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• VC2M7P01

  identify the sample space for single-stage experiments; assign probabilities to the possible outcomes and predict relative frequencies for related experiments.

  Elaborations

  • discussing the meaning of probability terminology, for example, ‘probability’, ‘sample space’, ‘favourable outcome’, ‘trial’, ‘experiment’ and ‘event’
  • listing sample spaces for games involving throwing a coin or a dice, spinners, or lucky dip
  • assigning the probability for throwing a 6 on a dice and using this to predict the number of times a 6 will occur when a dice is thrown multiple times

  VC2M7P01 | Mathematics | Mathematics Version 2.0 | Level 7 | Probability

• VC2M1N03

  quantify sets of objects, to at least 120, by partitioning collections into equal groups using number knowledge and skip counting

  Elaborations

  • counting a large collection of items using groups of fives or tens and skip counting to work out how many there are, and recording the amount and connecting the digits in the number to the grouped materials when using groups of 10
  • counting collections of objects, such as pencils or images of birds in a tree, by grouping them in tens to enable efficient counting, and connecting the digits in the number to the groups of tens and ones
  • counting a large collection of Australian $1 coins by stacking them in piles of 10, skip counting in tens and including any leftover coins to determine the total value

  VC2M1N03 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• 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

• 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

• 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

• VCMNA020

  Explore the concept of ‘none’, ‘one’ and ‘more’

  Elaborations

  • recognising a change in a collection’s size within the context of familiar, everyday objects, for example a group of cars, toys, lollies, fruit, vegetables, coins, books, materials or tools
  • demonstrating an understanding of one by selecting, giving or taking one object
  • responding to questions about group composition (for example ‘Which group has more?’ ‘Which group has none?’) verbally or by indicating through augmentative and alternative communication, actions or eye gaze

  VCMNA020 | Mathematics | Level B | Number and Algebra | Number and place value

• 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

• VC2M6P02

  conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials

  Elaborations

  • using digital tools to simulate multiple tosses of a coin or dice and comparing the relative frequency of an outcome as the number of trials increases; and identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
  • using online simulations of repeated random events to recognise emerging patterns, discussing and comparing expected results to the actual results
  • investigating the relative frequencies of all outcomes for a chance experiment and verifying that their sum equals one
  • systematically recording the outcome of large numbers of spins on a spinner and analysing the relative frequencies of outcomes, representing these as percentages

  VC2M6P02 | Mathematics | Mathematics Version 2.0 | Level 6 | 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

• VC2M7SP01

  represent three-dimensional objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations

  Elaborations

  • deconstructing packaging to identify shapes and nets
  • using different nets to construct prisms and determining which nets will make a cube, rectangular prism, triangular prism or pyramid
  • using aerial views of buildings and other three-dimensional structures to visualise the footprint made by the building or structure, identifying prisms that could approximate the structure
  • building objects by interpreting isometric and perspective drawings
  • using isometric and square grid paper to draw views of front, back, side, top and bottom of objects
  • exploring different two-dimensional representations of objects in Aboriginal and/or Torres Strait Islander artworks or cultural maps of Country/Place

  VC2M7SP01 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VC2MFSP02

  describe the position and location of themselves and objects in relation to other people and objects within a familiar space

  Elaborations

  • describing the position of an item in relation to other items in the space using language like ‘inside’, ‘underneath’ and ‘on top of’; for example, when asked ‘Where are the scissors kept?’, responding with ‘They are in a box, on the bottom shelf at the back of the classroom’
  • describing where they have moved themselves and items in relation to other items within a space, using familiar terms; for example, playing a hiding game and when asked ‘Where did you hide the ball?’, responding, ‘I hid it behind the garbage bin over there near the bench’
  • exploring Aboriginal and/or Torres Strait Islander instructive games, for example, Thapumpan from the Wik-Mungkan Peoples of Cape Bedford in northern Queensland, describing position and movement of self in relation to other participants, objects or locations

