Introduction to Change Over Time

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SWBAT use a simple model to explain the flow of elements into and out of a system.

Big Idea

Use this fun and simple game to introduce your students to concepts of Systems Thinking.

Getting Started

This is the first of a series of lessons that teaches the fundamentals of Systems Thinking and Systems Dynamics. 

I introduce this at the same time that I begin to teach about Climate Change as I see value teaching students to think about the dynamics of climate change while using the habits of a systems thinker, however, rather than imbed specific science content into the lessons, I have kept them generic so that they can be applied to a host of topics that the teacher sees fit. 

These lessons are based on work supported by The Waters Foundation and published by the Creative Learning Exchange


  • Large display area (easel pad, display board, or chalkboard)
  • Large easel graph pad
  • Colored markers and chalk
  • Rope or tape to mark out areas of the classroom floor
  • Student handout


5 minutes

Before the students enter the classroom, I create a large Stock and Flow diagram on the floor. This piques their interest as they enter the room. 

I begin this lesson telling my students that I am going to teach them a new set of skills that are both fun to use and will help us make sense of the science of our changing climate, which involves looking at a lot of different data sets and involves many different Earth Systems. We will learn and practice the habits of a system thinker and use both the skills and habits to build arguments based on data regarding Earth's changing climate.  


20 minutes

I start by explaining the basics of the game. While the game is quite simple for 8th graders, it is necessary as it builds a foundation of learning of how to use the Stock and Flow model and connects it to behavior-over-time graphs. As students play the game, they will learn that the change in the total number of students in the area depends on the number of students flowing in and out over time.

Pass out the student handout. It includes a place to record and graph data along with follow-up questions. 

To play the game, we control the flow of students into and out of the "stock." We can think of the stock like a bathtub. Water flows into the tub via the faucet (inflow) and out via the drain (outflow). 

The number of students in the stock changes over time as some players enter the area and other players leave during each round.

We will count the total number of players in the area after each round and record their observations on a class graph.

In the first game, the rule is: 2 students “In” and 1 student “Out” each round.

In the second game, we will play with different rules, make predictions and compare the results.

Ask two volunteers to walk through the In flow and enter the stock. Ask one of them to exit through the Out flow. Count how many players now remain in the stock – one player. Record that number on the next line in the column for “Players in the Stock” to begin Round 1.

Choose two new volunteers and play another round. Record 2 Players Going In and 1 Player Going Out. Count how many players remain in the stock (2) and enter this number to begin Round 2.

Repeat this process, recording the new numbers on the table. Students will soon be able to make predictions as they see patterns emerge. I stop after 5-6 rounds and ask them to fill in the rest of the table based in the pattern. 

(Note: The numbers in blue are the first round and those in red are from the second round.)

Next, you ask the students to graph the stock data, creating a "behavior-over-time" graph. The data will create a positive line with a slope of 1. This is graphing that most 8th graders should be familiar with. Then have them graph the flows. This will produce horizontal lines, as the flows are constant. 



10 minutes

Ask students to predict what the graphs would look like after a few more rounds. After 20 rounds?

Point put how they are using a graph think and communicate their ideas about change over time. They will use this same line of thinking when considering climate change data. 


20 minutes

Play a second round of the game with new rules. You may ask the students to set them if you like. 

I set the rules as follows:

  • In the stock: 0
  • Inflow each turn: 5
  • Outflow each turn: 2

Students enter these initial values into the second table and follow the same procedure as the first game. Once the pattern is clear, I have them complete the rest of the table then move on to graph the data on the same graphs as Game 1, only using a different color this time. 

Refer to the student work samples in the slide show below for examples of how this looks once completed.  


10 minutes

Once you have played the two games, have students work through the Explain portion of the lab. The questions are:

  • How does the graph show us what happened to the number of players in the stock in Game 1 and Game 2?
  • How are the lines for Game 1 and Game 2 similar?How are they different?
  • Which line is steeper? Why?
  • What makes a stock change?How can we make the behavior over time graph of the stock steeper?
  • How would the graph be different if there were some players in the stock at the start of the game?
  • What happens when an outflow is larger than the inflow?
  • What happens when the inflow and outflow are equal, say, 3 In and 3 Out each round?
  • Can you think of any experiences in life that resemble the In and Out Game. What makes the stock increase or decrease over time?

Encourage many stocks and flows examples from the class. This helps them start to make connections to the world around them. Below are some examples. 

You may also assign Global Climate Change and Energy: Stock and Flow, on the Schlumberger Excellence in Education Development (SEED) website, as a reading assignment. It includes some fun-to-play simulations.  

In the video below I asked tow of my students to reflect on how playing this game helped them understand stock and flow diagrams. 


20 minutes

Should you want to extend the lesson further and try out a few more simulations, PlanetSeed has an excellent web page that connects directly to this lesson. You could assign students to work in pairs to read each section and experiment with the simulations. There is a great one on trees to try.