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• VC2M8N04

  use the 4 operations with integers and with rational numbers, choosing and using efficient mental and written strategies, and digital tools where appropriate, and making estimates for these computations

  Elaborations

  • using patterns to assist in establishing the rules for the multiplication and division of integers
  • applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
  • recognising the effect of sign in the multiplication of integers, for example, (-1)4=1 and (-1)5=-1

  VC2M8N04 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M7N08

  compare, order and solve problems involving addition and subtraction of integers

  Elaborations

  • using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as -5<+2; -3>-6
  • discussing language such as ‘addition’, ‘subtraction’, ‘magnitude’, ‘difference’ and ‘sign’ and synonyms of these terms
  • ordering, adding and subtracting integers using a number line

  VC2M7N08 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7A03

  solve one-variable linear equations of increasing complexity with natural number solutions; verify equation solutions by substitution

  Elaborations

  • recognising that solving an equation is a process of determining a value that makes the equation true; and using substitution to determine whether a given number is a solution to an equation or not
  • solving equations using concrete materials, the balance model and backtracking, explaining the process
  • solving linear equations such as 3x+7=19 algebraically, and verifying the solution by substitution

  VC2M7A03 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M5N04

  recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

  Elaborations

  • recognising applications of percentages used in everyday contexts, for example, the bar model used for charging devices indicating the percentage of power remaining, and advertising in retail contexts relating to discounts or sales
  • creating a model by subdividing a whole (for example, using 10 × 10 grids to represent various percentage amounts) and recognising complementary percentages (such as 30% and 70%) combine to make 100%
  • creating a model by subdividing a collection of materials, such as blocks or money, to connect decimals and percentage equivalents of tenths and the commonly used fractions 12, 14 and 34; for example, connecting that one-tenth or 0.1 represents 10% and one-half or 0.5 represents 50%, and recognising that 60% of a whole is 10% more of the whole than 50%
  • using physical and virtual materials to represent the relationship between decimal notation and percentages, for example, 0.3 is 3 out of every 10, which is 30 out of every 100, which is 30%

  VC2M5N04 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M8P01

  recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts

  Elaborations

  • understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
  • using the relationship that for a single event A, Pr(A) + Pr(not A) = 1; for example, if the probability that it rains on a particular day is 80%, the probability that it does not rain on that day is 20%, or the probability of not getting a 6 on a single roll of a fair dice is 1-16=56
  • using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is 13 and probability of not throwing a 5 or 6 is 23

  VC2M8P01 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability

• VC2M10AP01

  explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities

  Elaborations

  • applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
  • understanding that a set with n elements has 2ⁿ different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table; for example, the set {a, b, c} has 2³ = 8 subsets which are { ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
  • using the definition of n! to represent and calculate in contexts that involve choices from a set; for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement?
  • performing calculations on numbers expressed in factorial form, such as n!r! to evaluate the number of possible arrangements of n objects in a row, r of which are identical; for example, 5 objects, 3 of which are identical, can be arranged in a row in
    5!3!=5×4×3×2×13×2×1= 20 different ways

  VC2M10AP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability

• 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

• VCASFU233

  Develop awareness of the sociocultural context, nature and status of Auslan and of the Deaf community in multilingual Australia

  Elaborations

  • identifying the importance of place and space in the Deaf community, exploring why some places and spaces ensure that a visual language is more accessible to deaf people and promotes a sense of cultural belonging, for example by identifying factors that make a classroom ‘Deaf friendly’, such as U-shape seating, minimisation of window glare/reflection, good lighting and acoustics, flashing lights, suitable interpreter location
  • identifying examples of deaf people’s visual orientation towards the world, such as using visual applause or being astute in reading body language
  • describing how and why deaf people use vibrating devices to alert them to alarms or information, or have flashing lights for the door, phone, alarm clock, baby cry alarm and other systems
  • understanding cultural values associated with the conferring of name signs on those such as second language learners of Auslan who are joining the Deaf community
  • explaining the role and function of Auslan–English interpreters and Deaf interpreters and the access and opportunities they provide
  • identifying and describing physical markers of identity among deaf people, including the use of sign language and/or hearing devices such as hearing aids, cochlear implants and FM systems
  • exploring variation in Auslan fluency among their classmates and members of the Deaf community, identifying the influence of variables such as where and when people learnt to sign and whether they are from a deaf or hearing family
  • investigating how Auslan and Deaf culture are promoted in the wider community, for example through the influence of organisations such as Deaf Australia; the work of high-profile individuals such as activists or actors; or through events such as NWDP Deaf Festival, Australian Deaf Games or Deaf art exhibitions
  • understanding the nature of the transmission of Auslan, for example how in most cases Auslan is not passed on from parent to child but often from child to child, or to children by adults outside the family, and knowing that some Deaf people learn Auslan as a late acquired language in early adulthood
  • exploring the nature of multilingualism in the Deaf community, including the use of Auslan, English and other signed and spoken languages, considering how and when people typically switch between languages and dialects
  • investigating the use of digital technology/communication by Auslan users, for example, social media, SMS/texting and NRS and VRS, discussing how these modes of communication impact on issues such as accessibility and communication between members of the Deaf community
  • investigating communication methods used by deaf and hard of hearing members of Aboriginal and Torres Strait Islander communities
  • discussing behaviour associated with cultural practices, language and traditions, for example, by discussing the concept of reciprocity as a manifestation of how community members share responsibility for each other’s wellbeing, or the value placed on the use of sign language for shared understanding and trust

