This activity is based on Linda Booth Sweeney & Dennis Meadows “Harvest” from The Systems Thing Playbook, a collection of wonderful exercises and simulations for guiding children (and adults) through the process of thinking about how interconnected systems work together. It is a thoroughly wonderful book, and this mathematical investigation would not be possible without it.
The basic idea is this: the students in your class are divided into groups, each of which represents a fishing boat. Each boat puts in an "order" to take a certain number of fish from the sea. If there are enough fish, the order is filled. If there is not enough fish, the boat goes without fish for that season. The remaining fish are "restocked' according to a simple mathematical formula: if there are fewer than 25 fish left, the total is doubled. If there are 25 or more fish remaining, the ocean "recovers" and goes back to its capacity of 50 fish.
The problem is that since there are only 50 fish in this "ocean," if students get greedy and take too many fish, the ocean will run out of fish for the season. Even worse, if the group takes too many fish, there won't be enough to restock the ocean to full capacity.
This activity is a wonderful way for your students to experience all the issues surrounding sustainability, and practice using mathematics in the process. They keep charts that show how the number of fish in the ocean changes as it is fished beyond its capacity. They collaboratively make decisions about how many fish to take that year, and then keep track of how many fish are left in the ocean. They also make graphs that show how the change in the number of fish remaining at the end of the season can lead to a sustainable harvest, or a "crash" of the system. Students also conduct a conference to decide how the fishing boats can collaborate to distribute the "catch" in order to create a sustainable fish harvest.
This is a wonderful activity where you can show your students in a vibrant and exciting way how mathematics can be used to model the intricacies of a sustainable system.