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AC9M8P01: Year 8 Mathematics Content Descriptor – Probability
AC9M8P01 Year 8 Mathematics

AC9M8P01 – Year 8 Mathematics: null

Strand
Probability
Substrand
Probability

This Content Descriptor from Year 8 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

Content Descriptor

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 \(1-\frac16=\frac56\)
  • • 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 \(\frac13\) and probability of not throwing a \(5\) or \(6\) is \(\frac23\)
  • • investigating how various applications of artificial intelligence use the probability of complementary events when assessing the likelihood of favourable and unfavourable outcomes and making informed decisions based on these probabilities; for example, in binary classification problems where data is classified into one of two categories, such as spam or not spam, fraud or not fraud

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 8 ASMATY8
Year 8 Mathematics Achievement Standard
By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools. Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems. They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.