Bar Model Method with Distributive Law  For Chicken-Rabbit Approach

“The esscence of mathematics lies in its freedom”

- Georg Cantor

Bar Model Method with Distributive Law For Chicken-Rabbit Approach

Ho Soo Thong

Abstract
This article illustrates a bar modelling  problem solving approach to a classical chicken-rabbit problem which involves distributive property situation. Ws will use the approach to related PSLE word problems.

A Classic Chickens-Rabbits Problem

The following classic word problem , chickens and rabbits in a cage, posed in the ancient Chinese book Sunzi Suanjing :

There are chickens and rabbits in a cage.
Look at the top of the cage – there are 35 heads.
Look at the bottom of the cage – there are 94 legs.
How many chickens and how many rabbits are there in the cage?

 The problem involves the Actual situation:

There are 35 chickens and rabbits and there is a total of 94 legs

where each rabbit has 4 legs and each chicken has 2 legs. 

The strategy here is to add the Supposed situation :

There are 35 chickens and therefore a total of 35×2 = 70 legs.

Figure 1 shows the bar models for the two situations.

cr-1

 

 

 

 

 

 

 

Therefore we have 23 chickens and 12 rabbits.

  

Variants of Chicken-Rabbit Problems

Now, we simplify the presentation in the same approach to a counting problem.

Example 1

There is a total of 33 triangles and squares, and they have a total of 113 vertices.
How many triangles and how many squares are there?

Solution

Figure 2 shows the bar model for number of vertices in the Actual situation and the Supposed situation in which we suppose that the shapes are triangles. A square has 4 vertices and a triangle has 3 vertices.

cr-2

Therefore, there are 19 triangles and 14 squares.

 

Next, we apply the Chickens-Rabbits problem solving problem to a simple finance problem.

 Example 2

Jennifer spent $ 24.80 for a total of 30 apples and oranges. 

An apple costs 70₡ and an orange costs 90₡.

How many apples and how many oranges did Jennifer buy?

Solution

Figure 3 shows the bar model for the amounts spent in the Actual situation and the Supposed situation in which we suppose that only apples are bought. An orange costs 20¢ more than an apple.

crt-3

Therefore, Jennifer bought 11 apples and 19 oranges

3. A Challenging Problem

Finally, we post a complex problem which requires the chicken-rabbit problem solving approach to be applied twice.

A total of 31 teachers and students plan for a two-nights excursion.
Teachers prepare 96 kg of food and 43 kg of camping equipment.
Each teacher will carry 4 kg of food. Among the students, each boy will carry 3 kg of food together with 2 kg of equipment and each girl will carry 3 kg of food together with 1 kg of equipment.
How many boys and how many girls are there in the excursion?

References
[1] Ho Soo Thong, Ho Shuyuan, Bar Model Method for PSLE and Beyond – AceMath, 2011
[2] Ho Soo Thong, Ho Shuyuan and Leong Yu Kiang Problem Solving methods for Primary Olympiad Mathematics, AceMath, 2012.