  VCASFU233 | Languages | Auslan | Second Language Learner | 7–10 Sequence | Levels 7 and 8 | Understanding | Language awareness

• VCLAE020

  Translate a range of texts that incorporate complex sentence structures and extensive vocabulary from Latin into Standard English, representing the style and purpose of the texts

  Elaborations

  • reading holistically to deduce the context and content of Latin texts, by identifying key words and phrases
  • applying expanded knowledge of vocabulary, grammar and problem-solving skills to translate compound sentences and complex sentences with nested clauses
  • conveying shades of meaning of a range of subtle vocabulary, for example, inferring the different connotations of a word in a particular context, such as virtus; causa; gero; ago
  • inferring the meaning of words and expressions, using knowledge of the text type and the author’s purpose and style, for example, res publica; rem gerere; se gerere
  • deducing the meaning of new words by drawing on prior knowledge, derivatives and connections with familiar words, for example, actores in scaena fabulam Graecam hilare agebant; dormire, obdormire; ferre, inferre, offerre
  • expanding the variety of English translations for verb tenses, for example, to express indignation, clamavit as ‘she did shout’, compared to ‘she shouted’ or ‘she has shouted’
  • recreating mood, tone and dramatic impact in English translations by selecting appropriate vocabulary, comparing and contrasting potential choices, for example, o tempora! o mores!
  • refining translations by exploring print and online Latin and English dictionaries and thesauruses to consider a variety of meanings, for example, manus, and synonyms, for example, contentus, felix, laetus
  • conveying emphasis and tone, such as indignation, anger, suspense, embedded in Latin word order, for example, effugere conati sunt, sed frustra
  • rendering the precise meaning of tenses in Latin into idiomatic English, for example, cotidie ibat; si veneris
  • expressing the meaning of idiomatic expressions and culturally specific terms by choosing appropriate English expressions and terms, for example, flocci non facio (I could care less); orationem habere (deliver a speech)
  • constructing and editing translations collaboratively with peers, using a range of ICT
  • improving own translations to increase accuracy and better reflect register, tone and characterisation
  • translating, independently or in collaboration with peers, unseen texts with compound or complex sentences, drawing on familiarity with the style and language of texts already studied

  VCLAE020 | Languages | Latin | Levels 9 and 10 | Engaging with texts | Translating

• 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

• VC2M10AA04

  explore the inverse relationship between exponential functions and logarithmic functions and the solution of related equations

  Elaborations

  • using the definition of a logarithm and the exponent laws to establish the logarithm laws
  • evaluating 10x for decimal values of x and relating this to a logarithm base 10 scale; solving exponential equations algebraically using logarithms with base 10, for example, 5000×1.01x=10 000⇒x= log10(2)log10(1.01)≈69.66 ; and connecting to the graph of the corresponding function

  VC2M10AA04 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M9SP02

  apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain, using language of similarity, ratio and scale, aspects that remain the same and those that change

  Elaborations

  • comparing the ratio of lengths of corresponding sides of similar triangles and angles 
  • using the properties of similarity to solve problems involving enlargement
  • investigating and generalising patterns in length, angle, area and volume when side lengths of shapes and objects are enlarged or dilated by whole and rational numbers; for example, comparing an enlargement of a square and a cube of side length 2 units by a factor of 3 increases the area of the square, (3×2)2=9×22=9 times the original area and the volume of the cube, 23, to (3×2)3=27×23=27 times the volume

