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Why do this problem?
All work on probability is based on ideas of randomness, an idea
which has precise mathematical meaning, while being informally used
in everyday life. A discussion of tricky ideas should challenge
students' understanding.
Possible approach
Stand rolling a die, or shuffling some cards as the students enter,
or while the discussion starts. If you have an interactive
whiteboard, you could leave a slideshow running the numbers1-10 set
to shuffle and loop. Ask students for initial ideas of what
randomness means, and a show of hands for how many already
understand it.
Put students into small groups (randomly?) and ask them to compose
one sentence that explains randomness. Organise a 'random relay' -
give each group a slip of paper with one of the statements from the
problem on it. They must decide whether they agree with it or not,
and settle on the main arguments in case they are called on to
argue with a group with the opposite opinion. They then get a new
statement to work on. Make it very clear that the whole group is
responsible for the answers, and that any of them might get called
to explain. Tell them that the points available are 10 for every
right answer, -20 for each wrong one, (to promote certainty above
speed).
Select a few items for debate where groups have reached different
final answers. Either arrange for representatives of the groups to
meet and convince each other, or arrange a public debate with one
champion from either view, and then questions from the floor.
The final scores for each group might reflect the general
misunderstanding of probability in the general population, the
ideas are difficult, but we can make sure that we understand the
basics - reiterate them from the board.
Key questions
How does your justification relate to the original statements made
about randomness? (perhaps worth displaying these on the board
throughout the lesson)
Possible extension
Focus on clarity of explanation and attempt to get good answers on
all statements.
Possible support
- If something is random, you can't ever work out what the next one
will be
- Even if it has been done lots of times, the next one could still
be anything
- When it's been done lots of times the overall results are very
predictable