Thinking Skills: Critical Thinking and Problem Solving

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?