“There should be no such thing as boring mathematics”

- Edsger Dijkstra


  Ho Soo Thong             Ho Shuyuan

Revised on 1 May 2020 



In the write-up “Euclidean Algorithm – A Bar Modelling Approach”, we illustrate a Line modelling approach to solving two word problems. 

In Singapore, school teachers use rectangular bars instead of line segments for a better visual bar model to depict a problem. The modelling approach, providing a visual aid for understanding and solving the problem, is known as the Bar Model Method

A solving strategy, known as Ratio Approach, is used for a wide range of problems involving ratios, fractions and simple percentages. To follow up, we will solve some recently PSLE questions  to illustrate a holistic Ratio Approach. In this approach, we will use the Unitary Method and apply the Greatest Common Unit Procedure (Euclidean Algorithm) for complex situations.


Bar Model Method involves Two Major Steps:  

1. Construct a holistic bar model for visible Algebraic Relations

2. Apply Simple Arithmetic Computations and Simple Algebra for unknowns. 


Ratio Approach to Recent PSLE Questions

Pupils can refer to the published Past Examination Papers for the original questions.

Example 1PSLE (13/01A/19)

The question involves three situations:

1. Algebraic Relation :     Number of stars in First Box = Number of stars inSecond Box .

2. First Box :                     Number of gold stars : Number of silver stars = 1 : 5 .

3. Second Box :                 Number of gold stars : Number of silver stars = 1 : 2 .

A holistic bar model is


Notes : 

1. The problem solving strategy is the Direct Counting Method based on the Part-Whole Concept. 

2. The solution involves a simple “Multiple” algebraic relation.


Here, we have an variant of the above PSLE question for practising the bar modelling ratio approach.

Exercise 1

There are two types of cookies in a small box and a large box.

The ratio of the number of sugar cookies to oatmeal cookies is 2 : 3 in the large box and is 2 : 7 in the small box. 

The total number of cookies in the small box is 60% of the number cookies in the large .

What fraction of the cookies in the two boxes are sugar cookies?




Example 3 -  PSLE 09/02/19

The question involves an activity and two situations.

Before Situation :      Number of boys : Number of girls = 4 : 1.

Activity :                      Add 6 boys and 6 girls

After Situation :        Number of boys : Number of girls = 3 : 1.



Example 4 – PSLE 8/02/2019

Solution to the harder PSLE question is shown in the write-up “Bar Model Approach To PSLE-2019 Questions”.