Lesson 24 Data relations

# Episode 1

Reasoning Resources: Pupils' household data
In National Curriculum terms this activity is set both in Handling Data, and Using and Applying Mathematics. Pupils who have not prepared should provide data to the best of their knowledge on slips of paper. You could explain that this kind of ‘random noise in the data’ often does not greatly affect the results.
Whole class preparation
The issue of male to female ratio has a probabilistic aspect: from TM20: Heads and tails, pupils may be able to see that there is a certain chance of ‘more girls’ or ‘no girls' in a household, even if there are equal numbers of boys and girls in the population as a whole. Collect the slips, and write the ratio of ‘females out of all members’ on the board in a two-
column table:
For the ‘Using and Applying’ aspect, it is important to involve the pupils as much as possible in the design of the investigation and the choice of ways of representing the data. The recording takes time with the class looking at emerging variations, e.g. that 4 = households vary in size greatly or not much, that some households have all females, while some have none, etc.
Involve the class in formulating the hypothesis to test in a way that all can understand. They could accept: ‘Does having more girls run in families?’ or ‘Do mothers tend to repeat what they have lived?’ or similar, with clear understanding that they are only using the data collected.

Once the hypothesis or question is agreed, ask for pupils’ initial ideas and suggestions on how they can use the data from the whole class to address the issue.How could we use the two columns to get an idea of whether the hypothesis is right or wrong?
Pair and small group work
Opportunity here for reviewing the appropriateness of the familiar data handling methods: comparing totals, bar charts, averages, etc. Give pupils five minutes in groups or pairs to come up with suggestions for ways of processing the data that they think would work, Point out that they do not need to start using the whole data yet. They may think of ways to simplify the data, e.g. by labelling each ratio as ‘more girls than boys’ equal’ and ‘less. Or they may think of totalling numbers to compare them.
Whole class sharing and discussion
This could be represented as a three column bar-graph with the headings, ‘more girls; equal, fewer girls! And the same thing could be done with the mothers’ families. This simplifies the distribution to three columns.

But even if the bars are asymmetrical, does this tell us what We want to know about whether the tendency runs in families? That challenge requires that pupils first recognise the limitation of working with one distribution.
Collect the groups’ ideas, and accept all suggestions as adding some information to the problem. This is an opportunity to show their range of concepts on data handling and how they can apply it.

Ask groups who suggest comparing totals what the meaning is of each total, and how useful that is for the given problem.

Some groups may have tackled different or partial problems, such as larger families compared to smaller families or families with no males.

Pupils may suggest a bar chart (if not, prompt them to do so). Ask how many bars they think they should use - whether it should be three (for more girls/equal/fewer than boys) or more divisions of the data. A similar bar chart can be produced for the mother's family data.

Some may suggest working out the fraction of girls in their own household and in their mother’s old household, and they may even suggest a stem-and-leaf representation of the numbers of families with each fraction.

It is unlikely at this point that pupils will suggest a correlation diagram, but they may approach the idea of confirming and disconfirming cases of the hypothesis.