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• VCKOU032

  Extend grammatical knowledge of Korean language, including the range of forms and functions of particles, suffixes, verb endings and irregular verb forms

  Elaborations

  • modifying nouns using an adjectival form of a descriptive verb suffixed by –(으)ㄴ, for example, 예쁜 꽃, 맑은 물
  • using particles such as –한테/에게, –한테서/에게서, –(으)로 (instrumental and directional), –보다, –와/과, –만, –도,–부터 and –까지, including honorific case markers –께, –께서, –께서는
  • recognising the meaningful parts of a verb, for example, 먹+어요
  • expressing ideas or events relating to the future, suggestions, plans and hopes using forms such as –(으)ㄹ 거예요 and –(으)ㄹ까요?
  • learning how to ask and answer negative questions, for example, 숙제를 안 했어요? 아니요, 했어요 / 네, 안 했어요)
  • connecting clauses using basic conjunctive suffixes (clausal connectives) –어/아서, –고, –(으)면, –지만
  • using basic complex-verb structures such as –어/아 주다, –어/아 보다, –지 말다with an –어/아요ending to express provision, trial and prohibition (읽어 주세요, 입어 보세요, 쓰지 마세요)
  • expressing time using structures such as: a noun + 때/동안; a noun +전/후에, for example, 방학 때; 일 년 동안; 한 달 전/후에
  • using some basic irregular verbs, such as 들어요 (듣다), 불러요 (부르다), 더워요 (덥다), 추워요 (춥다), 아름다워요 (아름답다)
  • expressing relative location using a structure: a noun + a location word + 에, for example, 식탁 위에 상자가 있어요
  • expanding metalinguistic knowledge by receptive use of:
    • intimate copula verb ending (a noun + (이)야)
    • expressions of intentions and likelihood: –겠어요, –(으)ㄹ 것 같아요
    • conjunctors connecting clauses (–(으)니까, –(으)러)
    • complex structures such as –어/아야 하다, –어/아도 되다, with the informal polite ending –아/어요 (가야 해요, 먹어도 돼요), recognising that they are in the same structure as –어/아 주다, –어/아 보다 and –지 말다 (verb stem + suffix + auxiliary verb) and that the auxiliary verbs add meanings such as obligation, permission and attempt
    • complex structures connecting verbs with various functions (to be introduced as a set phrase, for example, –기 때문에, –기 위해(서)
    • levels of politeness in speech, for example, formal polite, informal polite, intimate, for example, 해, 해요, 합니다
    • honorific suffix –시–, for example, 하십니다,가르치십니다

  VCKOU032 | Languages | Korean | 7–10 Sequence | Levels 9 and 10 | Understanding | Systems of language

• VCKOU183

  Use appropriate pronunciation rules and writing conventions to produce and read short texts in Korean that include some less familiar language

  Elaborations

  • applying pronunciation rules and writing conventions to reading and writing, inferring meanings of less familiar texts provided in Korean, such as 먹고, 어떻게 and 축하합니다 pronounced as 먹꼬, 어떠케 and 추카함니다
  • experimenting with pronunciation of less familiar texts
  • comparing how loan words from English are written in Hangeul and pronounced in Korean with how their original counterparts in English are written and pronounced, for example, 테니스versus ‘tennis’, 포크 versus ‘fork’, 인터넷 versus ‘internet’
  • composing texts, applying spacing rules in Korean

  VCKOU183 | Languages | Korean | F–10 Sequence | Levels 7 and 8 | 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

• VC2M10A09

  solve simultaneous linear equations, using algebraic and graphical techniques including using digital tools

  Elaborations

  • investigating situations involving simultaneous linear equations in context (such as multiple quotes for a job, or profit and loss) and solving the equations graphically, giving solutions in everyday language (such as ‘break-even point’ or ‘point to change providers’ for the job)
  • describing the solution of simultaneous equations within the context of the situation
  • using the algebraic methods of substitution and elimination, with and without the use of digital tools, and identifying which technique is the most efficient for a given pair of equations
  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs
  • investigating the strategies inherent in Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables

  VC2M10A09 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M2A04

  apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction

  Elaborations

  • using technology to construct a sequence of numbers based on constant addition or subtraction from a given starting value
  • sharing a set of objects equally between a small number of groups

  VC2M2A04 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• VC2M10A13

  solve simple quadratic equations using a range of strategies, including null factor law

  Elaborations

  • using techniques to solve quadratic equations, including grouping like terms, completing the square, the quadratic formula and null factor law, and choosing 2 integers with the required product and sum
  • using digital tools to explore the conditions for solutions to exist
  • using digital tools to explore both graphically and algebraically the link between the value of the discriminant and the number of real solutions to a quadratic equation

  VC2M10A13 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• 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

• VC2MFM01

  identify and compare attributes of objects and events, including length, capacity, mass and duration, use direct comparisons and communicate reasoning

  Elaborations

  • using language to describe the measurement attributes of length, mass, capacity and duration, and connecting the words with the appropriate attribute; for example, using words like ‘tall’, ‘short’, ‘wide’, ‘long’ and ‘high’ to describe the attribute of length
  • directly comparing pairs of objects to say which is longer/shorter, and explaining or demonstrating how they know; for example, standing back-to-back to determine who is taller or choosing to line up the bases of a spoon and fork to decide which is longer and explaining why
  • starting 2 events at the same time to decide which takes longer; for example, putting on a pair of sandals with buckles or Velcro, describing the duration using familiar terms and reasoning, ‘I took a longer time because I’m still learning to do up my buckles’
  • directly comparing pairs of everyday objects from the kitchen pantry to say which is heavier/lighter; for example, hefting a tin of baked beans and a packet of marshmallows or comparing the same pair of objects to say which is longer/shorter and discussing comparisons

  VC2MFM01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• VC2MFM02

  sequence days of the week and times of the day, including morning, lunchtime, afternoon and night-time, and connect them to familiar events and actions

  Elaborations

  • ordering images of daily events on a string line across the room, and justifying the placement by referring to morning, lunchtime, afternoon and night-time
  • distinguishing between the days of the school week and weekends, and recognising that the days of the week form a sequence that repeats, with Monday always following on from Sunday
  • sequencing the events from a story in the order in which they occurred, using language like ‘this happened first’ then ‘this happened next’
  • creating, interpreting and discussing classroom rosters, for example, a roster for watering the classroom garden, and asking, ‘Who watered the garden yesterday?’ or ‘Whose turn is it today?’
  • creating a pictorial diary to show the important events that happen on the various days of the week

  VC2MFM02 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• VC2MFN01

  name, represent and order numbers, including zero to at least 20, using physical and virtual materials and numerals

  Elaborations

  • responding to a request to collect a quantity of objects or reading a numeral and selecting the associated quantity of items from a collection to match the number required; for example, collecting 9 paintbrushes after hearing the word ‘nine’
  • recognising the order in the sequence of numbers to 20 and identifying the number that is ‘one less’ than a given number and the number that is ‘one more’; for example, playing instructive card games that involve reading and ordering number cards, or using counting songs, storybooks and rhymes to establish the forwards and backwards counting sequence of numbers in the context of active counting activities
  • understanding and using terms to indicate ordinal position in a sequence; for example, filling in the missing term in ‘first’, ‘second’, ‘third’, … ‘fifth’ …, or creating a number track using cards with the numerals zero to 20 and describing positions using terms such as ‘first’, ‘last’, ‘before’, ‘after’ and ‘between’
  • recognising, writing and reading numerals written on familiar objects; for example, recognising and reading numerals in images, text or illustrations in storybooks, or writing a numeral on a container as a label to show how many objects it contains
  • connecting quantities to number names and numerals when reading and reciting stories and playing counting games or determining and reasoning about the size of sets of objects within Aboriginal and/or Torres Strait Islander Peoples’ instructive games, for example, Segur etug from Mer Island in the Torres Strait region

