Bar Model Approach to PSLE-2019 Questions

“There should be no such thing as boring mathematics”

- Edsger Dijkstra

Bar Model Approach to PSLE-2019 Questions

  Ho Soo Thong       Ho Shuyuan 

Jan 2020


 To see the effectiveness of bar modelling approach, we present a holistic bar model to each of the three challenging 2019 PSLE questions. 

A holistic bar model can depict and relate all the mathematical situations of the question and compute for the required information from the embedded algebraic relations using simple arithmetic operations and effective algebraic manipulations (Simple Algebra).

The solutions illustrate some effective Problem Solving Strategies as described in the notes.





1. The bar model depicts three related “Fraction”situations.

2. For the two different distributions of the number of white beads, we look for the Greatest Common Unit.

3. Write down the required fraction and find the corresponding number of beads


For simplicity, we can use the Euclid’s Line-Segment Approach together with an algebraic symbol U as shown below.



For more examples showing the use of the Greatest Common Unit Procedure, you may read the following article. 

Ho Soo Thong, Advanced Bar Model Method for Counting Problems, Asia Pacific Mathematics Newsletter, Vol 2,No. 1, Jan 1912.





Notes :

  1. The bar model depicts the situations : (a) Kelvin paid $61.20 for some egg tarts, (b) Julie also paid $61.20 for 6 more egg tarts because of a 15% discount. 
  2. Using basic algebraic relation is Cost = number of units × unit cost, we make computation in 4 steps as shown
  3.  Visit the site for how to construct the bar model and how to perform simple computations.




Notes :

  1. The key to begin solving the problem is noting the difference between two successive rows is 2.
  2. The next step is deduce the total number of triangles and cumulative difference.
  3. In the final part, we can see a Sum-difference problem solving strategy for percentages