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.
In this post, we are going to touch on the following:
What are some examples of Excess and Shortage questions?
How do we recognise an Excess and Shortage question?
How do we solve Excess and Shortage questions?
Watch video tutorial to solve Excess and Shortage questions
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.
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.
- Both conditions lead to an excess.
- Both conditions lead to us having a shortage.
- 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.
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”
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.
- Think in term of the quantity that is different between the 2 scenarios.
- Form a Math sentence from each scenario.
- Make the 2 Math sentence equal.
- Draw a model to help you see better if needed.
- 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.
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
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:
For a video tutorial on another Shortage and Excess question using only the model method,
check this out!
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!