5.3 Carrying out investigations 223
The total time taken is:
short section: 2 minutes
long section: 2 minutes 24 seconds
left edge: 27 seconds
right edges: 2 × 16 = 32 seconds
emptying grass box: 6 minutes
Total: 11 minutes 23 secondsYou should now be able to convince yourself
(without doing much more work) whether
the up-and-down method would be better or
worse. This leaves only the round-and-round,
or spiral, method to investigate – you can do
this for yourself.
This exercise was surprisingly complicated:
it required quite a lot of calculation and
needed great care, both in deciding the order
of actions and arithmetically. This is typical of
investigative problems, in real life as well as in
examinations.
• We have seen that investigations are
closely related to models.
• In an investigation, we are not required
to develop a mathematical model,
although one may be used as part of the
investigation.
• An investigation will usually require a
search to be made of possibilities, which
may sometimes lead to the identification of
a maximum or minimum.
• Investigations, like models, can be open-
ended. In this case it is important to
concentrate on lines which lead to the
required answer rather than following all
possible paths.Summary