles and establishing the relationship between areas of similar figures and the ratio of corresponding sides, the scale factor
  • using images of proportional relationships to estimate actual measurements (for example, taking a photograph of a person standing in front of a tree and using the image and scale to estimate the height of the tree), discussing the findings and ways to improve the estimates
  • investigating theorems and conjectures involving triangles, for example, the triangle inequality and generalising links between the Pythagorean rule for right-angled triangles, and related inequalities for acute and obtuse triangles, determining the minimal sets of information for a triangle from which other measures can all be determined
  • using knowledge of similar triangles, Pythagoras’ theorem, rates and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree, and calculating the density and dry mass to predict how much paper could be manufactured from the tree

  VC2M9M03 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement