88 Unit 3 Problem solving: basic skills
Diagrammatic information
The map is a simple representation of the
only roads joining four towns.
Asten
Byburg
Carlstad
Dagholm
8 km 12 km
16 km
12 km
14 km
I live in Asten and wish to visit a friend in
Carlstad. I normally go via Byburg but have
discovered (before setting off) that the road
between Byburg and Carlstad is blocked by
an accident. How much will this add to my
journey?
Activity
Commentary
To solve this you need to look at the length of
the normal route and then consider the
alternatives. The journey is normally 8 km +
12 km = 20 km. If I cannot use the road between
Byburg and Carlstad, the only alternative
(shown on the map) is via Dagholm. The
distance will be 12 km + 16 km = 28 km. This is
8 km more than my normal route.
Summary
• In this chapter we have seen how data can
be presented in several different forms.
• We have also seen the importance of
reading the question carefully to ensure
that the correct pieces of data are
extracted from the information given and
used correctly.
Next we need to know how long each
match lasted. This is 2 × 20 minutes =
40 minutes. We must also note that Chorlton
High played the two extra periods in one
match − a total of 20 minutes. So their total
playing time was 4 × 40 minutes + 20 minutes
= 180 minutes or 3 hours in total.
Pictorial information
The picture shows a tiled floor where 24
individual tiles with different printing on them
are used to make up the overall pattern.
How many different patterns of tile are
needed to make up the overall pattern?
Activity
Commentary
Solving this requires a systematic evaluation of
the picture. We not only need to identify the
apparently different tiles, but also to look at
how tiles can be used in different orientations.
The procedure is to eliminate tiles one by one,
noting each time whether a new tile is needed
or whether one we have already seen can be
used in a different orientation.
In fact, only three tiles are needed:
If you did not get the right answer, can you
now convince yourself that three tiles as
shown is correct?