Tapping into mathematics
Tapping into mathematics

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Tapping into mathematics

5.6 An investigation

So far you have come across exercises and brain stretcher puzzles. The exercises are designed to help you practise certain skills and the puzzles are to get you to think a bit more generally. However now here is a different type of activity: an investigation.

Investigations are usually much more open-ended than exercises. With an investigation you often need to stop and think about what information you will need to tackle the task, and how you should interpret the results of your calculations.

Here is an account of a short investigation on the theme of saving public money. It is included here as an example of how an investigation might be tackled, with the calculator being used simply as a mathematical tool. In the account of the investigation there are two exercises for you to carry out – please do not give in to the temptation to miss these out.

The investigation arose as a result of a comment made by a politician in a radio interview. He claimed: ‘A hospital could save more money in one week by fixing a dripping tap than it spends in a week on a nurse's wages’.

Spend a few minutes thinking about the politician's statement. It is a serious claim and implies that significant sums of public money are wasted by ignoring apparently trivial items such as dripping taps. There is also, perhaps, a hint that if hospitals were more efficient about tackling problems like this they would have more money to spend on nurses' salaries.

Why do you think the statement might have been made? Do you think it is likely to be true? Do you think the politician made a calculation to come up with this comparison? Most people actually take such remarks at face value without questioning or challenging them. How could you check it out now?

There are two main aspects to think about.

  • How much water would be lost in one week? What would this mean in everyday terms?

  • Could you confirm or deny the politician's claim that a dripping tap costs a hospital more in a week than one nurse's wages?

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