Let's use an example to illustrate the Part-Whole Model.
Tom has 8 stamps and Jerry has 6 stamps. How many stamps do they have altogether?
Young children may learn this by physically counting the stamps one by one and find that the total to be 14. Some children may move on to grouping the stamps by twos and counting it in multiples of twos.
This is the concrete step within the CPA approach and it is useful for children who is learning it at the early stages of arithmetic.
In Singapore, we tend to group the stamps by multiples of 10 and we call this method: "Number Bonds". This is a preferred method to get young children to count easily when the sum exceeds 10. Students learn "Number Bonds" from ages 5 to 7 before moving on to using models to solve such questions. Both "number bonds" and model drawing are part of the Pictorial aspect. A detailed sharing on "Number Bonds" is at this post. In this post, we will continue to learn how the model diagram sits in the Pictorial aspect.
Transiting from the above Concrete to Pictorial aspect, both stamps from Tom and Jerry are rearranged to form one long chain of blocks. Each stamp is noted to be in one block.
From this simple model, students should instinctively realise that they need to add (+) the number of stamps from both Tom and Jerry to get the total. There is less need for the teacher to explain why addition needs to be performed.
Of course it is not sustainable for students to keep drawing the stamps during lessons and especially when the numbers get bigger. Instead, we simplify the pictorial model into small little blocks which is simple and neat. Below is an example of how it can be drawn.
This is essentially the Part-Whole Model. Whole refers to the sum of the objects that the problem is about. The Whole is made up of many Parts and all the Parts add up to the Whole.
Essentially you want your child to be able to come up with the solution 8 + 6 = 14. However some students may question or may not fully appreciate why we need to add (+) the two numbers. Hence there is a learning gap, whether knowingly or unknowingly, and the scaffolds provided by the Part Whole Method is essential in developing Mathematical thinking at the foundation level.
This is an example of how Part-Whole Model looks like.
Taken from PSLE Prep Programme.
Given that the Whole in question is made up of 2 Parts, then you can add the Parts to form the Whole.
Whole = Part + Part
You can also find one Part by subtracting one known Part from the known Whole.
Part = Whole - Part
That's it! Essentially the Part Whole Model helps students to quickly sketch a pictorial representation that aids their understanding of the word problem and come out with a logical solution based on their drawing!
In the next article, I will be sharing on the Comparison Model.