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• VC2M1N06

  use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem

  Elaborations

  • modelling problems involving repeated equal group situations, such as ‘How many wheels are needed for 3 cars?’, using materials and drawing a picture to show what they did, and recording the results with a number
  • modelling practical problems involving equal sharing situations; for example, sharing a set of dominoes between the 2 players in a game, and then counting or subitising to ensure they both have the same number of tiles
  • modelling money problems involving equal sharing; for example, sorting coins from a moneybox according to their denominations, sharing the coins equally between 4 people, and using counting or subitising to ensure they have equal amounts of each denomination

  VC2M1N06 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• 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

• Mathematics | Mathematics Version 2.0: Learning in Mathematics Version 2.0

  Learning in Mathematics emphasises the importance of providing opportunities for students to develop proficiency in mathematics. This development of proficiency is achieved in how content is explored or developed, that is, how students experience the thinking and doing of mathematics.

  Proficiency...

  Overview material | Mathematics Version 2.0

• VCMNA019

  Correspond ‘one’ with a single object

  Elaborations

  • showing understanding of object permanency, by tracking and finding an object
  • exploring ‘oneness’ and indicate one, for example one clap, experiencing one object, giving out materials one at a time, requesting one, hearing one sound or beat
  • distributing objects and materials with support, using basic one-to-one correspondence

  VCMNA019 | Mathematics | Level B | Number and Algebra | Number and place value

• VC2M4N01

  recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals

  Elaborations

  • using a bar to represent the whole, dividing it into 10 equal pieces with each piece representing 0.1 or one-tenth of the whole length and understanding that 2 pieces are 0.2 or two-tenths of the whole
  • using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth, and cutting the tenth into 10 parts to show the hundredths; or using deci-pipes to represent tenths
  • recognising that one is the same as ten-tenths and one-tenth is the same as ten-hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five-hundredths
  • making models of measurement attributes to show the relationship between the base unit and parts of the unit, for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five-hundredths of the next unit
  • counting large quantities of mixed notes and coins, writing the total using dollars and cents, and recognising the cents as parts of the next dollar
  • comparing the way money and measures are read and said, and explaining how they are the same and different; for example, explaining that $2.75 is said ‘two dollars seventy-five’ and 2.75 metres is said ‘two point seven five metres’, and recognising that the 7 means seven-tenths and the 5 means five-hundredths in both

  VC2M4N01 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VCMNA091

  Recognise and describe one-half as one of two equal parts of a whole

  Elaborations

  • sharing a collection of readily available materials into two equal portions
  • splitting an object into two equal pieces and describing how the pieces are equal

  VCMNA091 | Mathematics | Level 1 | Number and Algebra | Fractions and decimals

• 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

• VC2M3P02

  conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation

  Elaborations

  • identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial, and then responding to the questions ‘How did your results vary for each trial?’ and ‘How do the results vary across the class?’
  • conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, or using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials

  VC2M3P02 | Mathematics | Mathematics Version 2.0 | Level 3 | Probability

• 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

• 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

• VCMNA037

  Identify groups as being ‘one’, ‘more’ or ‘less’

  Elaborations

  • indicating the larger of two groups when presented with groups of significantly different number sets, for example group of paints, lollies, tools, dots, blocks, counters

  VCMNA037 | Mathematics | Level C | Number and Algebra | Number and place value

• VC2M2N03

  recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving

  Elaborations

  • creating halves of a range of collections sets by sharing collections into 2 equal groups; for example, comparing half of a set of 12 washers with half of a set of 8 bolts to identify how they both represent one-half of their respective set
  • creating halves using measurement attributes – for example, explaining that ‘a half is one part out of 2 equal parts of a whole’; equally folding a strip of paper, dividing a lump of playdough or separating a cup of water into 2 equal parts, and then selecting one of the parts and naming it ‘one-half’; or comparing half of a collection of 10 counters with half of a shape or object and explaining how each shows one-half of the respective whole
  • using repeated halving to subdivide shapes and objects in different ways to make corresponding halves, quarters and eighths; naming the parts and comparing the size of them to notice that they are all the same size; and demonstrating that a quarter is a half of a half and that an eighth is a half of a quarter
  • dividing a shape into equal parts and relating the number of parts to the unit fraction; for example, if there are 4 equal parts then each part is one-quarter and if there are 8 equal parts then each is one-eighth

  VC2M2N03 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VCMNA039

  Demonstrate in practical situations, ‘adding one more to’ and ‘taking one away from’ in everyday situations

  Elaborations

  • using shared experiences with concrete materials to add one more to or take away one from a group of objects, and count to find a total
    • experiencing addition and subtraction in games
  • communicating using language such as ‘more’ or ‘less’ to describe a change in a group using classroom resources and in practical situations

  VCMNA039 | Mathematics | Level C | Number and Algebra | Number and place value

• VCMSP102

  Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays

  Elaborations

  • understanding one-to-one correspondence
  • describing displays by identifying categories with the greatest or least number of objects

  VCMSP102 | Mathematics | Level 1 | Statistics and Probability | Data representation and interpretation

• VCMMG123

  Investigate the effect of one-step slides and flips with and without digital technologies

  Elaborations

  • understanding that objects can be moved but changing position does not alter an object’s size or features

  VCMMG123 | Mathematics | Level 2 | Measurement and Geometry | Location and transformation

• VCMNA245

  Express one quantity as a fraction of another, with and without the use of digital technologies

  Elaborations

  • using examples for the quantities to be expressed and understanding the reasons for the calculations

  VCMNA245 | Mathematics | Level 7 | Number and Algebra | Real numbers

• VCMNA018

  Use number names ‘one’, ‘two’ and ‘three’ in sequence to count in everyday situations

  Elaborations

  • assisting to count objects initially to three, by participating in activities, stories, songs and rhymes that involve number. This could include nodding as objects are counted, tapping an object as it is counted, tracking objects being counted, repeating some number names as objects are being counted
  • responding to number of names in everyday situations, for example waiting for counting down or up before starting an action, sound, activity; stepping, clapping, making a sound, tapping a switch for each number
  • exploring and using some number names by ‘repeating’ number name either verbally or through a communication system or augmentative and alternative communication (AAC)

  VCMNA018 | Mathematics | Level B | Number and Algebra | Number and place value

• VCMSP177

  Identify events where the chance of one will not be affected by the occurrence of the other

  Elaborations

  • explaining that the probability of a new baby being either a boy or a girl does not depend on the sex of the previous baby

  VCMSP177 | Mathematics | Level 4 | Statistics and Probability | Chance

• VCMSP176

  Identify everyday events where one cannot happen if the other happens

  Elaborations

  • using examples such as weather, which cannot be dry and wet at the same time

  VCMSP176 | Mathematics | Level 4 | Statistics and Probability | Chance

• 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