  VC2MFSP02 | Mathematics | Mathematics Version 2.0 | Foundation Level | Space

• VC2M1M02

  measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end

  Elaborations

  • using 2 different units (for example, icy pole sticks and pencils) to measure the length of an object (for example, a desk), and explaining why the number of units used may be different
  • comparing the length of 2 objects, such as a desk and a bookshelf, by laying multiple copies of a unit and counting to say which is longer and how much longer; and explaining why they should not have gaps or overlaps between the units, as this will change the length of the unit
  • measuring the distance between 2 locations using footsteps, comparing the results and explaining why there may be different results, for example, referring to the different lengths of footsteps as using different units
  • measuring and comparing the length of objects using blocks; for example, comparing the height of 2 toys by stacking blocks one on top of the other and counting how many it takes to reach the height of each object to decide which is taller

  VC2M1M02 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M3N09

  follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

  Elaborations

  • following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist, where appropriate, and identifying and describing emerging patterns
  • following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns
  • creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule ‘To multiply by 3 you double the number and add on one more of the number’ (for example, for 3 threes, you double 3 and add on 3 to get 9; for 3 fours you double 4 and add one more 4 to get 12 …)
  • creating a sorting algorithm that will sort a collection of 5-cent and 10-cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10

  VC2M3N09 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M2N01

  recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines

  Elaborations

  • recognising missing numbers on different number lines, for example, a number line with 1800 on one end and 2200 on the other, with every decade numbered
  • recognising and locating the position of pieces within hundreds chart puzzles using knowledge of the order of natural numbers
  • reading and writing numerals, and saying and ordering two-, three- and four-digit numbers using patterns in the number system, including numbers with zeros in different places and numbers that look and sound similar (such as 808, 880, 818 and 881)
  • collecting large quantities of materials for recycling (for example, ring pulls, bottle tops and bread tags) and grouping them into ones, tens and hundreds, and using the materials to show different representations of two- and three-digit numbers

  VC2M2N01 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M10SP01

  apply deductive reasoning to formulate proofs involving shapes in the plane and use theorems to solve spatial problems

  Elaborations

  • distinguishing between a practical demonstration and a proof; for example, demonstrating that triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent
  • developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
  • applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
  • investigating proofs of geometric theorems and using them to solve spatial problems, for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes, and using visual proofs to justify solutions
  • using dynamic geometry software to find the quadrilateral that has a vertex on each side of a rectangle and has the shortest possible path, and proving that the path forms a parallelogram

  VC2M10SP01 | Mathematics | Mathematics Version 2.0 | Level 10 | Space

• VC2M3SP02

  interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other

  Elaborations

  • designing the layout of a space; for example, designing a proposed games room or a classroom using a blank sheet of paper as the boundary and cut-outs of shapes to represent furniture from a top-view perspective
  • locating themselves within a space, such as a basketball court, oval, stage or assembly hall, guided by a simple hand-held plan indicating the different positions of the participants in the activity
  • sketching a map indicating where they have hidden an object within the classroom, swapping maps with partners and then providing feedback about what was helpful and what was confusing on the map
  • identifying differences in the representation of a place on a map, in an aerial photograph, in a street view and in a satellite image, and discussing the different information the representations can give
  • exploring land maps or cultural maps used by Aboriginal and Torres Strait Islander Peoples to locate, identify and position important landmarks such as waterholes

  VC2M3SP02 | Mathematics | Mathematics Version 2.0 | Level 3 | Space

• 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

• 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

• VC2M8P02

  determine all possible outcome combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific events in practical situations

  Elaborations

  • describing events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’
  • using the relation Pr(A and B) + Pr(A and not B) + Pr(not A and B) + Pr(not A and not B) = 1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A and B) = 0
  • using Venn diagrams or two-way tables to demonstrate the difference between events that are mutually exclusive, such as whether a coin toss will land on a head or a tail, and those that are not mutually exclusive, such as people who have blonde hair and people who have blue eyes
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams

  VC2M8P02 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability