## 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

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

2. Apply Basic Algebra

1. Obtain algebraic relations from bar models,
2. 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 ProblemA Bi-model Approach

2. A Direct Bar Model Approach to Number Problems

3. A Direct Bar Model Approach to Concentration Problems.