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• VC2M4P02

  conduct repeated chance experiments to observe relationships between outcomes in games and other chance situations, and identify and describe the variation in results

  Elaborations

  • playing games such as noughts-and-crosses or First to 20 and deciding if it makes a difference who goes first and whether you can use a particular strategy to increase your chances of winning
  • recording and ordering the outcomes of experiments using different physical or virtual random generators such as coins, dice and a variety of spinners
  • experimenting with tossing 2 coins at the same time, recording and commenting on the chance of outcomes after a number of tosses
  • shuffling a set of cards, drawing a card at random, and recording whether it was a spade, club, diamond or heart, or a picture card or numbered card; and repeating the experiment a number of times and discussing the results

  VC2M4P02 | Mathematics | Mathematics Version 2.0 | Level 4 | Probability

• VC2MFN02

  recognise and name the number of objects within a collection up to 5 using subitising

  Elaborations

  • recognising how many objects are in a collection or in images on a card with a quick look and saying the associated number without counting
  • playing instructive card games that rely on the recognition of numbers represented in different ways (for example, playing memory games, or matching pairs of quantities on dot cards or similar where the arrangement on each is different) or using subitising to compare and order collections and to say who has more when sharing items in a game

  VC2MFN02 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFN06

  represent practical situations that involve equal sharing and grouping with physical and virtual materials and use counting or subitising strategies

  Elaborations

  • using materials to role-play equal sharing; for example, sharing pieces of fruit or a bunch of grapes between 4 people and discussing how you would know they have been shared equally; or, when playing card games where each player is dealt the same number of cards, counting the number of cards after the deal to ensure they have the same amount
  • representing situations that involve counting several items; for example, starting with 9 beads or 6 $1 coins and then sharing them equally between 3 people by subitising or counting each group by ones to decide how many beads or coins each person will receive
  • exploring instructive games of Aboriginal and/or Torres Strait Islander Peoples that involve sharing; for example, playing Yangamini of the Tiwi Peoples of Bathurst Island to investigate and discuss equal sharing

  VC2MFN06 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2M10P02

  describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events; investigate the concept of independence

  Elaborations

  • recognising that a subsequent event can be dependent, and that this will affect the way its probability is calculated, for example, cards chosen from a standard deck without replacement, conditional selection problems from a fixed sample size, or the Bertrand’s box paradox

  VC2M10P02 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• 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

• VC2M1N01

  recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts

  Elaborations

  • reading, writing and naming numerals and ordering two-digit numbers from zero to at least 120, using patterns within the natural number system, including numbers that look and sound similar, for example, 16, 60, 61 and 66
  • using number tracks or positioning a set of numbered cards in the correct order and relative location by pegging them on an empty number line
  • using hundreds charts to build understanding and fluency with numbers; for example, collaboratively building a hundreds chart using cards numbered from zero to 99, or colour-coding the count of tens in a hundreds chart using one colour to represent the number of tens and another to represent the number of ones
  • recognising that numbers are used in all languages and cultures but may be represented differently in words and symbols (for example, through kanji numbers in Japanese and characters in Chinese) and that there are alternative numeration systems (for example, using special characters for 10 and 100 and other multiples of 10 in Japanese and Chinese numeration)

  VC2M1N01 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M9P01

  list all outcomes for two-step chance experiments both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes and events

  Elaborations

  • discussing two-step chance experiments, such as the game of heads and tails, describing the different outcomes and their related probabilities 
  • using systematic methods such as lists or arrays to record outcomes and assign probabilities, such as drawing the names of students from a bag to appoint 2 team leaders
  • using a tree diagram to represent a three-stage event and assigning probabilities to these events; for example, selecting 3 cards from a deck, assigning the probability of drawing an ace, then a king, then a queen of the same suit, with and without replacing the cards after every draw
  • assigning probabilities to compound events involving the random selection of people from a given population; for example, selecting 2 names at random from all of the students at a high school and assigning the probability that they are both in Year 9

  VC2M9P01 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability

• VC2M5P01

  list the possible outcomes of chance experiments involving equally likely outcomes and compare to those that are not equally likely

  Elaborations

  • discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card
  • discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn
  • commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning
  • investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5, and responding to the questions ‘Is this game fair?’, ‘Are some differences more likely to come up than others?’ and ‘How can you work that out?’
  • comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers
  • discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them

  VC2M5P01 | Mathematics | Mathematics Version 2.0 | Level 5 | Probability

• 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

• VC2M3P01

  identify practical activities and everyday events that involve chance, and describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’, explaining reasoning

  Elaborations

  • predicting what could happen next in practical activities that involve an element of chance, considering possible outcomes and using terms such as ‘likely’ or ‘unlikely’ to explain their predictions
  • classifying a list of everyday events or sorting a set of event cards according to how likely they are to happen, using the language of chance and giving reasons for classifications; and discussing how impossible outcomes cannot ever happen, and uncertain outcomes are affected by chance as they may or may not happen, whereas certain events must always happen so they are not affected by chance
  • making predictions and testing what would happen, for example, if 10 names were put in a box and names were then drawn out one at a time and replaced after each selection, discussing how likely it would be after 10 selections that all 10 names were drawn from the box or that one name was drawn multiple times

