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Why do this problem?
is very appropriate when starting off the topic of probability with young children. It gives the opportunity for pupils to make their own decisions and discover some important issues in this area of mathematics.
This task is probably best approached through a whole-group discussion. Learners will need to listen to each other's ideas and decide on the features of the school that affect the question. So, you will probably need to act as a catalyst and then a chairperson to allow pupils' ideas to flow.
Pose the question: "What can you say about the child who is first onto the playground tomorrow morning break time?", adapting it appropriately to suit your circumstances. You are likely to hear comments like:
"It will be someone in Miss Brown's class because she always lets her children out a little early."
"It will be a girl because I think there are a lot more girls than boys in this school."
"It will be a tall child because I've seen several tall children push their way to the front."
"It will be someone from Class 3 because their classroom is nearest the play ground." etc ...
Encourage pupils to justify their suggestions. Is there anything we know for certain about the child? Is there anything we can say is very likely? Very unlikely? How do we know? You could also challenge children to explain how they could become more certain about the 'characteristics' of the child first in the playground.
(I did, on one occasion, have the discussion come to a sudden stop when one girl said, "I know who it will be ? it'll be me because it's my turn to go onto the playground and ring the hand bell!")
It may be appropriate to record the group's ideas on individual strips of paper. (You could then order them from which they think are certain to be true and which they think are unlikely to be true.) The children will want to watch out at the appropriate time the next day to see who it is and then you can have a discussion about which predictions were correct.
Tell me about your thoughts.
Can you tell me why you think that?
How could we be more certain?
The pupils themselves are likely to come up with some further ideas for investigation. It may be that some want to conduct a survey about the first person on the playground over a few days so that they can make more accurate predictions on a future date. (See also The Car that Passes
Some pupils may need help expressing their thoughts so you may need a few particular questions to get them started, such as "will it be a boy or a girl?"; "do we know which class s/he is in?" etc.
You can read about some of the issues which might arise when teaching probability in this article.