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Using Comparison Model to Learn the Four Operations

In the previous post, we learnt how we can use the Part-Whole Model to learn and apply the Four Operations in word problems. In this article, we will learn how we can use the Comparison Model to learn and apply the Four Operations in word problems.


Using Comparison Model to Learn Addition / Subtraction


Question 1

Jane has $35 and Mary has $12 more than Jane. How much money does Mary have?


In this question, there are two people having different amount of money. The difference between the two quantities is $12. Let's draw two models, each for Jane and Mary where Mary has more money than Jane.

You can get your child to draw one block for either Jane or Mary and get your child to read the word problem and check who has more money than the other. Jane should have less money and one block should be drawn for Jane first. After which you can get your child to draw an exact model for Mary but with an additional block of $12 as a difference. At this point, there is no need to be very precise with the relative lengths of the blocks.


After drawing the pictorial model as shown above, it should be natural for your child to add (+) Jane's money and the difference to obtain Mary's money.


Get your child back to what we have learnt previously on the concept of difference.


Difference = Larger Quantity - Smaller Quantity


Larger Quantity = Smaller Quantity + Difference


Again, we will use the same question to introduce subtraction.


Question 2

Jane has $35 and Mary has $47. How much more money does Mary have than Jane?


In this question, two quantities are given and you are suppose to compare the difference. Hence you can guide your child in drawing a Comparison Model with the two quantities and then comprehend the question is looking for the difference between the two.

After drawing the pictorial model, some children may be able to deduce that the difference can be found from subtracting the smaller quantity from the larger quantity. However some children may require extra scaffolds. Hence, we can guide them using the Part-Whole Model.

From the above diagram, you may guide your child in separating Mary's money into two portions: one portion is exactly the same as Jane's which represents $35 and the other block is the excess amount. Ask your child what does the extra block represent or signify. Hopefully he or she recognises that extra block as the difference between the two quantities!

Example of more advanced word problem using Comparison Model

Taken from PSLE Prep Programme.


Using Comparison Model to Learn Multiplication / Division

While moving into multiplication and division, it is good to get your child to recall what is the difference between addition and multiplication and between subtraction and division. This is to get them ready with some prior knowledge from the previous article.


Question 3

Jean has 40 marbles. John has 5 times as many marbles as Jean. How many marbles does John have?

So you can start off with having one block which represents Jean having 40 marbles. Since there is a form of comparison of marbles between Jean and John, we adopt the Comparison Model and draw 5 identical blocks representing John having 5 times as many marbles as Jean.


We want to find out how many marbles John have and John's marbles are represented by 5 equal blocks of 40 marbles. Hence, we can guide our child to come up with the solution:


1 unit --> 40 marbles

5 units --> 40 marbles × 5 = 200 marbles


Each unit is actually a block and each unit has identical quantity. We will be using this type of solution for the rest of the series. This is also a form of proportionality which is an important concept in elementary / primary school mathematics. We will be sharing more in depth in the next series.


Next, let's use the same question to introduce division.


Question 4

John has 200 marbles. He has 5 times as many marbles as Jean. How many marbles does Jean have?


In this question, you are given the larger quantity and asked to find the smaller quantity. A similar Comparison Model can be drawn in the following.

From here, Jean's marbles are represented by 1 unit while John's are represented by 5 units. Hence, get your child to understand that the goal is to find out the number of marbles represented by 1 unit which is what Jean has. To do that, your child can find out the value of 1 unit from John's marbles. Since 5 equal units represent 200 marbles, we can find out the value of 1 unit.


5 units --> 200 marbles

1 unit --> 200 marbles ÷ 5 = 40 marbles


Revisit the concept of division with your child here if he or she has issues with understanding why we need to apply the division operation here.


Now. let's use the same question to get your child to learn a problem solving skill.


Question 5

Jean and John have 240 marbles altogether. John has 5 times as many marbles as Jean. How many marbles does John have?


We still guide our children to draw a Comparison Model as there is a comparison between two quantities. But in this question, we are given the total number of marbles instead.


From the pictorial diagram, we can guide your child to count how many units are represented by the total of 240. From there, we can use the division operator to find how many marbles John have.


6 units --> 240 marbles

1 unit --> 240 marbles ÷ 6 = 40 marbles

5 units --> 40 marbles × 5 = 200 marbles


It is always easier to first find the value of 1 unit before finding the number of units you are asked to.

Example of more advanced word problem using Comparison Model

Taken from PSLE Prep Programme.


In these two articles, I have shared how the Part-Whole and Comparison Model can be used to learn and apply the four operations in word problems.


In the next two articles, I will share on how the Part-Whole and Comparison Model can be used to learn and apply Fractions, Percentages and Ratios.

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