This scenario is a fun way for school age students to learn how to solve first-degree equations. The curriculum included in this document is suitable for an hour workshop with grades 3-7 participants.
Required material for this activity are 4 yellow and 4 Wooden Rooster Puzzles and a Beach Kit Box.
In this scenario each pair of participants receives the equipment (Figure 1).
They open the box and construct their beach.
Students of grades 6 and 7 will assemble 4 pink and 4 yellow wooden rooster puzzles. Students of lower grades only assemble 4 pink wooden rooster puzzles.
Note: In the following, please ignore all red parts if the participants are of grades less than 5.
The teacher explains about some pink or yellow roosters on one or both sides of a river. There are also some left brown or white beans on one or both sides of the river.
The following rules are given:
- Each pink rooster has eaten the same number of brown or white beans (But not both of them.) as the other pink roosters
- Each yellow rooster has eaten the same number of brown or white beans (But not both of them.) as the other yellow roosters.
- The color of beans that pink roosters have eaten are different than that of those the yellow roosters have eaten, but the number of eaten beans for all roosters are the same.
- Each brown bean on one side can be eliminated by one white bean in the same side and vice versa.
- It is also known that the total number of beans (eaten by roosters or left on turf) on both sides of the river are equals.
The question is: According to the above rules, how many beans and of what color has each rooster eaten?
By removing an equal number of brown roosters, and/or equal number of yellow roosters, and/or by removing an equal number of brown beans, and/or equal number of white beans from both sides of the river, based on the above rules, the participants can find the number and the color of the eaten beans.
For example, in figure 4 we want to find how many beans and in what color each rooster has eaten.
The students will remove the yellow rooster and one pink rooster from the left hand side, because the brown and white beans inside them eliminate each other (See rules 3 and 4.).
They also separate and remove 4 brown beans from both sides (Based on role 4).
Now it is clear that the pink rooster has eaten 4 brown beans. Hence, referring to the original problem, the two pink roosters have eaten 4 brown beans each and the yellow rooster has eaten 4 white beans. In the above example, the students indirectly solved the equation:
2X+4-X=8
More complicated examples can be presented to higher grades and less complicated for lower grades. The teacher may have lots of example for the students and can create many sub-scenarios from this activity.
After doing sufficient examples, the teacher leaves each pairs and ask them to create their own examples. One student makes an arrangement and the other one should find the number and color of beans that each rooster has eaten.
At the end of the session, for each pairs, the teacher writes an equation on a piece of a paper and they should illustrate it on their beach. For example, figure 7 illustrates the equation
2X + (-3) + (-X) = -4X + 12
