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Using Comparison Model to Learn Fractions, Percentages and Ratios

In the previous article, I shared glimpses of how Part-Whole Model can be used to learn Fractions, Percentages and Ratios. In this article, I will be sharing on how you can use Comparison Model to learn and apply Fractions, Percentages and Ratios on top of the four operations.


The basics of Fractions, Percentages and Ratios will be discussed in separate articles and this article is purely on the union of Fractions, Percentages and Ratios with Comparison Model.


Using Comparison Model to Learn Fractions


Question 1

John has 1/3 of the money that Peter has. If both of them have $200 in total. How much money does Peter have?


In this question, there is a comparison between the money John and Peter had. Since John has 1/3 of the money Peter has, we can draw the model of Peter having 3 equal units while John having 1 equal unit. The question also gave the total sum of money to be $200.


With the pictorial diagram, you can guide your child in deducing that 4 equal units representing $200. From here, your child is able to formulate the solution.


4 units --> $2000

1 unit --> $2000 ÷ 4 = $500

3 units --> $500 × 3 = $1500


Hence, it is important that your child knows the meaning of 1/3 before he or she can comprehend this problem sum.


Using Comparison Model to Learn Percentages


Question 2

Mary baked 64 tarts and buns. The number of tarts is 60% of the number of buns. How many tarts did Mary bake?


In this question, there is also a form of comparison in the number of tarts and buns. Since the number of tarts is 60% of the number of buns, we can convert 60% into fractions. It is always recommended to convert it to fractions so that we can use the mathematical thinking as shown in the previous question to solve the problem.


60% = 3/5


Therefore, refer your child to the example on fractions and get him or her to draw a model which is similar to the above example. Your child should also be able to draw this model diagram.

With this pictorial diagram, your child should be able to deduce that 8 units represent 64 tarts and buns. Therefore, able to formulate a solution to find the number of tarts.


8 units --> 64 tarts and buns

1 unit --> 64 ÷ 8 = 8

3 units --> 8 × 3 = 24 tarts


Hence, the key in solving this question is the interpretation of 60%. If students are able to convert 60% to 3/5, they would have solved the problem easily. Hence, this reinforces the importance on the skill of being able to convert fractions, percentages and ratios interchangeably as a prequisite in mastering model drawing.


Using Comparison Model to Learn Ratios


Question 3

The number of stickers Harry and Potter had was 4 : 5. The total number of stickers both of them had was 81. How many stickers does Harry have?


In this question, there is also a form of comparison between the number of stickers Harry and Potter had. The comparison is written in a form of ratios.


Since the number of stickers Harry and Potter had was 4 : 5, this means that Harry had 4/5 of the number of stickers Potter had.


With this conversion between ratios and fractions, you may guide your child to Question 1 involving fractions to draw the Comparison Model.

With this pictorial diagram, your child is able to deduce that 9 units represents 81 stickers and hence able to find the number of stickers Harry have.


9 units --> 81 stickers

1 unit --> 81 stickers ÷ 9 = 9 stickers

4 units --> 9 stickers × 4 = 36 stickers


Similarly, the main issue in solving this problem is interpreting the ratio involved in the word problem. By converting it to fractions, students are able to draw the Comparison Model with ease.

An application of Comparison Model in more complicated word problem.

Taken from PSLE Prep Programme.


In these two articles, we have shared on how the two basic types of model drawing: Part-Whole and Comparison Model can be used to learn and apply Fractions, Percentages and Ratios.


In the next article, I will be sharing on various extensions of Part-Whole and Comparison Models in various word problems.

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