What is the Assumption Method?

The Assumption Method, also known as the Supposition Method, is one of the most common Singapore Math problem-solving techniques.

Introduced in Primary 4 (P4) Math classes, students can use this method to solve similar Guess and Check questions that they have learnt in Primary 3 (P3).

This Math heuristic still remains useful even if students move on to the upper Primary levels such as Primary 5 and Primary 6.

Since the Assumption Method is known to be faster and more systematic, it is usually preferred as compared to the Guess and Check Method to solve certain Math questions.

making assumptions

How does the Assumption Method work?

Like its name suggests, we will first need to make an ASSUMPTION (or Guess) about something (That explains why the Guess and Check method and the Assumption is related). After that, we will work step-by-step to solve the question.

Before we learn how to do the Assumption Method, we will first need to know how to identify the kind of question that can be solved by it.

Examples of Assumption Method Questions

Here are some examples of Primary 3 to Primary 6 Math problem sum questions that can be solved by using the Assumption Method.

There are 15 cats and birds in a park. There are 42 legs altogether. How many cats are there?

Iron Man made a total of 21 gadgets and masks for $3 340. It cost him $190 to make each gadget and $140 to make each mask. How many masks did he make?

How do we identify questions that use the Assumption Method?

The characteristics of the questions will be as follows:

  1. There will be 2 types of objects mentioned in the question and they have something in common.
  2. The total number of objects and the total number of the common property will be given.
  3. The individual number of each object and the individual number of the common property are unknown.

Using the first question as an example, the 2 types of objects that are involved are the cats and birds while the common property between them is the number of legs.

We have 15 cats and birds and a total of 42 legs. Since this is a Primary 3 or 4 Math problem, the P4 students are expected to be able to deduce that a cat has 4 legs and a bird has 2.

The individual number of each object and the common property is unknown.

In this case, we do not know the individual number of cats and birds nor do we know the individual number of cats’ legs or birds’ legs.

Such a problem can be solved with either the Guess and Check method that has been taught in Primary 3 or we could use the Assumption Method which is a little more advanced.

Steps for using the Assumption Method

Let’s start with what we know.  We have 15 pets.

Step 1:

ASSUME everything to be of the same type

Since we don’t know the number of each subject, we’ll make things easier for us by assuming all the pets are of the same type.

Since a cat has 4 legs while a bird has 2, we are going to imagine that all the pets are birds.

assumption-method-step-1
Step 2:

MULTIPLY to find the total value

Next, let’s calculate the total number of legs that we have.

Total number of birds’ legs = 15 x 2 = 30

However, there are supposed to be 42 legs in all according to what is given in the question. How many legs are we missing in our assumption? Let’s find out!

Step 3:

Find the DIFFERENCE

Subtracting the number of birds’ legs that we have from the actual total number of legs given in the word problem, 42 – 30 = 12. Looks like we are short of 12 legs. Where can we get the extra legs from?

Remember that there were supposed to be cats and birds? Since we were working with only birds all along. It’s time to bring in the cats!

Step 4:

Find the EFFECT of replacing 1 item with the other

When we replace a bird with a cat, we’ll get an extra of 2 legs.

assumption-method-step-2
Step 5:

REPLACE subjects until the number is accounted for

Now, let’s replace each bird with a cat until we get enough legs to account for the 12 missing legs.

assumption-method-step-3

Looks like we need to have 9 birds and 6 cats to give us 42 legs.

Problem solved!

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Conclusion

So that’s how you do the Assumption Method! The next time you see Guess and Check questions for Primary 4, try using the Assumption Method instead of Guess and Check and see how much faster it takes to get the answer.