Demand+for+Services

//**anticipated length**: 10 sessions of 50 minutes each//

The subunit is designed to introduce students to the challenges of increasing human demands for services from the environment. It begins with a simplified version of the Easter Island's population success and ultimate collapse. The Easter Island activity uses a descriptive approach to introduce the challenges of ever increasing human demand for resources. Marooned II! begins a more mathematical treatment of the topic. Students act out the distribution and storage of a limited number of fish available on the Island. A simple spreadsheet model is developed to expand on the solutions students develop to plan with a limited food supply. The topic of models, particularly mathematical models, to simulate complex systems is introduced and several models of growth are reviewed and the usefulness of systems analysis combined with mathematical modeling is discussed. The spreadsheet model of the Marooned populations demands is paired with a Vensim model.
 * Students will understand, linear growth, exponential growth and the mathematics of growth rates
 * Students will be able to describe the phases of growth curves and explain carrying capacity
 * Students will be able to work with simple mathematical models in a spreadsheet
 * Students will identify different types of models and, in general terms, be able to describe how models are used

Using the story of growth and collapse of the human population on Easter Island, students will explore the possible causes and relate those causes to the more general case of human demands for services from the Earth. . || ||   || Short accounts of key periods in the history of human populations on Easter Island. These stories will be shared in a modified "jigsaw" format with small groups of students discussing each of the stories and then combining their observations to discuss overall conclusions. . || ||   || Individual student reporting form from group discussions. . || ||   || . ||  ||   || This PowerPoint introduces the concept of a __//system//__ and then shows how to use that concept as a tool for determining a sustainable allocation of the food supply available on the island. This lecture can be used after the Marooned II activity to analyze the results and lead to the introduction of mathematical models in a later lecture (below). Background and instructions to students to set up the __//Marooned II!//__ activity. || ||   || Student report form that assembles the information that will be useful for the spreadsheet modeling activity that follows. Introduction to models - mathematical and physical - as tools for evaluating possible solutions to complex problems.
 * Description || Materials || N.C. Essential Standards ||
 * **ACTIVITY (TEACHER)**
 * EASTER ISLAND**
 * **HANDOUTS**
 * **REPORT FORM**
 * **ACTIVITY (TEACHER)**
 * MAROONED II!**
 * I**n this activity students return to the tropical island where they were marooned in Unit 1. This time they must catch and ration fish, the only food source on the island. This provides a physical model to be translated into mathematics.
 * **LECTURE**
 * .** || [[file:Marooned! Part II - Island Systems.pptx]] ||  ||
 * **HANDOUT**
 * **REPORT FORM**
 * .** || [[file:Marooned! - Student Data Report Form.docx]] ||  ||
 * **LECTURE**
 * .** || [[file:Models - Energy and Sustainability.pptx]] ||  ||
 * VIDEO:

Very basic for real beginners. The video shows how to input and copy a formula and sum numbers in a column. || media type="youtube" key="h2WY_lJwdnk" height="215" width="260" ||  || Includes graph. Graph will be generated as numbers are input. . || ||   || Placeholder ||   ||   ||
 * HOW TO - SPREADSHEETS**
 * **SPREADSHEET (COMPLETED VERSION)** || [[file:Marooned Part II - Data Table & Graph.xlsx]] ||  ||
 * **SPREADSHEET (PARTIAL VERSION)**
 * **VENSIM MODEL** || [[file:Simple Island Fraction Distribution Model.mdl]] ||  ||
 * VENSIM - HOW TO GET STARTED