Rich tasks
- This task asks students to play games and decide whether they are fair or not and to justify their position. This task can be given at the start of a topic or done as the students gain enough understanding to complete it.
Fair or not fair?
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1. Fair or not fair?
- Encourage students to replay the games several times before they decide whether the outcomes are fair or unfair. This provides more opportunity for the students to experience uncertainty in situations involving chance.
- It is important to listen to students as they discuss and justify their decisions about the fairness of the games as this may reveal misconceptions about ‘probability’.
Likelihood page 310
- Understand that the outcomes of a probability event may or may not be equally likely to occur.
- Use certain, likely, unlikely and impossible to describe the probability of an event.
- Put events in order of likelihood.
- Know that the results of previous trials don’t affect the outcome of an event.
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Teacher note
- It is important that students in your class develop a shared understanding of the words certain, likely, unlikely, impossible, which are used in this text. Students could create a chart or wall display with a continuum, definition or examples to indicate the relative likelihood associated with each word.
Some other common misconceptions which you may also identify are the belief that it is more difficult to throw a 6 on a die (because they have waited to throw a six in order to move at the beginning of a board game); or when throwing a coin and getting Head, Tail, Head, Tail … they may expect another Head to continue the pattern; alternatively if the pattern is Head, Head, Head … they may expect either another Head (continuing the pattern) or Tail (to break the pattern and keep a balance closer to the theoretical or ‘fair’ outcome).
Another common misconception is that the results of an experiment may not be the same as the theoretical probability. For example, in question 6 on page 314, the blue and green poi have been drawn five times each but the theoretical probability of drawing a blue poi is twice as great as drawing a green poi because there are twice as many blue poi.
Fair or unfair? page 315
- Draw bar charts, pictograms, strip graphs, and pie charts (using choice cards or by making a circle from a strip graph) to display categorical or numerical data.
- Make conclusions about data recorded on different charts, plots and graphs.
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Teacher note
- It is important that students understand the concept of ‘fairness’ in a game as representing equal opportunity to win for all players. In some games a random element in the design will mean that the knowledge and skills of a player will not lead to an advantage; in others these factors will make a difference in an otherwise ‘fair’ game. A discussion around the meaning of fair may be necessary so that students can see the difference between fairness and skill.
Outcomes page 316
- List all the possible outcomes of a one or two stage event.
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Teacher note
- Encourage students to identify all possible outcomes before beginning a probability experiment. For example, when tossing a conventional die, the outcome will be either 1,2,3,4,5,6. It is important that students also identify outcomes which are not possible. For example, when pulling a counter from a bag which has red, blue and green counters, it will not be possible to draw out a yellow counter.
- Students might find tally charts and dot plots helpful for organising frequency data from experiments.
- Towards the end of Level 2 teachers may introduce ways of recording the possible combinations in two-stage experiments, such as taking objects from two bags or tossing a coin and a die, by using organised lists and tables.
