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• VC2M8P01

  recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts

  Elaborations

  • understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
  • using the relationship that for a single event A, Pr(A) + Pr(not A) = 1; for example, if the probability that it rains on a particular day is 80%, the probability that it does not rain on that day is 20%, or the probability of not getting a 6 on a single roll of a fair dice is 1-16=56
  • using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is 13 and probability of not throwing a 5 or 6 is 23

  VC2M8P01 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability

• VCMMG288

  Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other

  Elaborations

  • investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas
  • investigating the area of circles using a square grid or by rearranging a circle divided into sectors
  • solving problems given one of radius, diameter, circumference or area of a circle, then the other quantities are determined from this

  VCMMG288 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VC2M8P03

  conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results

  Elaborations

  • using digital tools to conduct probability simulations involving compound events
  • using a random number generator and digital tools to simulate rolling 2 dice and calculating the difference between them, investigating what difference is likely to occur more often
  • using online simulation software to conduct probability simulations to determine in the long run if events are complementary

  VC2M8P03 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability

• 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

• VC2M8M07

  use mathematical modelling to solve practical problems involving ratios and rates, including distance-time problems for travel at a constant speed and financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

  Elaborations

  • modelling simple motion problems, finding one of distance travelled, time taken or average speed, given the other 2 quantities
  • modelling and solving problems related to situations such as scales on maps and plans, the mixing of chemicals or ingredients, or calculating magnification factors applying relevant ratios and proportions
  • modelling problems involving converting money amounts using different exchange rates and applying them when planning and budgeting for overseas travel
  • modelling situations involving financial contexts (for example, income tax, using taxation rates on annual income, comparing different taxation brackets and rates of pay) or comparing the benefits of different phone plans using different call rates and associated fees to determine the best plan
  • modelling situations involving the use of ratios in radiocarbon dating methods, including the ratio of carbon-14 to carbon-12 isotopes in organisms, to measure dates of Aboriginal and Torres Strait Islander Peoples’ habitation on the Australian continent
  • modelling situations involving ratio and its application in the making of string and cordage by Aboriginal and/or Torres Strait Islander Peoples, including the ratio of length to the mass of a rope, the strength of the ply in proportion to a rope’s pulling force, and the proportion of fibre for the length of string required

  VC2M8M07 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M8N03

  convert between fractions and terminating or recurring decimals, using digital tools as appropriate

  Elaborations

  • identifying when a fraction has a terminating decimal expansion from the prime factorisation of its denominator; for example, 724=0.2916_ does not have a terminating decimal expansion, while 725=0.28 does
  • identifying terminating, recurring and non-terminating decimals and choosing their appropriate representations such as 13 is represented as 0.3_

  VC2M8N03 | Mathematics | Mathematics Version 2.0 | Level 8 | Number