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• 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

• VC2M4M04

  estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle

  Elaborations

  • classifying the interior angles of a range of shapes, using examples of angles to identify acute, obtuse, right and reflex angles
  • identifying angles within the environment and estimating whether they are acute, obtuse, right or reflex
  • creating a right-angle template using cardboard or a double-folded piece of paper and using it to compare angles in the environment, commenting on whether they are smaller than or greater than a right angle
  • using different measuring tools such as a spirit level or set squares to determine whether lines or objects are straight, square or perpendicular (at right angles)

  VC2M4M04 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VCMMG291

  Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology

  Elaborations

  • understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures
  • establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles are equal
  • exploring tiling patterns in art and design

  VCMMG291 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VC2M6N07

  solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools

  Elaborations

  • explaining how 13 of a quantity can be achieved by dividing by 3, and how knowledge of 13 of a quantity can be used to find 23 or 43 of the same quantity, using situations involving money, length, duration, mass or capacity
  • investigating percentage discounts of 10%, 25% and 50% in an online toy sale, using their equivalent decimal representations of 0.10, 0.25 and 0.50 to calculate the amount of discount on sale items, with and without digital tools
  • linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding a 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%
  • explaining the equivalence between percentages and fractions, for example, 3313 % and 13 , keeping to percentages that are equivalent to fractions with small denominators such as 6623 % and 12.5%
  • representing a situation with a mathematical expression, for example, numbers and symbols such as 14 × 24, that involves finding a familiar fraction or percentage of a quantity; and using mental strategies or a calculator and explaining the result in terms of the situation in question

  VC2M6N07 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M7N06

  use the 4 operations with positive rational numbers, including fractions and decimals, to solve problems using efficient mental and written calculation strategies

  Elaborations

  • solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
  • choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 18, 0.125 or 1251000
  • developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 23 of 12 , giving 12 of 23=13
  • solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
  • developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
  • carrying out calculations to solve problems using the representation that makes computations efficient, such as 12.5% of 96 is more efficiently calculated as 18 of 96, including contexts such as comparing land use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases or decreases in energy accounts each account cycle

  VC2M7N06 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M6N03

  apply knowledge of equivalence to compare, order and represent common fractions, including halves, thirds and quarters, on the same number line and justify their order

  Elaborations

  • applying factors and multiples to fraction denominators (such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths) to determine equivalent representations of fractions in order to make comparisons
  • representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators
  • explaining equivalence and order between fractions using number lines, drawings and models
  • comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, 58 is greater than 12 can be written as 58 > 12 , because half of 8 is 4; 16 is less than 14 , because 6 > 4 and can be written as 16 < 14

  VC2M6N03 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M1N02

  partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones

  Elaborations

  • building knowledge and understanding of the part-part-whole facts to 10, using physical and virtual materials; for example, using virtual ten-frames through a digital app or website to identify pairs of numbers that combine to make 10
  • using physical and virtual materials to partition numbers into counts of tens and ones; for example, recognising 35 as 3 tens and 5 ones or as 2 tens and 15 ones
  • using part-part-whole reasoning and physical or virtual materials to represent 24, then partitioning 24 in different ways and recording the partitions using numbers; for example, 10, 10 and 4 combine to make 24 or 10 and 14 combine to make 24

  VC2M1N02 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M5N03

  compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line

  Elaborations

  • using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total
  • creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games
  • connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 14 on a fraction wall represents the area of one-quarter of the whole, while on the number line 14 is identified as a point that is one-quarter of the distance between zero and one
  • using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 210 is located at the same position on a parallel number line as 15 because 15 is equivalent to 210
  • converting between mixed numerals and improper fractions to assist with locating them on a number line

  VC2M5N03 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M5P02

  conduct repeated chance experiments, including those with and without equally likely outcomes, and observe and record the results; use frequency to compare outcomes and estimate their likelihoods

  Elaborations

  • discussing and listing all the possible outcomes of an activity and conducting experiments to estimate the probabilities (for example, using coloured cards in a card game and experimenting with shuffling the deck and turning over one card at a time) and recording and discussing the results
  • conducting experiments, recording the outcomes and the number of times the outcomes occur, and describing the relative frequency of each outcome; for example, using ‘I threw the coin 10 times, and the results were 3 times for a head, so that is 3 out of 10, and 7 times for a tail, so that is 7 out of 10’
  • experimenting with and comparing the outcomes of spinners with equal coloured regions compared to unequal coloured regions; and responding to questions such as ‘How does this spinner differ to one where each of the colours has an equal chance of occurring?’, giving reasons
  • comparing the results of experiments using a fair dice and one that has numbers represented on faces more than once, explaining how this affects the likelihood of outcomes
  • using spreadsheets to record the outcomes of an activity and calculate the total frequencies of different outcomes, representing these as a fraction; for example, using coloured balls in a bag, drawing one out at a time and recording the colour, and replacing them in the bag after each draw
  • investigating Aboriginal and/or Torres Strait Islander children’s instructive games (for example, Diyari koolchee from the Diyari Peoples near Lake Eyre in South Australia), to conduct repeated trials and explore predictable patterns, using digital tools where appropriate

