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### Number and algebra

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### Advanced mathematics

# Discussing Risk and Reward

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Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Risk, reward and chance are fundamental concepts which really
start to come alive during A-level and beyond; this collection of
short questions and discussion points provides many
opportunities to stimulate conversation and interest amongst a
class and bring elements of statistics to life.

Statistics in school can sometimes seem full of computation
and resources such as this one can provide the insights and sense
of purpose which might be obscured by the complicated
procedural aspects of statistics.

It can be used at a wide range of levels and
sophistications.

This problem can be used at various places in the curriculum
and it can be used for a sequence of short lesson starters across a
term, studied in more focus during key lessons or used to liven up
a lull in a lesson.

However, before first use, it is a good idea to get the idea
of risk-reward across to the group and stress the point that there
is not necessarily a 'right' answer to some of the questions.

Here are a few usage
suggestions:

- Give out all parts of the problem and let students discuss those points which catch their interest. After a while share comments and thoughts about the mathematics and issues which arose.
- Choose specific parts of the question and ask certain students to argue in favour of it and others against it. Ask for volunteers to 'debate' it in front of the class. You could split the questions between different groups so the audience hears debate on questions that they have not considered themselves in detail. During the debate, really focus the minds of the students on the mathematical clarity of the arguments. Unclear, vague arguments should be picked up on.
- Hand out the questions and ask the students to identify what mathematics and statistics are relevant to the question
- Require the students to compute numerical answers to many of the questions.
- Put this problem up as a poster for students to reflect on throughout the term.

Who here is a risk taker? Who here is more of a cautious
person? Why?

What would prompt you to do something risky?

What mathematics is associated with risk and
probability?

When discussing these concepts, are you convinced that your
explanations are clear and precise?

This activity can be considered at sophisticated levels and
there are many possible lines of investigation which might arise.
Encourage gifted students to pursue lines of enquiry which seem of
interest. Consider, in particular, point 10.

Some students might not perceive this type of activity as real
maths. Reassure them that it is a necessary part of developing
statistical skill and intuition to consider carefully activities
such as this one.