## Bar Model Method

Ho Soo Thong Ho Shuyuan

**Euclidean Algorithm – A Line Modelling Approach**

2,400 years ago, the great mathematician *Euclid *used line segments to represent mathematical quantities in his well-known *Euclidean Algorithm *used for finding the greatest common divisor of two positive integers. He opened the door for the modelling approach to problem solving.

The following illustrates the use of the *Euclidean Algorithm *and the *Euclidean Division Algorithm *for *a *line modelling approach to finding the *Greatest Common Divisor *(*GCD *) of two positive integers 357 and 105.

From the following bar model, 21 is the greatest common divisor of 357 and 105. The other divisors are 3 and 7.

The result can be applied to solve the following word problem :

*Jane has 357 apples and 105 oranges. **The apples and oranges are to be distributed equally among the baskets with no leftover. **What is the greatest number of baskets of fruits Jane can have?*

Other than the two above algorithms, Euclid’s book “*Elements*” contains propositions about numbers and particularly the *Distributive Law*. These form the core mathematics in the *Foundation Mathematics* of today’s heuristic approach to problem solving in schools.

**Effective Bar Model Method ****for Challenging Problems**

For primary schools, our website alpha-psle.sg highlight the basic mathematics for effective bar model approach to the word problems in recent *PSLE *(*Primary School Leaving Examinations* 2012 – 2017, Singapore) papers. For more challenging problem, we need the effective bar modelling problem solving strategies in two major steps:

1. Understand the problem using basic mathematics

- Understand mathematical situations with given algebraic relations,
- Construct bar models for a pictorial view of the problem.

2. Apply Basic Algebra

- Obtain algebraic relations from bar models,
- Apply basic algebra to obtain solutions.

In the site barmodelhsot.com, the following articles contains challenging problems at Primary Olympiad Level:

1. *Bar Model Method for a Job Problem* – *A Bi-model Approach*

2. *A Direct Bar Model Approach to Number Problems*

3. *A Direct Bar Model Approach to Concentration Problems*.