Learn how to solve Maths questions using the supposition method

In the realm of mathematics, the supposition method stands as a powerful problem-solving tool. This method, also known as the assumption method, serves as an indispensable approach to tackle complex mathematical challenges. In this article, we will delve into the intricacies of the supposition method, equipping you with the knowledge and skills needed to excel in your PSLE Maths exam.

Understanding the supposition method

The supposition method, at its core, involves making educated assumptions to simplify a mathematical problem. It's particularly useful when faced with intricate equations or proofs that seem insurmountable at first glance. This method allows students to break down complex problems into more manageable components, making it easier to derive solutions.

How to know if you can solve a question using the supposition method?

Usually, if a question has two values and two totals to consider: the total quantity and the total value, then you can use the supposition method.

For example:

Katherine bought $8$ pencils and erasers for $$21$. Each pencil costs $$3$ and each eraser costs $$2$. How many pencils did Katherine buy?

In this question, you can see that you are given two values - $$3$ and $$2$, and you have two totals: $8$ (pencils and erasers) and $$21$ (cost).

This means, that you can use the supposition method to solve this question.

Key steps in applying the supposition method

1. Identify the problem

The first step in applying the supposition method is to clearly understand the problem at hand. Break it down into its constituent parts.

So, for the above example, we know that:

Total quantity → 8 pencils and erasers
Total value → $$21$ (The total amount Katherine paid)
2 values → 1 pencil costs $$3$, 1 eraser costs $$2$

2. Formulate assumptions

Once you've grasped the problem's essence, begin formulating assumptions. These educated guesses should simplify the problem without compromising its integrity. Use logical reasoning to create these assumptions.

For our question, we need to find out the number of pencils Katherine bought. So, let's assume that she only bought erasers and did not buy any pencils.

3. Apply assumptions

With your assumptions in place, apply them to the problem. This often involves substituting variables or changing the problem's parameters to align with your assumptions.

So, for our example:

Assume Katherine bought all erasers:
8 (erasers) × 2 (value of 1 eraser) = 16 (amount paid for 8 erasers)

4. Solve the simplified problem

Now that you've simplified the problem through your assumptions, solve this modified version. This should be significantly easier than tackling the original, complex problem.

Let's solve the modified version of the problem:

Total value difference (the total value difference between what was given to us in the question and what we assumed):

21 (the amount that Katherine paid) – 16 (the amount she paid for 8 erasers) = 5.

Value difference (the cost difference between 1 pencil and 1 eraser):

3 (cost of one pencil) – 2 (cost of one eraser) = 1

The number of pencils Katherine bought:
5 (total value difference) ÷ 1 (value difference) = 5

5. Backtrack and verify

After obtaining a solution, backtrack to the original problem. Validate whether your assumptions and subsequent solutions hold true in the context of the initial problem.

Ok, let's check our assumptions.

Katherine would have paid 5 (number of pencils as calculated above) x $$3$ (cost of each pencil) = $$15$.

Now, the number of erasers that Katherine bought = 8 (total number of items Katherine bought) - 5 (number of pencils) = 3.

So, the price that she must have paid for erasers is 3 (as calculated above) x $$2$ (cost of each eraser) = $$10$.

That means she paid $$15 $ (what she paid for pencils) + $$10$ (what she paid for erasers) = $$21$

This is given in the example. This means our supposition is correct.

6. Present your solution

Once you've successfully applied the supposition method to derive a solution, present your findings clearly and concisely. Use appropriate mathematical notation and explanations to ensure your solution is easily understood.

Advantages of using the supposition method

- Simplicity

It simplifies complex problems, making them easier to solve.

- Versatility

Applicable across various mathematical domains.

- Problem solving

Enhances your problem-solving skills by encouraging creative thinking.

- Understanding

Deepens your understanding of mathematical concepts by breaking them down.

In conclusion, the supposition method serves as a valuable tool in the student’s toolkit. When employed effectively, it can simplify seemingly insurmountable problems, enabling the students to arrive at elegant solutions. By understanding the key steps involved, you can harness the power of this method to excel in your PSLE Maths exam.