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

Ho Soo Thong

  June 2016

Abstract
This article illustrates the use of related bar models of two mathematical quantities for a visual view of a counting approach to a complex job problem.

Arithmetic of fractions has been used in the traditional approach to solve job problems in schools. A counting approach in the Bar Model Method was recently illustrated in [1].

In this article, we will illustrate a bi-model approach to a complex job problem at Primary Olympiad level.

Problem
Some workers are to work at two sites, A and B. The amount of work at site A and the amount of work at site B is in the ratio 3 : 2.
They began work in a morning, 60% of the workers are at site A and the rest of workers are at site B. In the afternoon the number of workers at site A is half of those at site B. The work at site B is done at the end of the day.
Next morning, 20 workers finished the remaining work at site A.
What is the total number of workers?

Solution
Noting that 60% = 3/5 , Figure 1 shows a comparison bar model for the distribution of numbers of workers.

Next, we let

a morning job of a worker = an afternoon job of a worker = 1 unit of job

In Figure 2, we refer to the distribution of workers in Figure 1 and construct bar models for work done at sites A and B.
A fraction bar model is added to depict the ratio 3 : 2.

 

Total number of workers = 3b = 30.

References
[1] Ho Soo Thong, Bar Model Method for Job Problems, AceMath 2013
[2] 朱华伟, 小学数学培优竞赛,中国少年儿童出版社2011
[3] 严军,小学数学奥赛优化解題,吉林教育出版社2007