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The Shape of Change Models
Author(s): Jeff Potash, & John Heinbokel Subject: Cross-Curricular
  These are the models that accompany The Shape of Change lessons.

Complex Systems Connection: Some lessons in the Shape of Change series can be used to illustrate specific characteristics of complex systems. Please see individual lessons for more information.
  Zipped (Models & PDF)
The Shape of Change
Author(s): Rob Quaden, Alan Ticotsky, & Debra Lyneis Subject: Cross-Curricular
  Eleven hands-on lessons/activities that promote critical thinking, teamwork and dialogue.

Complex Systems Connection: Some lessons in the Shape of Change series can be used to illustrate specific characteristics of complex systems. Please see individual lessons for more information.
  Link to the file: http://www.clexchange.org/cleproducts/shapeofchange.asp
The Mammoth Extinction Game
Author(s): Gene Stamell, A Ticotsky, & R Quaden Subject: Cross-Curricular
  Prepared with the support of the Gordon Stanley Brown Fund. In this interdisciplinary science, math, and social studies lesson, third graders examine how the wooly mammoth became extinct about 11,000 years ago. With a game and a hands-on model they learn about graphing, probability anda exponential decay in math, and they are intorduced to system dynamics modeling as a useful tool for looking at problems.
  Zipped (Models & PDF)
The In and Out Game: A Preliminary System Dynamics Modeling Lesson
Author(s): Alan Ticotsky, Rob Quaden, & D. Lyneis Subject: Implementation
  Prepared with the support of the Gordon Stanley Brown Fund. The In and Out Game is a preliminary system dynamics modeling lesson for kindergarten and primary grade students which is also adapted for use with upper elementary and middle school students. Yo
  Zipped (Models & PDF)
The Bank Balance Problem (D4264-1)
Author(s): Kamil Msefer Subject: Math
  Exponential growth could be taught using this model. Introduction to concept of limits and differential equations, modeling and positive feedback loops.
  PDF
Systems Tools in High School: Interdisciplinary Learning in a Science Classroom
Author(s): Alan Ticotsky Subject: Implementation
  A summary of how one teacher teaches across the curriculum. Chris DiCarlo teaches high school classes in several different disciplines at Innovation Academy Charter School (IACS). While technically in the science and math departments, he has taught physic
 
Shape of Change (Lesson 8): The Rainforest Game, including Stocks and Flows
Author(s): Rob Quaden, Alan Ticotsky, & Debra Lyneis Subject: Cross-Curricular
  From "The Shape of Change." In this simulation game, students act out the lives of trees, following different planting and harvesting policies. Students may be surprised to learn that, while the game seems very active, the stock/flow map of the game is quite basic.

Complex Systems Connection: Short and Long Term Conflicts, Separate Cause and Effect. People sometimes decide to use natural resources to meet present goals (satisfy customers, increase profits) and ignore long-term consequences. Delays in a system involving renewable resources can make it difficult to understand how present decisions to use the resource will affect long-term sustainability.
  PDF
Shape of Change (Lesson 7): The Tree Game Puzzle, including Stocks and Flows
Author(s): Rob Quaden, Alan Ticotsky, & Debra Lyneis Subject: Cross-Curricular
  From "The Shape of Change." This puzzle is an extension of the Tree Game. After playing the Tree Game, students explore what happens to the number of trees in a forest following a variety of planting and harvesting policies. In the Stocks and Flows lesson, students begin to learn to clarify their thinking, and experience the power of making stock/flow maps.

Complex Systems Connection: Short and Long Term Conflicts, Cause within System. People sometimes decide to use natural resources to meet present goals (satisfy customers, increase profits) and ignore long-term consequences. In systems where renewable resources are used up, people often blame others. Decisions to use the resource faster than it can be replenished is the real cause, however.
  PDF
Shape of Change (Lesson 6): The Tree Game, including Stocks and Flows
Author(s): Rob Quaden, Alan Ticotsky, & Debra Lyneis Subject: Cross-Curricular
  From "The Shape of Change." Students explore what happens to the number of trees in a forest over time as a forester plants and harvests each year. With the included Stocks and Flows lesson, they gain experience anticipating and observing how a stock changes with different inflow and outflow rates.

Complex Systems Connection: Cause within System, Short and Long Term Conflicts. People sometimes decide to use natural resources to meet present goals (satisfy customers, increase profits) and ignore long-term consequences. In systems where renewable resources are used up, people often blame others. Decisions to use the resource faster than it can be replenished is the real cause, however.
  PDF
Shape of Change (Lesson 5): The Infection Game, including Stocks and Flows
Author(s): Rob Quaden, Alan Ticotsky, & Debra Lyneis Subject: Cross-Curricular
  From "The Shape of Change." Students play a game that simulates the spread of an epidemic. The included Infection Game stock/flow map combines all the elements that were used in the previous lessons. Students apply all that they have learned about behavior over time graphs, stocks and flows, and reinforcing and balancing feedback loops to understand how and why the infection spread among them.

Complex Systems Connection: Separate Cause and Effect. For some illness/disease, symptoms appear long after initial infection. Sometimes people travel great distance while infected because they are unaware of the infection. Medical "detectives" faced with an epidemic must understand how the infection spreads and how quickly. Delays in the system make this more difficult.
  PDF
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