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Using Part-Whole Model to Learn the Four Operations

In the previous article, I shared the Part-Whole Model as one of the two basic types of Singapore Model Method. In this article, I will be sharing how the Part-Whole Model can help students learn the Four Operations and how they can use Part-Whole Model to solve word problems.


Using Part-Whole Model to Learn Addition and Subtraction

In the previous post, we shared about Part-Whole Model to be used when the word problem involves many Parts of a Whole.


Question 1

There are 26 boys and 13 girls in the class. How many students are there in the class altogether?


In this question, you are given two Parts : the number of boys and girls respectively. The question wants to find out the Whole which is made up of the two Parts. Therefore we can draw the Part-Whole Model to find out the Whole from the two Parts.

With this pictorial diagram, students can instinctively understand that they need to apply the addition operation to find the total number of students in the class.


Let's use back the same question to introduce subtraction so that students do no need to consider another context to learn a related concept.


Question 2

There are 39 students in the class. 13 of them are boys. How many students in the class are girls?


In this question, you are given the Whole and one of the two Parts. Hence we can use the Part-Whole Model to find the quantity of the missing Part.

With this pictorial diagram, students can instinctively understand that they need to apply subtraction to obtain the number of girls.


With these two examples, you may change the question to test your child's understanding of the two operations and at the same time, comprehending the question and coming up with the Part-Whole Model in solving the word problem.


This is also another example of Using Part-Whole Model to solve more complicated word problem in Grade 5 which involves fractions which will be covered in subsequent articles.

Example of Part-Whole Model used in a Grade 5 word problem.

Taken from PSLE Prep Programme


Using Part-Whole Model to learn Multiplication / Division

The main difference in using Part-Whole Model to introduce multiplication and division than addition and subtraction is the equality of Parts.


Parts involved in addition and subtraction are usually unequal Parts. However for multiplication and division, the Parts must be equal.


Question 3

Mary reads the same number of pages of a book everyday. She reads 7 pages of the same book for 6 days. How many pages are there in the book?


In this question, you are given 6 Parts and asked to find the Whole. Your child may be guided to add (+) all the Parts to find the Whole which is possible but not sustainable. Hence, you may highlight that for this questions, all the Parts are equal and then introduce the multiplication operation (×).

You can guide your child in drawing the Part-Whole model with 6 identical Parts to form a Whole. They can add all the Parts and obtain the final answer. However, you may guide your child in applying the multiplication operation, 7 × 6 = 42.


With this pictorial diagram, your child can relate the relationship between addition and multiplication. You should also get your child to differentiate between the two operations.


Let's use back the same question to introduce the division operation.


Question 4

A book contains 42 pages. Mary reads the same number of pages each day. It took her 6 days to finish reading the book. How many pages does Mary read each day?

In this question, the Whole and number of equal Parts are given. Your child is supposed to find out the value of each equal Part. You can guide your child in drawing this pictorial model and introduce the division operation.


total number of pages ÷ number of days = number of pages read each day


42 ÷ 6 = 7


With this pictorial diagram, you can introduce the division operation to your child and get your child to understand when division can be used.


To further extend, you can get your child to attempt this question:


Question 5

A book contains 42 pages. Mary reads 6 pages each day. How many days did Mary take to finish reading the book?


This is to further extend the use of the division and get your child to understand the application of division operation.


This is an example of using Part-Whole Model for equal Parts

Taken from PSLE Prep Programme


While concluding this segment of the lesson, you may wish to get your child to think about what are some differences between the solutions of Question 1 and 2 compared to 3, 4 and 5. Guide your child in identifying that the equality of quantity is the determining factor so that your child can differentiate between the two and be able to draw models based on the word problem.


With such methods, you can kill two birds with a stone: learning and applying basic arithmetic operations in word problems and drawing the Part-Whole Model.


In the next articles, I will be sharing on how the Comparison Model can be used to learn and apply basic arithmetic operations in word problem.

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