Planning tool

Students:

• discuss and list all the possible outcomes of a chance experiment
• conduct and record outcomes of a chance experiment
• describe the relative frequency of each outcome
• explain the difference between chance experiments that have equally likely outcomes and those that do 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. 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. For example:
  • The probability of rolling a 6 on a die is  16 , so this would be the expected probability. This means if the dice was rolled 600 times, it would be expected the number 6 would come up 100 times.
  • Conduct an experiment where the students roll the dice 10 times and record 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 2 dice would have a 1 in 12 chance of rolling a total. However, this is not always 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 (  212 ).
• confuse events with outcomes, for example, when rolling 2 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 2 chances out of a possible of 36.

To address these misconceptions, 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 investigate a chance experiment and list the outcomes.

Why are we learning about this?

• We are learning to list the outcomes of a chance experiment to know all of the possibilities.

What to do

1. Play the Twelve-pointed star game with another person.
2. Open this website for the rules and instructions of how to play. You will need two dice and a print-out of the board. If you do not have the materials, you can draw the board on a sheet of paper and you could use this online random dice generator.
3. Record the results of your game and what you found out about the probabilities when rolling two dice.
   • What totals are most likely?
   • What totals are least likely?
4. Use data to explain your answers.

Success criteria

I can:

• investigate probability using a simple chance experiment
• list outcomes of a chance experiment
• explain why some totals of rolling two dice are more likely to come up than others.