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  • This is often used by medical researchers. For example, they may have developed a new medical treatment and they want to find out whether it is better than the old treatment, the same, or worse. If they know that it won’t harm people (sometimes they are not sure about this!), they might get permission from the appropriate go­vern­ment department to allow doctors to prescribe the new medicine. The doctors will then fill in questionnaires about how their patients responded, and give the information to the researchers to study.

4 You don’t always have to ask people for information. Many questions can be answered just by doing some research on your own. For example:

4.1 Are the storybooks in the English section of the library longer than the story­books in the other languages? To answer this question, you have to look at the last page number in each book and make some calculations

4.2 If I want to write a story for a magazine, how many words must the story be? Look at several issues of the magazine you want to write for and count the words in all the short stories. If you can calculate the average length (you will still learn about averages) of their stories, then you know how long yours must be.

5 How popular are your favourite actors? Type their names into an Internet search engine and count how many hits (number of articles with the name) the search engine finds.

6 You can do an experiment in your class. Read the description below and plan exactly how things will be done, who will do what job and how you will record the results. When you are sure of all the details, you can proceed with the e x periment.

EXPERIMENT

  • You will need two kinds of fizzy cool drink or fruit juice – choose two that some people say taste exactly the same; it will be very good if they also look the same. Blindfold the person who will be tested (the taster). Everyone (except the experimenter and the assistant) should take a turn to be the taster.
  • Someone (the experimenter) pours out a little of each drink where it can’t be seen. Use differently coloured cups. Only the experimenter will know which drink is in which cup, and this is filled in on a list that is kept secret. When the taster decides which is which, the experimenter’s assistant makes a note of the cup colour.
  • The experimenter looks at the answers, and depending on the cup colour decides whether the taster was right or wrong. After everyone has had a turn to be a taster, it may be possible to decide whether the drinks can really be told apart!
  • If there is time the class may think of another question that can be answered by an experiment. The experiment can be designed and carried out to see if there is an answer.ACTIVITY 3

To investigate the validity of the information–gathering process

[LO 5.2]

  • There is another important part of getting information that must be discussed before we can continue. Do the following e x ercise in a small group of four or five learners.
  • Say that you would like to know how many people in South Africa watch the news on TV.
  • Well, you can go to every single person in the country and ask them, tally the answers and add them up and you’ll have a very accurate answer – if nobody tells a lie, of course.
  • This would be a very long and expensive job. During the census , the government tries to ask a few important questions of every single person. This costs a lot of money, and they don’t manage to be perfectly accurate.
  • Perhaps we don’t have to ask everybody – we can ask a few and get an answer in that way. If there are 45 million people in the country, we can ask 45 of them whether they watch the news and then, if 30 say they do, maybe this means 30 million South Africans also do.
  • Statisticians call this process sampling . If the total population we are interested in is too big, we can look at a smaller number (the sample ) and multiply from that to get the real answer.
  • Imagine the learners in your class have to gather the data to answer the question. You decide to take turns to spend an hour each weekday standing at a filling station to ask motorists whether they watch the TV news. This is good because you are under a roof, and the motorists have to stop and wait a few minutes anyway, so most of them might not mind giving you an answer if you ask nicely with a smile?
  • Imagine that this works wonderfully. For two weeks you have been at the filling stations in the area and you have a lot of tallies. You very cleverly counted how many people you asked, how many wouldn’t answer, and how many said NO and how many said YES.
  • Now transform these figures into an accurate estimate of how many of the total population of the country watch the TV news.
  • Discuss in your group exactly how you would do this survey.
  • Also discuss how accurate you can expect the answer to be – in other words, if you could get everybody in the country to answer, would that “real” answer be the same as the one you calculated from your tallies? Write a short and clear summary of the conclusions your group came to after the discussions.

Assessment

LO 2
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
We know this when the learner:
2.1 investigates, in different ways, a variety of numeric and geometric patterns and relation­ships by representing and generalising them, and by explaining and justifying the rules that generate them (including patterns found in nature and cultural forms and patterns of the learner’s own creation;
2.2 represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:
2.2.1 verbal descriptions;
2.2.2 flow diagrams;
2.2.3 tables;
2.2.4 formulae and equations.
LO 5
Data HandlingThe learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions and to interpret and determine chance variation.
We know this when the learner:
5.1 poses questions relating to human rights, social, economic, environmental and political issues in South Africa;
5.2 selects, justifies and uses appropriate methods for collecting data (alone and/or as a member of a group or team) which include questionnaires and interviews, e x periments, and sources such as books, magazines and the Internet in order to answer questions and thereby draw conclusions and make predictions about the environment.

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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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