Introduction

The first thing I tell my students to do whenever they are faced with Math word problems is to read the question and underline the keywords.

You may have heard this tip, but sometimes when I receive my students’ papers, I see that they underline everything!

🤔 What Exactly Does Underlining Keywords Mean? 🤔

It means that when we remove all the other words that are not underlined, we should still have the information required to solve the question.

In this blog post, you will learn how highlighting the correct keywords can guide you in solving word problems using the Assumption Method.

## How To Underline Keywords In Math Problem Sums

Take a look at the first sentence in the question: Eunice has a total of 100 notes in her purse.

The keyword is not her purse or the person. The keyword in the first sentence is the total number of notes she has. In this case, let us underline the phrase total of 100 notes.

You must think that Eunice is very rich to have that many notes. But is that really the case? That depends on the types of notes she has!

The next thing we should check is the types of notes that Eunice has. In the next sentence, it says that she has \$10 notes and \$50 notes.

Let’s proceed to the next sentence: Given that the total value of the notes is 2,120…

We found another key piece of information here! Let’s underline the total value of her notes. She has a total of \$2,120.

Lastly, we want to know what the question is asking so we can derive a plan on how to solve the question. It is asking for the total number of \$50 notes that Eunice has.

## Can We Use The Guess And Check Method?

Now that we have analysed the question, we need to come up with a plan.

How do we solve this question?

For this type of question, most students will say, “Teacher, I want to do Guess and Check.”

✅ What Is Guess And Check? ✅

Guess and Check is a problem-solving strategy in which you guess the answer to the problem and check to see if it is correct.

However, some students struggle with using this technique because they do not know what to guess and what to check.

Aside from this, some are clueless about which strategy to use to identify the patterns — should the value of their guesses decrease or increase?

However, if we do not know the answers to these questions, we will be guessing blindly and take a long time to solve one question!

We cannot spend too much time trying to solve just one question during examinations so Guess and Check might not be the best method for solving this question.

## Solving Using The Assumption Method

Instead of Guess and Check, we can use the Assumption Method to solve this question faster.

So how do we know when we can use the Assumption Method?

🤔 When To Use The Assumption Method? 🤔

You can use the Assumption Method when you have the following information:

1. Total Units
2. Individual Value
3. Total Value

The first thing we need to know is the Total Units which is given in the first sentence. We know that Eunice has 100 notes.

Second is the Individual Value. Eunice has two types of notes — \$10 and \$50.

Lastly, we need to know the Total Value. What is the total worth of all her 100 pieces of notes? It’s \$2,120.

With these three pieces of information from the question, we know that we can use the Assumption Method!

🤔 What Is The Assumption Method? 🤔

It is an answering technique in which you make an assumption based on the given information.

In this case, we will assume that Eunice has a certain number of \$10 and \$50 notes.

## Making An Assumption

Let’s try to be very generous first and make Eunice super rich. Let’s assume that all her 100 notes are \$50 notes!

However, we would know that this is not the case by checking the total value that she will have.

But Eunice only has \$2,120, not \$5,000! So our assumption is wrong.

🧐 Did you know that you can use the Assumption Method for these P5 Math topics? 🧐

💯 Whole Numbers
🍕 Ratio
💨 Rate

## Assumption VS Actual

In this case, let us draw a model to illustrate our assumption versus the actual amount that she has.

When we assumed all the 100 notes to be \$50, she would have \$5,000. But actually, Eunice has some \$50 notes and some \$10 notes. We do not know how many pieces of each note she has, but the total value is \$2,120.

Let us draw the same model and break down the total value into individual notes.

For our assumption, let’s say her first note is \$50, the second note will be another \$50, and so on until it reaches the 100th note.

For the Actual case, Eunice has some \$50 notes and some \$10 notes. Let’s say the first and second notes are \$50. Then, let’s change the next two notes and say that they are \$10, and so on until we reach the 100th note.

When you compare the models for our assumption and the actual case, you will see that there are a lot of gaps in the second model highlighted in blue.

To fix this, we are going to push our \$10 notes to the left side of our illustration so that the gaps will be pushed to the other end, as illustrated by the blue highlights in the model below.

Meanwhile, the \$2,120 will be made up of your \$50 and \$10 notes.

## TED Method

Now, let’s use the TED Method to compute.

💡 What Is The TED Method?💡

It is an answering structure used when solving using the Assumption Method.

When using the TED Method, you compute for the following:
1️⃣ Total Value of Assumption
2️⃣ Each Gap’s Value
3️⃣ Difference between Assumption and Actual

Let’s recap. We assumed that all 100 notes are \$50 notes so the Total Value in our assumption is \$5,000.

Now, let us compute the value of Each gap.

Each gap is worth \$40!

We know that the total value of our assumption is \$5,000 and the actual total value is \$2,120. Can you compute their difference?

Therefore, the gaps are worth \$2,880!

Let’s now find out how many gaps take up \$2,880.

There are 72 gaps.

Each gap means we changed \$50 to \$10. So one gap is one \$10.

We now know the total number of \$10 notes, but the question wants us to find out how many \$50 Eunice has.

Eunice has 100 pieces of notes and now, we know that 72 of them are \$10 notes. How many pieces are \$50 then?

Therefore, Eunice has 28 pieces of \$50 notes.

## How Can This Question Be Tested Differently?

Let’s take a look at the different variations of examination questions that will still require you to use the Assumption Method.

For example, instead of asking for the total number of \$50 notes, some examination questions will ask you for the total number of \$10 notes, so make sure to read the question carefully!

## Conclusion

Knowing the fastest way to solve Math problem sums is crucial, especially with the limited time you have during the examinations.

I hope that after reading this blog post, you will be able to spot the identifiers (Total Units, Individual Value, Total Value) so you’ll know when to use the Assumption Method.

Stay tuned for more articles that help you tackle challenging Math questions.

If you like our methodology, we've some ongoing weekly Math classes: