80 Unit 3 Problem solving: basic skills
• relating one set of information to another
in a different form – this involves using
experience: relating new problems to ones
we have previously solved.
When solving problems, either in the real
world or in examinations, you are given, or
have, or can find, information in various
forms – text, numbers, graphs or pictures – and
need to use these to come up with a further
piece of information which will be the
solution to the problem.
The processes described above are the
fundamental building blocks of problem-
solving and can be expanded into areas of
skill that may be brought together to solve
more complex problems. The chapters in this
unit divide these into smaller identifiable skill
areas which can be tested using multiple-
choice questions. Examples of such sub-skills
are searching for solutions and spatial
reasoning (dealing with shapes and patterns).
Later units deal with more complex problems,
which can only be solved using several of
these sub-skills in combination, and are closer
to the sort of problem solving encountered in
the real world.
The activity below gives an example of a
simple problem; you can give either a simple
answer or a more complicated one, depending
on the degree of detail you consider necessary.Luke has a meeting in a town 50 miles
away at 3 p.m. tomorrow. He is planning
to travel from the town where he lives to
the town where the meeting is by train,
walking to and from the station at both
ends.
List the pieces of information Luke needs in
order to decide what time he must leave home.
Then work out how you would proceed to plan
his journey from these pieces of information.Activity
Commentary
The chances are that you missed some vital
things. You may have thought that all he
needed was a railway timetable. Unless you
approached the problem systematically, you
may not have thought of everything.
Let us start by thinking of everything he
does from leaving his house to arriving at the
meeting.
1 He leaves his house.
2 He walks to the station.
3 He buys a train ticket.
4 He goes to the platform.
5 He boards the train when it arrives.
6 He sits on the train until it reaches the
destination.
7 He leaves the train.
8 He walks to where his meeting is being
held.
You can construct the pieces of information
he needs from this list. They are:
1 The time taken to walk from his house
to the station.
2 The time needed to buy a ticket.
(Remember to allow for queues!)
3 The time to walk to the platform.
4 The train timetable.
5 The time taken to walk from the station
to where the meeting is being held.
Did you find them all? Perhaps you thought of
some that I missed. For example, I didn’t think
of allowing for the train being late. You could
estimate this by experience and allow some
extra time.
Now, to find out when he should leave home
we need to work backwards. If his meeting is at
3 p.m., you can work out when he must leave
the destination station to walk to the meeting.
You can then look at the timetable to see what
is the latest train he can catch (allowing extra
for the train to be late if appropriate). Then see
from the timetable when this train leaves his
home town. Continuing, you can determine
when he should have bought his ticket, and
when he should leave home.