  VC2M9SP02 | Mathematics | Mathematics Version 2.0 | Level 9 | Space

• VC2M10A16

  solve equations graphically or using systematic numerical guess-check-and-refine with digital tools, with consideration of whether all solutions have been found

  Elaborations

  • refining intervals on graphs and/or in tables of values to determine with increasing accuracy when the values of 2 functions are approximately equal
  • applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as x2=2x

  VC2M10A16 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A08

  solve linear inequalities and graph their solutions on a number line

  Elaborations

  • representing word problems with simple linear inequalities and solving them to answer questions
  • graphing regions corresponding to inequalities in the Cartesian plane (for example, graphing 2x+3y<24) and verifying using a test point such as (0, 0)

  VC2M10A08 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VCIDU083

  Analyse the ways in which Indonesian varies according to spoken and written forms, cultural context and subcultures

  Elaborations

  • comparing spoken and written texts (for example, spoken and print advertisements, face-to-face conversations and emails) to understand how mode relates to linguistic structures and features, and how this affects meaning
  • analysing examples of colloquial language, such as that used by sub-groups (for example, Bahasa gaul, Bahasa SMS), and comparing these to formal forms
  • understanding how body language varies across cultures, for example, lowering body position when speaking to someone in authority to show respect; not raising voice or laughing loudly; smiling and nodding while listening to people, even when hearing bad news
  • understanding that many Indonesians are familiar with a range of languages (for example, Bahasa baku, Bahasa daerah, Bahasa gaul and English) and can shift between these depending on the context, and considering how this compares to those who are monolingual

  VCIDU083 | Languages | Indonesian | F–10 Sequence | Levels 9 and 10 | Understanding | Language variation and change

• VC2M8A01

  create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties

  Elaborations

  • rearranging and simplifying linear expressions involving variables with integer coefficients and constants; and using manipulatives such as algebra tiles to support calculations, for example, using manipulatives to demonstrate that 2x+4=2x+2 , 3a-b=3a-3b, or 5m+2n+3m-4n= 5m+10n+3m-4n=8m+6n
  • demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language
  • using the distributive, associative, commutative, identity and inverse properties to expand and factorise algebraic expressions using strategies such as the area model

  VC2M8A01 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VC2M10AA10

  experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

  Elaborations

  • applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as fx=2x2-3x-7
  • applying transformations to the graph of x2+y2=1
  • identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
  • identifying intervals on the real number line over which a given quadratic function is positive or negative
  • using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay

  VC2M10AA10 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M7N09

  recognise, represent and solve problems involving ratios

  Elaborations

  • using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios 1:4 and 1:1:2
  • using fractions to solve ratio problems involving comparison of quantities and considering part-part and part-whole relations; for example, dividing a set into the ratio 1:2 by determining the number of parts as 3
  • sharing quantities in a given ratio; for example, sharing an amount of money in a given ratio, such as sharing $20 in the ratio 2:3
  • applying ratios to realistic and meaningful contexts – for example, mixing 500 millilitres of a liquid with a concentration of 1:4 means 15 concentrate and 45 water so, 0.2 of 500 millilitres is concentrate and 0.8 of 500 millilitres is water – and interpreting results in context

  VC2M7N09 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M6N08

  approximate numerical solutions to problems involving rational numbers and percentages, using appropriate estimation strategies

  Elaborations

  • using familiar fractions, decimals and percentages to approximate calculations, such as 0.3 of 180 is about 13 of 180, or 52% is about 12
  • choosing appropriate estimation strategies including rounding to the nearest whole number, knowledge of multiples of 2, 5 or 10 and partitioning numbers, in contexts such as measuring or cost per unit
  • recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between
  • recognising the usefulness of estimation to check calculations for contexts such as dividing wood into a number of lengths, calculating cost per unit, reducing a recipe or dividing the cost of dinner for a group into individual amounts
  • verifying solutions by estimating percentages in suitable contexts, such as discounts, using common percentages of 10%, 25%, 30%, 50% and 1%
  • investigating estimation strategies to make decisions about steam cooking in ground ovens by Aboriginal and/or Torres Strait Islander Peoples, including catering for different numbers of people and resources needed for cooking

  VC2M6N08 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M10AN02

  perform operations on numbers involving fractional exponents and surds

  Elaborations

  • exploring the notion that amn= a1nm= anm= amn=am1n , where m is a non-zero integer and n is a natural number, and evaluating corresponding expressions; for example, 823=832= 22=4  and 823= 823=643=4

  VC2M10AN02 | Mathematics | Mathematics Version 2.0 | Level 10A | Number