  VC2M5P02 | Mathematics | Mathematics Version 2.0 | Level 5 | Probability

• VC2M8SP01

  identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations

  Elaborations

  • developing an understanding of what it means for shapes to be congruent or similar
  • using the enlargement transformation and digital tools to develop sets of similar shapes
  • investigating sufficient conditions to establish that 2 triangles are congruent
  • applying logical reasoning and tests for congruence and similarity, to problems and proofs involving plane shapes
  • comparing angle and side measurements of shapes under transformation to answer questions such as ‘What changes?’ and ‘What stays the same?’
  • establishing that 2 shapes are congruent if one lies exactly on top of the other after one or more transformations, including translations, reflections and rotations, and recognising that the matching sides and the matching angles are equal

  VC2M8SP01 | Mathematics | Mathematics Version 2.0 | Level 8 | Space

• VCMSP372

  Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation

  Elaborations

  • using the standard deviation to describe the spread of a set of data
  • using the mean and standard deviation to compare numerical data sets
  • constructing distributions for the mean and standard deviation of simple random samples from a population

  VCMSP372 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• VCMSP325

  Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’

  Elaborations

  • using stem-and-leaf plots to compare two like sets of data such as the heights of girls and the heights of boys in a class
  • describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’ and 'symmetric' and 'bi-modal'

  VCMSP325 | Mathematics | Level 9 | Statistics and Probability | Data representation and interpretation

• VC2M1ST01

  acquire and record data for categorical variables in various ways including using digital tools, objects, images, drawings, lists, tally marks and symbols

  Elaborations

  • discussing methods of collecting data to answer a question such as ‘What types of rubbish are found in the playground?’, sharing ideas and trying out some of the suggested methods, reviewing the data collected and explaining how they might change the way they collect data next time
  • collecting and recording information on a topic of interest using lists (for example, ‘How many people follow a particular football team’ or ‘What colour eyes each person has’), examining the data to generate some questions that it could answer, and then rearranging the data or collecting different data to answer the question
  • creating a tally to record data while observing events such as the year level of students using the bike shed, deciding on the possible categories before the observations are taken, and then reviewing the data afterwards to notice whether the tally was effective
  • using star charts with stickers or emojis to represent class data; for example, using emojis on a personal feeling chart to represent how they are feeling each day or using emojis to represent activities on the class calendar
  • exploring ways of representing, sharing and communicating data through stories and symbols used by Aboriginal and Torres Strait Islander Peoples

  VC2M1ST01 | Mathematics | Mathematics Version 2.0 | Level 1 | Statistics

• VC2M8ST01

  distinguish between a population and a sample, and investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the practicalities and implications of obtaining data through sampling, using a variety of investigative processes; for example, investigating situations when random sampling or non-random sampling is used to collect data and the implication of each sampling method
  • discussing how observations, experiments and sampling methods can be impacted by bias; for example, recognising that a sampling bias occurs when certain members of a population are more likely to be selected in a sample than others, such as a survey conducted at a shopping centre, and recognising that environmental conditions may bias the results of scientific investigations if experiments are conducted at different times or under different conditions
  • using digital tools such as simulations and digital measuring devices to observe, measure and record qualitative and quantitative data, discussing precision and the implications of error

  VC2M8ST01 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VCPSCSO032

  Identify the characteristics of an effective team and develop descriptions for particular roles including leadership, and describe both their own and their team’s performance when undertaking various roles

  Elaborations

  • describing team roles referring to leader, recorder and reporter
  • developing role descriptors which describe the skills and behaviours of collaborative teams
  • assessing the effectiveness of roles within a collaborative group from an individual perspective
  • articulating what successful teams look like, feel like and do

  VCPSCSO032 | Capabilities | Personal and Social Capability | Levels 5 and 6 | Social Awareness and Management | Collaboration

• VCSIS140

  Communicate scientific ideas and information for a particular purpose, including constructing evidence-based arguments and using appropriate scientific language, conventions and representations

