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## Probably ...

This problem is designed for you to work on in a group of about four.

You will need a set of these cards for your group. Each card has a statement on it. These are the six statements:

$6$ is the hardest number to throw on a dice.
A game is fair if you play it properly.
I will see someone I know on the way home from school.
It always rains in the summer holidays.
If you buy lots of raffle tickets, you're sure to win a prize.
It's easier to get heads than tails when you flip a coin.

The idea is for you to decide, as a group, whether you agree or disagree with each statement. Talk together about what you think and once you have made a decision, make a note of the reasons for your choice.

If possible, discuss your group's reasons with the rest of the class.

We would love to hear about your decisions, with your reasons of course!

### Why do this problem?

Probability is an area which children can find difficult, largely due to the difference between experimental and theoretical probability. This problem is designed to get children talking freely about issues associated with probability. It could be used for you to assess children's understanding at the start or end of work on this topic.

### Possible approach

Divide the class up into groups of four to six and give each group one set of these cards. It might be that you want groups to choose a card at a time and discuss it altogether immediately. Alternatively, you could encourage each child to take one card from the set and to think about it on their own before discussing it with other members of the group.

Give groups a suitable period of time to discuss each card. They must reach a consensus, deciding whether or not the group as a whole agrees with the statement. Each group could be given a large sheet of sugar paper on which to record their decision and reasons for each card.

It will be important to allow plenty of time for the whole class to discuss their thoughts together. Listen out for those children who want to 'qualify' the statements further - this demonstrates higher-order thinking. Depending on their experience, you might expect groups to begin to quantify their reasons to the dice and coin statements. This final discussion has the potential to be very powerful as children often have the tendency to believe that mathematical probability has nothing to do with 'real-life'. This is your chance to deal with any misconceptions in a non-threatening way.

### Key questions

Tell me what you have discussed so far.
How are you going to come to an agreement?
Can you explain why you think that?
How do you know?

### Possible extension

Some children might enjoy creating their own statements for others to discuss. You might like to encourage each group to make up one of their own and pass it to another group.

### Possible support

This activity presupposes that the children are used to working in groups. There may be disputes amongst group members but try to encourage them to sort these out themselves rather that you stepping in. Some children may need your support in constructing arguments and justifications.

You can read about some of the issues which might arise when teaching probability in this article.