The Part-Whole Concept

The Part-Whole Concept is one of the three main concepts in the Model Method which all math models are derived from, the other two being the Comparison Concept and the Change Concept . The Singapore Math Primary Curriculum adopts a concrete-pictorial-abstract progressive approach to help pupils tackle seemingly difficult and challenging word problems. Mathematics Teachers in Singapore usually make use of concrete objects to allow students to make sense of the part-whole relationship between two or more parts. Once the pupils can visualize the part-whole relationships, they will then move on to put these relationships in rectangular bars as pictorial representations of the math models concerned.

To illustrate the part-whole concept, take a look at the following problem:

Ann has 3 balls. Bob has 2 balls. How many balls do they have altogether?

We can first give the child concrete objects, like 3 balls and another 2 balls, and let the child put the two groups of objects together to find the total.



When they are comfortable with adding concrete objects, we can then proceed to teach them to draw pictures of the concrete objects within boxes to illustrate the equation 3 + 2 = 5

part-whole-concept-001


After that, we can teach the kids to go on to draw the boxes without the objects.

part-whole-concept-002


Eventually, the equation can be visualised as a whole made up of 2 parts and the pupils can easily see that to find the whole, they just need to add up the 2 parts.

part-whole-concept-003


So, 3 + 2 = 5

Therefore, they have 5 balls altogether.




Hence, we can see that the relationship among the 3 quantities (the whole and 2 parts) can be summarised as follows:

part-whole-concept-004


To find the whole given two parts, just add the two parts together:

Part + Part = Whole




To find one part when we are given the whole and the other part, just subtract the given part (or known part) from the whole.

Whole - Part = Part



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