Rich tasks
- These are problem solving open-ended questions that require students to investigate probability. The tasks can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place, or given as homework or extension.
- Can I play?
> More on "Rich tasks for this Chapter"...
1. Can I play?
- Encourage students to design their own games either individually, as a pair or as a group. Then play each other’s games, but guess before starting who is going to win.
- You could turn this into a competition to see who can make up the best game, which could then be taken to another class or group to play. Encourage students to design the game so any “unfairness” is not glaringly obvious – they don’t want the players to be able to immediately see who will win.
Understanding probability
- Understand that probability is about the chance of outcomes occurring.
- Recognise that it is not possible to know the exact probability of many everyday events.
- Know that when a probability experiment is repeated the results will vary.
> More on "Understanding probability"...
Teacher notes
- It is important for students to understand that whenever an experiment is repeated, the results are unlikely to be the same.
- Begin to get students to understand that if an experiment is repeated many times, like tossing a coin, the number of times an outcome occurs gets closer to the expected outcomes.
- Encourage students to discuss probability, and what they know and don’t know, as they carry out the practical experiments.
- You could set up some of the experiments described in the questions in Activity 1.
- Deciding if games are fair or unfair helps students to understand probability. They realise that in unfair games one student has a better chance of winning because more of the outcomes favour them.
- Encourage students to discuss and talk about their ideas in pairs or groups.
Outcomes
- Write a list or table of all the possible outcomes of a single event, or two events that happen simultaneously, or two events that happen one after the other.
> More on "Outcomes"...
Teacher notes
- Although formal calculations of probabilities are not done at this stage, you could encourage students to make the link between the fraction of outcomes that satisfy an event and how likely the event is to happen.
- For example, when a die is rolled, three out of six of the outcomes are odd numbers so you would expect to get an odd number half of the time.
- Encourage students to work systematically to find all of the outcomes. Tables will help with this. NOTE Tree diagrams are explored in book 3B.
