P5 Math Problem-solving Technique: Gap & Difference Method

Introduction

Did you know there are different variations for P5 Math word problems?

If you are not sufficiently exposed to how questions can be tested in your Math examinations, you will likely miss out on important keywords to decide which problem-solving technique to use!

We previously talked about the Common Difference Method. Click the link if you missed out on that!

In this blog post, we will share the keywords you have to look for when using the Gap & Difference Method.

We will also be looking at some question variations you may find in your examinations to help you solve them accurately even when presented differently.

🧐 Did you know that you can use the Gap & Difference Method for these P5 Math topics? 🧐

💯 Whole Numbers
🍰 Fractions
🍕 Ratio
📊 Percentage
🔢 Decimals

Let’s Take A Look At This P5 Math Question

Identifying Keywords

Let us first identify the keywords in the problem.

The first sentence says Kenric bought some pencils.

Is the keyword Kenric? No! The keyword is some pencils. Therefore, we do not know the exact number of pencils that he bought.

🔎 What Does ‘If’ Mean? 🔎

When you see the word “if,” it means that the scenario did not happen yet and it is just giving you an imaginary situation.

The next sentence states “If he gave 5 pencils to each student, he would be short of 24 pencils.”

This tells us that he plans to give 5 pencils to each student, but he will be short of 24 pencils.

The third sentence says “If he gave 2 pencils to each student, he would be short of 6 pencils.” Kenric is imagining giving 2 pencils to each student, but he would be short of 6 pencils.

Solving Using Gap & Difference Method

🔎 What Is The Gap & Difference Method? 🔎

The Gap & Difference Method is an answering technique that can be used when the following pieces of key information are available:
1. “If” – “If” / “When” – When”
2. Excess / Shortage

Let’s Solve Part (A)

First, let us draw a model to illustrate the situation.

Take note that the yellow highlight indicates the actual number of pencils that Kenric has.

For the first case, if he gives the students 5 pencils each, he would be 24 pencils short. Therefore, the 24 pencils are not part of the actual number of pencils that Kenric has.

Now, let’s look at the second “If.” If he gives everybody 2 pencils each, he will be 6 pencils short. Therefore, the 6 pencils are also not part of the actual number of pencils that he has.

Let us break down our model into smaller pieces.

We can see that there are gaps in the second model as illustrated by the green highlights.

We can fix this by pushing all our 2s to the left side of our illustration so that the gaps will be pushed to the other end as seen below.

Now, let us compute the value of each gap.

The value of each gap is 3.

Next, let us compute the difference.

The difference is 18.

Next, let’s find out the number of gaps.

Each gap is equal to 3, so how many 3s do I need to fill the difference of 18?

This means that there are 6 gaps.

Each gap is equal to one student.

Therefore, 6 gaps = 6 students.

Answer For Part (A)

There are 6 students.

Let’s Solve Part (B)

Let us compute using our first “If.”

Kenric wanted to give 5 pencils for each student. We know that there are 6 students. How many pencils will he need?

Remember that he does not have all 30 pencils because in the first case, Kenric is 24 pencils short.

He only has 6 pencils!

We can also use the second case to check.

For the second case, Mr. Kenric wanted to give 2 pencils to each student. We knew from part (a) that there are 6 students.

Again, Mr. Kenric does not have all the 12 pencils and is 6 pencils short.

 

Answer For Part (B)

There are 6 pencils.

How Can This Question Be Tested Differently?

Take note that some questions are phrased differently. Teachers do not always use “If.” Sometimes, they use “When.”

Aside from this, instead of the shortage, you can also be given the leftover or excess.

There are also instances when the shortage or excess will not be directly stated, requiring you to compute for it.

In the case of the question above, we know that each girl had 10 strawberries except for the last girl who only had 3 strawberries. This means that there is a shortage of 7 strawberries.

Conclusion

After reading this blog post, I hope that you remember to use the Gap & Difference Method when you see these pieces of key information in the question:

1. “If” – “If” or “When” – “When”
2. Excess or Shortage

Also, keep in mind that P5 Math word problems have different variations. This is why it is important to keep answering practice questions to familiarise yourself with the different phrasings of the same question type.

Stay tuned for more P5 Math blog posts!