Lessons from The Lorax: Using Graphs to Study Change 

Author(s):
Rob Quaden, & Alan Ticotsky 
Subject:
CrossCurricular 

In this lesson, students read The Lorax and draw graphs to illustrate the changes that happen over the course of the story. Using simply stated questions, readers grapple with the complex themes in the book and movie. Students will investigate how cycles compete for dominance, and think about how the needs of business and natural resources can collide.
Complex Systems Connection: Separate Cause and Effect, Short and Long Term Conflicts.
Shortterm focus on making money results in depletion of resource and environmental degradation over time and the collapse of the business. Actions and consequences are separated by time. 

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Lessons in Mathematics Section 0: Overview 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 0 covers basic skills in representing equations using a visual modeling tool, the STELLA software. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 1: Linear Behavior 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 1 on linear motion covers the theory of finite differences and distancetime and positiontime exercises using a motion detector. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 2: Quadratic Behavior 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 2 on quadratic behavior covers the theory of finite differences and distancetime and positiontime exercises using a motion detector. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 3: Exponential Behavior 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 3 covers the theory of finite differences for exponential functions. Students build models of many processes, including bacteria growth, drug elimination from the body and compounding interest, among others. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 4: Review 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 4 reviews previous concepts, combines model structures to solve new problems and extends problems from previous lessons. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 5: Oscillatory Behavior 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 5 covers sinusoidal functions, including simple harmonic motion. Distance versus time lessons using a motion detector are also included, as are lessons on predatorprey systems.
Complex Systems Connection: Cause within System. The lessons in this section can be used as building blocks for the Oscillations curriculum that illustrates "the cause of the problem is within the system." 

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More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 6: Convergent and Logistic Behavior 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 6 takes students through the steps from exponential to convergent to logistic models, culminating with an application to a system of deer and vegetation.
Complex Systems Connection: Cause within System. The lessons in this section can be used as building blocks for the Oscillations curriculum that illustrates "the cause of the problem is within the system." 

PDF
More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 7: Differential Equations 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 7 builds on the skills of Sections 5 and 6 using classic problems studied with differential equations. Exponential, convergent and logistic models are presented using examples from contagious disease, the path of lead through the body and predatorprey interactions. This section also compares the numerical derivation of Euler's Method to a corresponding version in STELLA.
Complex Systems Connection: Cause within System. The lessons in this section can be used as building blocks for the Oscillations curriculum that illustrates "the cause of the problem is within the system." Available from iseesystems. 

PDF
More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics Section 8: Miscellaneous Topics 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 8 presents a natural extension of linear and exponential growth study  arithmetic and geometric sequences. Application to an agespecific population is also included. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx
