Math Strategies: Assumption VS Guess and Check

Guess-and-Check is one of the first strategies students learn in primary schools to solve problem sums.

It is a very common and easy-to-understand strategy that almost every student can master for PSLE Math.

Though easy to apply, it might not be easy to use Guess-and-Check to solve questions whereby numbers involved are big.

A student might need to make many guesses before he can successfully “guess” the correct answer.

Personally, I have seen countless times many students wasting a lot of time using this strategy during examinations but still not get the correct answers.

Much time is wasted drawing rows of a table and making many guesses. In the end, many students did not even get a single mark for the working shown.

As a result, a more efficient strategy, Assumption, was taught and adopted by many Math teachers and tutors to replace the conventional  Guess-and-Check method.

I know of some educators who instruct their students only to use Guess-and-Check as the last resort when they are really clueless on what to do to solve some problem sums. 

However, if you analyse some questions (even in recent PSLE papers), you will find that some questions can only be solved by Guess-and-Check method and not Assumption. 

For the purpose of understanding how to use Assumption to solve certain type of problem sums, an easier question with small values is shown below.

Diagrams are also used so that this strategy can be understood more easily.

Without further ado, let’s solve one question here using Assumption.

Question

There were some peacocks and deer in an enclosure of a zoo. Mary counted 7 heads and 24 legs altogether. How many animals of each type were in the enclosure?

1. Understand the Problem

There were some peacocks and deer in an enclosure of the zoo.
(There are two variables)

Mary counted 7 heads and 24 legs altogether
(Since there are 7 heads, the total number of deer and peacocks is 7)

How many animals of each type were in the zoo?
(I have to find the exact number of each variable)

2. Think of a Plan

Since the numbers involved are small, it is easy to use Guess-and-Check to find the answer quickly. But what if the numbers involved are very big? Hundreds of animals and thousands of legs?

It might be easier and faster to use Assumption to solve the problem. One attempt is all it is needed to find the answer compared to using Guess-and-Check.

Questions that can be solved using Assumption usually have two variables and a student is required to find the quantities of both variables. In this case, the number of peacocks and deer are not known.

The total number of the two variables is usually given in the question – There are 7 heads, so there are 7 animals in all in the enclosure.

3. Act on the Plan

Step 1: Assume that all animals are deer

Step 2: Total number of legs = 7 × 4 = 28

Draw 7 animals with 4 legs so that total number of legs is 28

Step 3: Number of extra legs = 28 – 24 = 4

Step 4: 4 ÷ 2 = 2 (Number of animals to have 2 legs taken away)

Take away 2 legs from 2 animals so that total number of legs is 24

Step 5: Number of peacocks = 2

Number of deer = 7 – 2 = 5

4. Check My Answer

Total number of legs for peacocks = 2 × 2 = 4

Total number of legs for deer = 5 × 4 = 20

Total number of legs for all the animals = 4 + 20 = 24 (Correct!)

More Examples of Problem Sums Involving Assumption or Guess-and-Check

Example 1

Mrs Kumar bought 50 chicken and beef pies. Each chicken pie cost $2 and each beef pie cost $2.80. The total cost of the chicken pies was $13.60 more than the total cost of the beef pies. How many more chicken pies than beef pies did she buy?

Method 1: Assumption

Assume all are chicken pies  

$2 X 50 = $100 (more than beef pies)

For every chicken pie replaced with a beef pie, the difference in total between CP and BP would be = $2 + $2.80 = $4.80

100 – 13.60 = 86.40

86.40 ÷ 4.80 = 18 (number of beef pies)

50 -18 = 32 (number of chicken pies)

32 -18 = 14

Method 2: Guess-and-Check

Answer: 32 – 18 = 14

Important Tips to take note of for Guess-and-Check

• Draw a proper table with columns and rows
• Do not show just one set of data with the correct answer. It is good to provide a few sets (minimum of 3 sets) of data to show how you eventually work towards the correct answer.
• Show working clearly with the necessary columns.
• Label all the columns with sub-headings.
• Make sure that there is a “check” column.
• Write down the final answer and not just stop with many data in the table.

  

• Make clever guesses at the beginning and work your guesses in the direction nearer to the numbers required.

Example 2

90 people went for a health check at a private clinic. Their average mass was 62 kg. Given that the average mass of the women was 50 kg and the average mass of men was 68 kg, how many men were there?

Example 3

In a restaurant, the tables are set with either 4 or 5 chairs. If the ratio of the number of tables to the number of chairs is 5 : 24, what fraction of the tables are set with 5 chairs? Express your answer in the simplest form.

Note: Can this problem be solved with Guess and Check?

Example 4

Tarzan has 242 coins in his piggy bank. It contains only 10¢, 20¢ and 50¢ coins. The total number of 10¢ and 20¢ coins is 2 $\frac{2}{3}$ times the number of 50¢ coins. The total value of the coins is $57.20. How many 10¢ coins are there in Tarzan’s piggy bank?

Conclusion

Guess-and-Check must be carried out in an “efficient” way and not in a random guessing manner hoping to get the answer.

Work your guesses in the direction nearer to the numbers required so as not to waste too much time during examination.

It is suitable to use this strategy when you are clueless on what to do or when the numbers involved are not too great. 

Assumption can be used for problem sums with greater numbers involved. One attempt is all it is needed to solve a problem sum and precious time can be saved.

However, this strategy can be quite difficult to understand and apply for some students. Some questions cannot be solved using assumption too, especially when the total value of a variable is not given. In this case, Guess-and-Check must be applied.