Chance - Progression Points

Dimension

Level

Progression Point

Measurement, chance and data

1.0 Standard

… Students recognise and respond to unpredictability and variability in events, such as getting or not getting a certain number on the roll of a die in a game or the outcome of a coin toss.

1.25

• Awareness that some events are equally likely to occur; for example, a head or a tail showing when a coin is tossed

1.75

• Ordering of familiar events in terms of their probability between impossible and certain

2.0 Standard

… Students predict the outcome of chance events, such as the rolling of a die, using qualitative terms such as certain, likely, unlikely and impossible.

2.5

• Identification of events which are equally likely

3.0 Standard

… Students compare the likelihood of everyday events (for example, the chances of rain and snow).

They describe the fairness of events in qualitative terms.

3.25

• Use of fractions to assign probability values between 0 and 1 to probabilities based on symmetry; for example, Pr(six on a die) = 1/6

4.0 Standard

… Students calculate probabilities for chance outcomes (for example, using spinners) and use the symmetry properties of equally likely outcomes.

They simulate chance events (for example, the chance that a family has three girls in a row) and understand that experimental estimates of probabilities converge to the theoretical probability in the long run.

4.75

• Use of random numbers to assist in probability simulations and the arithmetic manipulation of random numbers to achieve the desired set of outcomes
  
• Calculation of theoretical probability using ratio of number of ‘successful’ outcomes to total number of outcomes

5.0 Standard

… Students identify empirical probability as long-run relative frequency.

They calculate theoretical probabilities by dividing the number of possible successful outcomes by the total number of possible outcomes.

They use tree diagrams to investigate the probability of outcomes in simple multiple event trials.

6.0 Standard

Students estimate probabilities based on data (experiments, surveys, samples, simulations) and assign and justify subjective probabilities in familiar situations.