Rich tasks for this chapter - page 325
- 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.
- Scratch and win
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1. Scratch and win
- You could get students to work in pairs to design their own scratch and win cards and carry out some experiments to help them find the probability of winning.
- You could get students to run a competition to see who can raise the most money for charity by selling their scratch and win cards.
- You could ask students to investigate similar promotions and decide whether they are fair.
Putting probabilities in order - page 326
- Understand that probability is about the likelihood of an event occurring.
- Understand that it is not possible to know the exact probability of something occurring in most everyday situations, for example the chance of a day in August being fine.
- Put probabilities of events in order.
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Teacher notes
- Students need to understand that some probabilities cannot be found or estimated unless data is collected or an experiment is done.
- It is important that students understand that some events are certain and have a probability of 1 because they will always happen, and some probabilities are impossible and have a probability of 0 because they never happen. Point out that all other probabilities are fractions between 0 and 1 because they happen some of the time.
Experimenting with probability - page 329
- Understand that when carrying out an experiment the results vary from trial to trial.
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Teacher notes
- It is important that students understand that whenever an experiment is repeated the results are unlikely to be the same.
- Introduce the idea to students that if an experiment is repeated many times, such as tossing a coin, the number of times an outcome occurs will get closer to the expected outcome.
- Encourage students to discuss probability and what they know and don’t know as they carry out the practical experiments.
- A probability can be worked out theoretically without collecting any data or doing an experiment, but only if there are clearly identifiable equally likely outcomes that you can list. To get the theoretical probability for the event that you are considering, you divide the number of outcomes that are favourable by the total number of outcomes. For example, when you roll a die there are six equally likely outcomes and so the probability of throwing a five for example is 1/6. However, if you are asking for the probability that I will be wearing red clothes the next time you see me, you would have to collect some data on the colours I wore each time you saw me for, say, 100 times. Then you could make an estimate of the probability that I would be wearing red based on the relative frequency of my wearing red. In this second example you would have to collect some data because there are no equally likely outcomes for you to list and use to calculate a theoretical probability.
Outcomes and probability - page 332
- Write down, using a list or table, all the possible outcomes of a single stage or two-stage event.
- Know how to work out the fraction of times an event is expected to occur in simple situations such as rolling a die, tossing
a coin etc. - Students should accept that experimental samples from simple situations, for example tossing a coin ten times, vary from
one another, and from the proportions expected, that is, most times five heads do not come up.
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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 three out of six or ½ the time.
- Encourage students to work systematically to find all of the outcomes. Making tables to record the outcomes will encourage this behaviour.
