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Excess and Shortage

Explained Simply

What is the Excess and Shortage Concept?

The Excess and Shortage Concept, also known as the Gap and Difference concept, is one of the big “Math ideas” that appears in many Singapore Math problem sums.

Students are exposed to Math questions with this concept since Primary 3 and these Excess and Shortage Questions continue to appear in increasing difficulties throughout Primary 4, Primary 5 and Primary 6.

Therefore, learning to identify this concept will be useful to many students as questions that deals with this concept are commonly seen in homework and exams.

Examples of Excess and Shortage Questions

Here are some examples of Primary 5 and Primary 6 Math problem sum questions that require the application of the Excess and Shortage Concept.

These Math problem sums can be grouped into 3 kinds of situations – excess and excess, excess and shortage and lastly, shortage and shortage.

  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 can we tell that a Math question is on Excess and Shortage?

In order to spot Math questions that deals with the Excess and Shortage concept, we will need to be looking out for 2 scenarios that are used as comparisons. Most of the time, each scenario starts with the keyword “If”. That’s why such Excess and Shortage questions are also affectionately known as the “Double-if” questions to some.

The 2 scenarios in these Double if Maths questions usually results in 3 types 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

As you can see, the Excess and Shortage Math Concept isn’t that hard when you follow the steps we’ve shared and understand the logic behind it. Of course, there’s no better way to test out your understanding than to try to apply the concepts to some Excess and Shortage questions yourself!

Do try out these Excess and Shortage 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