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Using Part-Whole Model to Learn Fractions, Percentages and Ratios

In the previous articles, we shared that the Singapore Model Method consists of two basic types of model drawing: Part-Whole and Comparison Model. We also shared how Part-Whole Model can be used to learn and apply the four operations in simple word problems.


In this article, we will be sharing on how your child can use the Part-Whole Model to learn and apply Fractions, Percentages and Ratios in simple word problems on top of the four operations!


Using Part-Whole to Learn Fractions

Fractions represent parts of a Whole. A fraction is actually a Part-Whole Model essentially.

For example:


represents 1 out of 3 equal parts


represents 2 out of 3 equal parts


More about fractions will be discussed in another article.


Question 1

John bought 35 sweets.


of the sweets are red in colour. The rest are green in colour.


How many red and green sweets did John buy respectively?


In this question, your child is given the Whole and also know the proportion of red and green coloured sweets.

Hence, guide your child in drawing the Part-Whole Model with 7 equal Parts:

1 of them are red sweets while the remaining 6 are blue sweets.

In this pictorial model, your child should be able to deduce that 7 equal units represents 35 sweets with 1 unit representing the number of red sweets and 6 units representing blue sweets. Therefore, coming up with this solution:


7 units --> 35 sweets

1 unit --> 35 sweets ÷ 7 = 5 blue sweets

6 units --> 5 sweets × 6 = 30 red sweets


Therefore, when fractions are involved in a word problem your child should have the idea of equal units while approaching the question.


Using Part-Whole Model to Learn Percentages

Fractions can also be expressed as Percentages. When a Whole is divided into 100 equal Parts, one of the Parts is 1 out of 100 and is expressed as 1%.




More about Percentages and the inter-conversion of Fractions and Percentages will be discussed in another article.


Question 2

Mr Ted earns $4000 a month. He saves 25% of it and spends the rest. How much money did he spend in a month?


In this question, the Whole is given and the proportion of savings and spending is also given. Your child needs to decipher the meaning of 25% into fractions in order to draw a model.

Therefore, it is utmost important for your child to be able to convert percentages to fractions before getting your child to learn model drawing.






If your child has difficulties in converting percentages to fractions, please revisit the concept before coming back to model drawing.


Hence, with the pictorial model, your child will be able to deduce that Mr Ted's $4000 can be represented by 4 equal units where 1 unit represents Mr Ted's saving and 3 equal units represent Mr Ted's spending.


4 units --> $4000

1 unit --> $4000 ÷ 4 = $1000 (savings)

3 units --> $1000 × 3 = $3000 (spending)


Therefore, your child needs to first be able to convert percentages to fractions and then able to draw the Part-Whole Model in order to solve the word problem.


Using Part-Whole Model to Learn Ratios

Besides fractions, ratios are also used to compare two quantities. Hence, it is also important for your child to be familiar in converting ratios into fractions too.


More about ratios and its conversion to fractions will be discussed in other articles.


Question 3

Peter has 39 stamps. The ratio of local and foreign stamps is 3 : 10 respectively. How many local stamps does Peter have?


In this question, the Whole is given and the proportion of local and foreign stamps are also given. Hence, your child should be able to use the Part-Whole Model to solve this word problem.

Since the ratio of local and foreign stamps is 3 : 10 respectively, we can represent the number of local and foreign stamps to be 3 equal units and 10 equal units respectively.


As such, the Whole is 13 equal units and is represented by 39 stamps. We can then find the various Parts.


13 units --> 39 stamps

1 unit --> 39 stamps ÷ 13 = 3 stamps

3 units --> 3 stamps × 3 = 9 local stamps


These three questions serve to act as starters for parents/teachers who want to introduce the coupling of fractions, percentages or ratios with Part-Whole Model. You may tweak the questions to test your child's understanding.


In essence, fractions, percentages and ratios are comparisons of two or more quantities. They are interchangeable and considered prerequisites in drawing basic models as shown. In this article, I have shared glimpses of how fractions, percentages and ratios can be weaved into simple word problems and how the Part-Whole Model can couple in learning these fundamental concepts.


In the next article, I will be sharing on how Comparison Model can be used to learn and apply Fractions, Percentages and Ratios through simple word problems.

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