SWBAT create a model to show feedback in a system and explain how a model can be used to explain change over time.

In this second lesson on systems thinking, students learn how to graphically represent how and why things change over time using causal loop diagrams.

This is the second lesson on systems thinking and a follow up to the The In and Out Game. In that game, students learned about stocks and flows and how to construct behavior over time graphs from data collected. In this simulation, they learn to construct another visual tool -- a feedback loop. Feedback loops are helpful when creating explanations about change over time in a system, like that of Earth's changing climate.

They will play a simple game to track the rate of growth of friendships in the class when students employ their friendship skills and behave in friendly ways. You will play a few different rounds, changing up the rules so that students make connections to the the effect of the rates of growth.

**Materials**

- Large display area (easel pad, display board, or chalkboard)
- Large easel graph pad
- Markers, chalk
- Set of name cards of class members in a paper bag or container

10 minutes

To engage the class and review the last lesson on stocks and flows, I begin with the set of Everyday Stocks and Flows problem set.

The problems are as follows:

- Amount of water in a bathtub.
- Money in a piggy bank.
- Students in the classroom during the course of a day.
- Students in the dining room.
- Numbers of wins for a sports team you know.
- Your hunger from the time you awake to the time you go to bed.

Credits: Lesson adapted from Alan Ticotsky © 2013 Creative Learning Exchange www.clexchange.org

25 minutes

In the "Making Friends" game, students play a part in a simple simulation to investigate the rates of growth possible in building friendships when students behave in friendly ways and everyone is included. If you have not taught the previous lesson (In and Out Game) on stocks and flows, it's a good idea to begin there.

Explain that students are going to play a simulation game in which players pretend to make friends. They will play until all the members of the class are on the Friends Team.

Choose two or three students to begin the game on the Friends Team and remove their names from the container of name cards. (Choosing three works well if the total number of players is a multiple of three; otherwise choose two.) Move the chosen players to a designated area of the classroom where the Friends Team will meet. Record the data on the data table.

Refer to the Making Friends Student Sheet for the remainder of the instructions.

**Structure/Purpose of Game:**

Of the two games played in Making Friends, Game 1 is based on the same stock/flow structure as the In and Out Game. During each round of the game, the number of new friends is constant. This causes the total number of friends to increase at a steady rate. However, the structure of Game 2 is completely different. In that game, the number of existing friends caused an increase in the number of new friends, because each existing friend choose a new friend in each round. As a result, the number of friends increased at an increasing rate. This represents the fundamental concept of feedback.

The set up for the game and materials are minimal.

Students play and graph two different versions of the Making Friends game.

In the first game, two students are added to the friendship team each round. Adding a constant number each time produces a straight line on the graph, or linear growth. It takes a long time to get everyone on the team.

In the second game, each student already on the friendship team recruits a new member each round. As the team grows larger, the number of new members also grows larger in each round. It takes only a few rounds to include everyone. This accelerating growth produces a curved line because the size of the team determines the number of new players. This pattern is called *exponential* *growth*.

In both games, the shape of the line on the graph represents the nature of the growth – an important and nontrivial concept for students.

*Credits: Adapted from Making Friends: The Shape of Change. The Creative Learning Exchange (http://www.clexchange.org)*

15 minutes

In this part of lesson you will make the connections between the game and how it can be used to explain feedback systems. Students will practice drawing Causal Loop Diagrams related to the game and other examples that can be used to connect these skills to our study on climate change.

I have included the text from The Shape of Change: Stocks and Flows that details how to lead your students through this critical part of the lesson.

Permission granted from the publisher: The Creative Learning Exchange.

In the video below, one of my students reflects on how playing this game was helpful to his understanding of feedback loops.