  VC2MFN01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2M7M02

  solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units

  Elaborations

  • building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length
  • developing the connection between the area of the parallel cross-section (base), the height and the volume of a rectangular or triangular prism to other prisms
  • connecting the area of the floor space and the number of floors of a high-rise building to calculate the volume of a building
  • using dynamic geometry software, spatial reasoning and prediction to derive the formula for the volume of prisms

  VC2M7M02 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M4M03

  solve problems involving the duration of time including situations involving ‘am’ and ‘pm’ and conversions between units of time

  Elaborations

  • calculating the amount of time between 2 events, such as the start and finish of a movie, a bus journey or a flight, including cases where the starting and finishing times are written using ‘am’ and ‘pm’ notation
  • converting units of time using relationships between units, such as 60 minutes in an hour and 60 seconds in a minute, to solve problems; for example, creating a daily timetable for an activity such as an athletics carnival or planning an exercise routine with activities and rests
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ explanations of the passing of time through cultural accounts about cyclic phenomena involving the sun, moon and stars

  VC2M4M03 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M5M04

  estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names

  Elaborations

  • using a protractor to measure angles in degrees and classifying these angles using angle names; for example, an acute angle is less than 90°, an obtuse angle is more than 90° and less than 180°, a right angle is equal to 90° and a reflex angle is more than 180° and less than 360°
  • estimating the size of angles in the environment using a clinometer and describing the angles using angle names
  • using a ruler and protractor to construct triangles, given the angle measures and side lengths
  • using a protractor to measure angles when creating a pattern or string design within a circle
  • recognising the size of angles within shapes that do and do not tessellate, measuring the angles and using the sum of angles to explain why some shapes will tessellate and other shapes do not

  VC2M5M04 | Mathematics | Mathematics Version 2.0 | Level 5 | 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

• VCMMG345

  Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

  Elaborations

  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements

  VCMMG345 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning

• VCMMG346

  Solve right-angled triangle problems including those involving direction and angles of elevation and depression

  Elaborations

  • applying Pythagoras's Theorem and trigonometry to problems in surveying and design

  VCMMG346 | Mathematics | Level 10 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG290

  Solve problems involving duration, including using 12- and 24-hour time within a single time zone

  Elaborations

  • identifying regions in Australia and countries in Asia that are in the same time zone

  VCMMG290 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG229

  Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies

  Elaborations

  • understanding which attributes of a shape remain the same or change under the effects of transformations such as size, shape or orientation
  • creating tessellations with simple shapes or simple composite shapes

  VCMMG229 | Mathematics | Level 6 | Measurement and Geometry | Location and transformation

• VC2M6N01

  recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane

  Elaborations

  • extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (−2) and (+2) and their relationship to zero as −2 < 0 < 2
  • using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event
  • using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero (for example, elevators, above and below sea level) and distinguishing a location by referencing the 4 quadrants of the Cartesian plane
  • recognising that the sign (positive or negative) indicates a direction in relation to zero – for example, 30 metres left of the admin block is (−30) and 20 metres right of the admin block is (+20) – and programming robots to move along a number line that is either horizontal or vertical but not both at the same time
  • representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line

  VC2M6N01 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M5N08

  check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context

  Elaborations

  • interpreting a series of contextual problems to decide whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
  • recognising the effect of rounding addition, subtraction, multiplication and division calculations, and rounding both numbers up, both numbers down, and one number up and one number down; and explaining which estimation is the best approximation and why
  • considering the type of rounding that is appropriate when estimating the amount of money required; for example, rounding up or rounding down when buying one item from a store using cash, compared to rounding up the cost of every item when buying groceries to estimate the total cost and not rounding when the financial transactions are digital

  VC2M5N08 | Mathematics | Mathematics Version 2.0 | Level 5 | Number