  VC2M3P01 | Mathematics | Mathematics Version 2.0 | Level 3 | Probability

• VC2M2N04

  add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies

  Elaborations

  • using the associative property of addition to assist with mental calculation by partitioning, rearranging and regrouping numbers using number knowledge, near doubles and bridging-to-10 strategies; for example, calculating 7 + 8 using 7 + (7 + 1) = (7 + 7) + 1, the associative property and near doubles; or calculating 7 + 8 using the associative property and bridging to 10: 7 + (3 + 5) = (7 + 3) + 5
  • using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, or 93
  • representing addition and subtraction problems using a bar model and writing a number sentence, explaining how each number in the sentence is connected to the situation
  • using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens, which is 50, and 4 ones add zero ones is 4 ones, which is 4, so the result is 50 + 4 = 54
  • using a physical or mental number line or hundreds chart to solve addition or subtraction problems by moving along or up and down in tens and ones; for example, solving the problem ‘I was given a $100 gift card for my birthday and spent $38 on a pair of shoes and $15 on a T-shirt. How much money do I have left on the card?’
  • using Aboriginal and Torres Strait Islander Peoples’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences

  VC2M2N04 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M4P01

  describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events

  Elaborations

  • using lists of events familiar to students and ordering them from ‘least likely’ to ‘most likely’ to occur; and considering and discussing why the order of some events might be different for different students
  • predicting the outcome of a coin toss after 5 heads have been tossed in a row, discussing the assertion that because so many heads came up, it is more likely that a tail rather than a head will come up next; and discussing with reasons why this assertion is correct or incorrect
  • predicting how likely it is – from least likely to most likely – that they would select a red ball from a bag containing 10 red balls and 5 white balls, from a bag containing 20 of each, or from a bag that has 25 red balls and 20 white balls, justifying their decision
  • identifying school activities where the chance of them taking place is affected by the chance of other events occurring; for example, given that there is a high chance of a storm on Friday, there is only a small chance that the coastal dune planting project will go ahead
  • listing the outcomes of everyday chance situations and identifying where one cannot happen if the other happens; for example, discussing that it cannot be hot and cold at the same time, or selecting a card from a deck and discussing if it is red it cannot be a spade or a club
  • identifying different dependent events where the chance of one outcome occurring will be affected by the occurrence of other outcomes and different independent events where the chance of one outcome occurring will not be affected by the occurrence of other outcome(s)

  VC2M4P01 | Mathematics | Mathematics Version 2.0 | Level 4 | 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

• 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

• VC2M4N07

  choose and use estimation and rounding to check and explain the reasonableness of calculations, including the results of financial transactions

  Elaborations

  • using proficiency with basic facts to estimate the result of a calculation and say what amounts the answer will be between; for example, 5 packets of biscuits at $2.60 each will cost between $10 and $15 as 5 × $2 = $10 and 5 × $3 = $15
  • using rounded amounts to complete an estimated budget for a shopping trip or an excursion, explaining why overestimating the amounts is appropriate
  • recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down, and one number up and one number down, and explaining which is the best approximation and why

  VC2M4N07 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M10ST02

  construct scatterplots and consider a line of good fit; comment on the association between the 2 numerical variables in terms of strength, direction and linearity

  Elaborations

  • discussing the difference between association and cause and effect, and relating this to situations such as health, diversity of species and climate
  • using statistical evidence to make, justify and critique claims about association between variables, such as in contexts of climate change, migration, online shopping and social media 
  • informally using a line of good fit by eye and using digital tools to compare and discuss the reliability of any predictions
  • investigating the relationship between 2 variables of spearthrowers used by Aboriginal and Torres Strait Islander Peoples by using data to construct scatterplots, make comparisons and draw conclusions 

  VC2M10ST02 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M10M04

  use mathematical modelling to solve practical problems involving direct and inverse proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation, including the impact of measurement errors on the accuracy of results; evaluate and modify models as necessary...

  Elaborations

  • exploring contexts where measurement errors may impact research results and how measurement data impacted by error can result in biased findings
  • using plans and elevation drawings to investigate making changes to building designs, employing appropriate scales and converting to actual measurements within the context to make decisions about changes
  • analysing and applying scale and ratios in situations such as production prototypes and 3D printing; for example, using a 3D printer to produce scaled versions of actual objects
  • estimating the scale of an object by measuring a linear dimension and using typical life-size dimensions to determine the scale factor; for example, measuring the dimensions of a toy car to determine a scale that can be used to estimate the dimensions of a life-size car
  • investigating compliance with building codes and standards in design and construction, such as for escalators in shopping centres

  VC2M10M04 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M1N05

  use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials; use calculation strategies to solve the problem

  Elaborations

  • modelling problems involving addition and subtraction presented in stories, using a Think Board to represent the problem, solving the problem using physical materials and explaining the connections between any materials used, the Think Board diagram and the numbers within the story
  • modelling simple money problems involving addition and subtraction using whole dollar amounts; for example, setting up a shop and role-playing practical problems of buying and selling goods, using addition and subtraction with play money and prices in whole dollar amounts; or solving the problem ‘I had $14 and was given $15 for my birthday’ using addition to answer the problem
  • modelling a variety of different additive situations to solve practical problems; for example, keeping track of the number of people on a bus as it stops to pick up and drop off passengers or the number of people entering a lift

  VC2M1N05 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• 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

• VC2MFN05

  represent practical situations, including simple financial situations, involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies

  Elaborations

  • using role-play and materials to represent mathematical relationships in stories; for example, role-playing ‘Eight kangaroos were drinking at the river and 3 hopped away’, drawing a picture and using materials to represent the situation, discussing, and recording the result of the action with a numeral
  • role-playing or actively engaging in situations that involve quantifying or comparing collections of items or simple money transactions; for example, engaging with the question ‘Do we have enough scissors for our group so that each person has their own pair?’, or role-playing using $1 coins to pay for items in a shop where items are priced in whole dollars
  • representing situations expressed in Aboriginal and/or Torres Strait Islander stories, such as ‘Tiddalick, the greedy frog’, that describe additive situations and their connections to Country/Place
  • representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory

  VC2MFN05 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number