  Elaborations

  • using secondary sources as well as students’ own findings to help explain a scientific concept
  • using a range of representations, including mathematical and symbolic forms, to communicate science ideas
  • presenting results and ideas using formal experimental reports, oral presentations, multimodal presentations, poster presentations and contributing to group discussions

  VCSIS140 | Science | Levels 9 and 10 | Science Inquiry Skills | Communicating

• VCSIS138

  Analyse patterns and trends in data, including describing relationships between variables, identifying inconsistencies in data and sources of uncertainty, and drawing conclusions that are consistent with evidence

  Elaborations

  • exploring relationships between variables using spreadsheets, databases, tables, charts, graphs and statistics
  • describing data properties (for example mean, median, range, outliers, large gaps visible on a graph) and their significance for a particular investigation sample, acknowledging uncertainties

  VCSIS138 | Science | Levels 9 and 10 | Science Inquiry Skills | Analysing and evaluating

• VCTRU114

  Understand and apply features of the Turkish sound and writing systems, including pronunciation and spelling patterns, to produce different types of texts and to participate in extended interactions

  Elaborations

  • recognising and applying the vowel elision rule to suffixes of multisyllabic words, understanding how this is related to the spelling and pronunciation of words, for example, oğul-oğlu, burun-burnu, beyin-beyni, göğüs- göğsü and karın-karnı
  • using homophones such as gül, yüz, dolu, yaz, kır, ekmek, Pazar, ben, aç and çay in spoken and written texts, and learning how homophones affect meaning in sentences and in familiar idioms, for example, Gülü seven dikenine katlanır, Güle güle gidin and Gülmekten kırılıyordum
  • developing understanding of and applying the principles of word stress when pronouncing unfamiliar words and phrases, for example, stressing the first syllable of each word in the sentence Atatürk, cumhuriyeti kurdu
  • developing a glossary of ICT terms and meanings, and using these in their own sentences and texts, for example, bilgisayar, fare, yükleme/indirme, ağ, e-posta, biligisayar korsanı, yazıcı and aktarma
  • varying the use of tone for emphasis during extended interactions and to contribute to the cohesion of longer spoken texts

  VCTRU114 | Languages | Turkish | 7–10 Sequence | Levels 9 and 10 | Understanding | Systems of language

• VCVIU014

  Examine the structures and language features of a range of short familiar personal texts, including descriptive, informative and imaginative texts, and identify audience and purpose

  Elaborations

  • identifying the audience, purpose and structural features of short familiar texts in Vietnamese, such as messages, notes, signs, instructions, personal emails/letters, diary entries/blog posts, advertisements, announcements, recipes, stories, songs and poems
  • recognising structural features of familiar personal, informative and imaginative Vietnamese texts, for example, the date on diary entries and letters, titles for stories, and greetings for emails or conversations
  • discussing ways in which different grammatical elements are used for different textual purposes, for example, the use of imperatives in a set of instructions (Đứng lên! Ngồi xuống! Mở tập ra! Nghe và lặp lại!) in recipes and other procedural texts, time and place markers (ngày xửa ngày xưa, hôm qua, hôm nay, ngày mai, tuần tới) in stories, adjectives (đẹp, tốt, bền, tiện lợi) in advertisements, and personal pronouns (ông, bà, tôi, anh, chị, em) in conversations
  • understanding how to create textual cohesion by using linguistic elements such as cohesive devices (thứ nhất, thứ nhì, trước tiên, kế đến, rồi, sau cùng) and conjunctions (và, với, hay, hoặc, vì, nhưng) to sequence and link ideas
  • understanding the use of features of particular text types in simple written, spoken or digital form, such as class signs and rules, birthday invitations, personal profiles, or recipes of favourite foods or drinks

  VCVIU014 | Languages | Vietnamese | 7–10 Sequence | Levels 7 and 8 | Understanding | Systems of language

• VCZHC052

  Locate, classify and organise relevant information, including analysing data in simple diagrams, tables and graphs, and re-present this information for known audiences

  Elaborations

  • comparing travel brochures to identify places of interest, public transport information and activities
  • recognising the word/phrase boundaries in 我们学校/有/二百八十七个学生 and applying knowledge of Chinese information-sequencing rules, for example, using the knowledge that Chinese speakers organise information from most general to most specific in order to locate details in a Chinese address
  • identifying the common organising categories in tables or graphs, for example, deducing that 国籍 means ‘nationality’ by determining the meanings of 中国，澳大利亚 etc. in a table column

  VCZHC052 | Languages | Chinese | Second Language Learner | F–10 Sequence | Levels 7 and 8 | Communicating | Informing