Thinking Skills: Critical Thinking and Problem Solving

226 Unit 5 Advanced problem solving

Commentary

This exercise asks three quite clear questions

which can be answered by analysing the data

in the table in an appropriate manner.

1 The graph is shown below.

2006 2007 2008 2009 20102011

0

10

20

30

40

50

60

70

<19 pupils 19–25 pupils >25 pupils

Year

Percentage of pupils

This shows the percentage of pupils

in larger classes to have fallen over the

period shown, and the percentage of

pupils in smaller classes to have risen.

This also means that (unless the total

number of pupils has fallen dramatically)

the number of pupils in smaller classes

must have risen at the expense of the

number of pupils in larger classes.

2 Taking the 2011 figures, we can assume

1000 children in total (it is easier to work

with numbers rather than percentages).

We then have 202 children in classes

averaging 10 each, or 20.2 classes; 567

children in classes averaging 22 each, or

25.8 classes; and 232 children in classes

averaging 30 each, or 7.7 classes. This is

a total of 20.2 + 25.8 + 7.7 = 53.7 classes.

The percentages are 37.6% of classes with

under 19 pupils; 48.0% of classes with

19–25 pupils; and 14.3% of classes with

over 25 pupils.

3 Using the calculations for question 2, we

have a total of 20.2 + 25.8 + 7.7 = 53.7

classes for 1000 pupils, or an average

class size of 18.6 children. This is lower

than the quoted average in the table,

presumably because the estimated sizes

of classes in each category in question 2

were wrong. Similar calculations for 2006

give percentages for each class size as

follows:

<19: 26.5%

19–25: 48.1%

>25: 25.4%

with an average class size of 20.9.

This shows that the number of classes

in the middle size range has stayed

relatively constant, whilst the number of

larger classes has shrunk and the number

of smaller classes increased, leaving the

overall average relatively constant.

Longer questions at A Level can involve

analysing quite complex data and

determining what conclusions may be drawn

from it. The activity below is of this type.

The graph shows which types of charities in

the UK benefit from donations from individual

members of the general public. The total

amount donated to charities by individuals

was estimated to be £11 billion.

38

26

24

17

14

13

11

9 8 7 7 5 3 1

17

11

10

11

6

16

4 3 3 5 4 3 2 1

010203040

Medical research

Hospitals

Children

Overseas

Animal

Religious

Disabled

Homeless

Elderly

Health

Schools

Environment

Sports

Arts

Proportion of people

who donate %

Proportion of total

amount %

UK Giving 2011, NCVO

Activity