Planning tool

Students:

• order events from impossible to certain, including ‘least likely’ to ‘most likely’ to occur
• explain the effect on probabilities when an item is not replaced in a chance experiment.

Some students may:

• be still developing their language skills and not fully understand the language of chance to then be able to relate these to the likelihood of an event occurring.
• tend to believe in luck (for example, they will have a better chance at rolling their favourite numbers).
• make predictions based on likes and interests (for example, their favourite colours for spinners).
• not realise that chance has no memory (for example, if a student has rolled four sixes in a row, they often believe the fifth roll cannot possibly be another six).
• not be yet able to understand the difference between independent and dependent events and not be able to explain the effect of replacement.

Teachers should use true/false statements to help uncover any student misconceptions as students discuss and respond to questions and examples. For example, statements can include:

• When rolling a die, the event of rolling a 6 is less likely than rolling a 3.
• If I toss 4 heads in a row, it is highly likely that the next will be tails.
• If there are 100 jellybeans in the bag with 50 green and 50 red, the event of selecting a green will always be a fifty-fifty chance even if the jellybeans are not replaced after each selection.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning to describe possible everyday events and their chances of occurring.
• We are learning to use probability to solve a problem that draws on your understanding of probability.

Why are we learning about this?

• We use probability as a numerical measure of how likely an event is to happen.

What to do

Work out this problem, and record how you worked it out.

1. Each box of cereal has a small prize, and there are five different prizes to collect. How many boxes of cereal would you expect to buy to get all of the different prizes?
2. Can you think of a way to model this problem without buying any cereal?

Success criteria

I can:

• compare the likelihood of outcomes in a simple chance experiment
• conduct simple experiments with random generators
• make statements that acknowledge ‘randomness’ in a situation.