Planning tool

Students:

• use the language of chance
• order events on a probability scale from impossible to certain
• list possible outcomes of chance experiments
• describe what it means for outcomes to be equally likely and compare the number of possible and equally likely outcomes of chance events
• explain why some games are fair, and others are not.

Some students may:

• 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).
• be confused when comparing observed frequencies and expected frequencies, as they may not yet understand why observed frequencies might produce different results to expected frequencies. Conduct experiments where students must record the results, that is, their observations. They can then compare these to the expected results. Some examples:
  • The probability of rolling a 6 on a die is  16 , so this would be the expected probability. This means if the die was rolled 600 times, it would be expected the number 6 would come up 100 times.
  • Conduct an experiment where the student rolls the die 10 times and records the results for each roll (a frequency table could be used to record results). At the end of the experiment, students tally the number of times a 6 appeared. For example, the number 6 may have come up 2 times in the 10 rolls. As a fraction, this would be written as   210 which simplifies to  15 . In this case, the observed frequency does not match the expected frequency. Discuss why this is the case. Ask students to think about how to achieve an observed result that is closer to the expected result. What would happen if we rolled the dice another 10 times and then another 10 times again? Digital tools enable students to do this efficiently.
• incorrectly believe that similar to rolling one die where there is a 1 in 6 chance, rolling two dice would have a 1 in 12 chance of rolling a total. However, this is not the case. For example, rolling a total of 7 has a 6 out of 36 ( 16 ) chance, whereas rolling a total of 4 has only a 3 in 36 chance (  112 ).
• confuse events with outcomes, for example, when rolling two dice and getting a total of 3 the outcome of [2,1] is different to [1,2] however the outcome is still a total of 3. There are two chances out of a possible of 36.

To address these, ask students to conduct repeated chance experiments, recording and interpreting the results.

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 list the outcomes of a chance experiment.

Why are we learning about this?

• We are learning about probability and fairness.

What to do

1. Play a game which usually uses dice, but instead of dice use your own spinning top.
2. Make a spinning top that has an equal chance of an outcome happening. You will need a piece of card, felt markers and a pencil poked through the centre of the card to use an axis on which to spin.
3. Record how you made your spinning top, and how you made sure there is an equal chance of an outcome happening.

Success criteria

I can:

• create a spinning top that has outcomes that are equally likely
• list the possible outcomes of my spinning top.