P5 Math Problem-solving Technique: Common Difference

Introduction

Welcome to another P5 Math blog post!

We previously talked about the Gap & Difference Method — the keywords to look out for and a step-by-step guide to solving problems using this method.

In this blog post, we will be discussing another P5 Math Problem-solving Technique — the Common Difference Method.

Common Difference is one of the 4 Change Strategies.

🔎 What Are The 4 Change Strategies? 🔎

1️⃣ One Item Kept The Same
2️⃣ Difference Kept The Same (or Common Difference)
3️⃣ Total Kept The Same
4️⃣ All Items Changed

Let’s Take A Look At This P5 Math Question

Identifying Keywords

To help us decide which problem-solving strategy to use in this question, let us first highlight the keywords.

In the first sentence, we can highlight the keywords Karen is 10 years older than her younger brother.

Moving on to the second sentence, the keywords are the total age in 12 years time is 50.

Are we talking about the present time here? No. “In 12 years’ time” means 12 years later. So this means that 12 years later, their total age will be 50.

However, this is not what the question is asking. It wants us to compute Karen’s age 2 years ago.

Solving P5 Age Problems Using Common Difference Method

When solving Age Problem questions, we are going to use the Common Difference Strategy.

💡 What Is Common Difference?💡

This means that there is a constant amount of change in the numbers.

To explain it further, let’s say that Mummy and you have a 25-year age difference, which means that Mummy is 25 years older than you.

Next year, that difference will remain the same because both of you will grow older by one year.

👩‍👦 Remember This When Solving An Age Question 👩‍👦

The age difference will always stay the same.

Thought Process

Let us draw a model to illustrate the question.

This figure illustrates the age of Karen and her brother now. Karen’s block is longer because she is older.

In 12 years’ time, Karen will be 12 years older so let us add 12 for her.

How about her brother? Will her brother’s age stay the same after 12 years? No. He will also be 12 years older.

Let’s compute for the difference in their age after 12 years.

The difference remains 10 years.

But can you easily visualise the 10-year difference when you look at the illustration above? It can be tricky, right? Let us redraw our model so we can see the difference better.

We added 12 years at the beginning of the illustration so you won’t get confused about the 10-year age difference.

Next, we know that the sum of their ages is 50.

Let us fill in the missing information in our table. We know that these are going to have the same value so let us write 1 unit for each.

Let us now solve it.

We can now put 8 each for Karen and her brother’s current age.

Next, let us compute Karen’s age.

Karen is 18 years old now.

However, the question wants to know Karen’s age two years ago. So let us subtract 2 from her current age.

Therefore, Karen was 16 years old two years ago.

How Can This Question Be Tested Differently?

There are different types of Change Strategies questions.

This question is not an Age Problem, but you can see that each of them gave away the same number of stickers, so just like in the previous question, the difference will always stay the same.

Conclusion

I hope that after reading this blog post, you have gained a better understanding of how to solve Age Problems using the Common Difference Method.

Make sure to read the given information in the question thoroughly to avoid missing out on important keywords.

Stay tuned for more Math problem-solving tips!