Thinking Skills: Critical Thinking and Problem Solving

124 Unit 3 Problem solving: basic skills

Summary

•   We have seen how problems may involve

making choices and decisions.

•   Decisions may involve selecting one item

from a number of options or making a

decision on an action.

•   In solving these problems it is important

to choose an efficient way of working

so the correct answer is obtained and

calculations are carried out in the most

effective and simplest way in order to

reduce the chance of error.

chickpeas Eve could sell with the least she has

in stock and minimum in the drums she buys.

The least she has in stock is half a drum,

which might be as little as 5kg; this will make

up a minimum of 10 packs. She has 14 packs in

stock, so at least 24 in total. She needs at most

7 × 15 = 105 packs, so may need as much as 81

× 0.5 kg = 40.5 kg. At 10 kg per drum, she will

need 5 drums to be sure she can last the week.

You might also like to work out what is the

fewest drums she might need.

This illustrates a particular type of decisions

question – where the decision is based on the

minimum (or sometimes the maximum) to

fulfil a criterion.

After four throws you have scored 17.

Should you throw once more? Consider the

chances of getting different scores and how

much you will win or lose. What is best on

average?

What should you do if you have a score

other than 17?

2    Clyde’s local supermarket has an offer

on petrol, depending on the amount you

spend in the store. If you spend $20–$30

you get a voucher that gives you 2¢ per

litre off petrol; if you spend $30–$50, you

get 3¢ per litre off; and if you spend over

$50 you get 4¢ per litre off. Clyde’s car will

take 30 litres of petrol.

Consider for what range of total

purchase prices in the supermarket it is

worth his buying a small amount extra, so

that the reduction in the petrol cost will

make his total bill smaller.

3    Students at a school have to decide what

subjects they are going to study next year.

English, science and mathematics are

all compulsory, but they can choose the

remaining four subjects.

1    In a game of pontoon dice, you continue

throwing a single die until the sum of all

your throws exceeds 21 (bust) or you

decide to stop. You win plastic counters

depending on the score you stop at.

Stopping score Counters won or lost

1 to 12 0

13 or 14 Win 1

15 or 16 Win 2

17 or 18 Win 3

19 Win 6

20 Win 8

21 Win 10

Over 21 Lose 4

End-of-chapter assignments