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Gap and Difference

Explained Simply

What is the Gap and Difference Concept?

The Gap and Difference concept (or the Excess and Shortage concept) is one of the common concepts that appears in many Singapore Primary School Math problem sums that stumps many students. If you are one of these students or a concerned parent who’s also stuck whenever you see Double Ifs Math questions, this step-by-step guide is for you!

Gap and Difference Question Examples

Here are some examples of Primary 5 and Primary 6 Gap and Difference Maths problem sum questions.

  1. Aunt May wanted to give some children a red packet each for Chinese New Year. If she gives each child $5, she will have $24 left. If she gives each child $8, she will have $6 left. How many children were there?
  1. Ali owns a few nasi lemak stalls. If he places 5 helpers in each stall, he will have 3 extra workers who are out of work. If he places 7 helpers in each stall, he will need another 25 helpers. How many nasi lemak stalls does he own?
  1. Mario wants to give out an equal number of blue shells to each friend. If he gives 10 blue shells to each friend, he will be short of 30 blue shells. If he gives 8 blue shells to each friend, he will be short of 6 blue shells. How many friends did he have?
download-this-worksheet

Try the questions yourself and see if you can solve them

How do we know that this is a Gap and Difference Math question?

To spot Gap and Difference Maths questions, we will need to be looking out for 2 situations that are used as comparisons. Each situation starts with the keyword “If” and that’s why these questions are also known as “Double-if” questions to some.

The 2 scenarios in these Double if Maths questions usually results in 3 kinds of outcomes.

  1. Both conditions lead to an excess.
  2. Both conditions lead to us having a shortage.
  3. One condition leads us having an excess and the other leads us to a shortage.

Let’s see it with an example question!

Here’s what to do if you see a random question and start wondering if it’s an Excess and Shortage question.

  1. Mario wants to give out an equal number of blue shells to each friend. If he gives 10 blue shells to each friend, he will be short of 30 blue shells. If he gives 8 blue shells to each friend, he will be short of 6 blue shells. How many friends did he have?
Step 1: Find the “if” keywords.

First scenario – “If he gives 10 blue shells to each friend”
Second scenario – “If he gives 8 blue shells to each friend”

Step 2: Identify any excess or shortage.

First situation – Mario doesn’t have enough blue shells since he needs 30 more. (Shortage)
Second situation – He needs another 6 more blue shells. (Shortage)
Hence, both scenarios lead to a shortage.

How do we solve such questions?

In Primary 3 and Primary 4, students are taught to use Guess and Check to derive their answers. However, as they move on to Primary 5 and 6, a more sophisticated approach such as model drawing or the unitary method is preferred.

Method:

  1. Think in term of the quantity that is different between the 2 scenarios.
  2. Form a Math sentence from each scenario.
  3. Make the 2 Math sentence equal.
  4. Draw a model to help you see better if needed.
  5. Solve the equation.
Step 1: Finding the quantity that is different between the 2 scenarios.

In this question, since the number of blue shells that Mario gives to each friend is different in each case, we will be looking at the number of blue shells that Mario has.

Step 2: Expressing that quantity as a Math sentence in each scenario.

[Scenario 1]

What is the number of blue shells that Mario has?

If Mario gives 10 blue shells to each friend, he will be short of 30 blue shells.

If 1 unit = Total number of friends Mario has,

Total number of blue shells given to them = 10 x 1 unit = 10 units

However, since he doesn’t have enough shells and needs 30 more,

Actual number of shells that Mario has = 10 units – 30

[Scenario 2]

What is the actual number of shells that he has this time?

Total number of blue shells given to his friends = 8 x 1 unit = 8 units

In order to do that, Mario needs another 6 more shells.

Hence, actual number of shells that Mario has = 8 units – 6

Step 3: Making the 2 statements equal.

This is simple and very straightforward.

Since the no. of shells Mario has is the same in the 2 cases,

10 units – 30 = 8 units – 6

Step 4: Drawing a model to help you “see” better.

Sketching the model, you will probably have something similar to the one shown:

Step 5: Solving the equation

From the model above, can you see that 2 units = 30 – 6 = 24?

Therefore 1 unit = 24 / 2 = 12!

Since 1 unit represents the no. of Mario’s friends, we know that he has 12 friends!

Problem solved!

For a video tutorial on another Shortage and Excess question using only the model method,
check this out!

Conclusion

Do you have a better understanding of the Gap and Difference Math concept now? Be sure to follow the steps we’ve shared the next time you bump into Math questions that uses this concept. Of course, there’s no better way to test out your understanding than to try to apply the concepts to some Gap and Difference questions yourself!

Do try out these Gap and Difference questions for Primary 5 and Primary 6 on your own and see how much you have learnt!

download-this-worksheet

Try the questions yourself and see if you can solve them