1. Modeling with STELLA Maryland Virtual High School of Science and Mathematics

2. STELLA Characteristics n A dynamic concept map n Focuses on change over time n Makes visible the feedback in a system n Allows the input of data and equations n Expresses output as data tables and graphs n Appropriate for math levels from pre- algebra through calculus

3. Money Model Money(t) = Money(t - dt) + (monthly_earnings - monthly_expenditures) * dt INIT Money = 100 monthly_earnings = 2000 monthly_expenditures = 1900

4. Model Output - Graph

5. Model Output - Table

6. Money Model with Feedback

7. Feedback Output

8. Benefits of Modeling n Solve Real World Problems n Learn from Personal Experiences n Connect Data and Processes n Clarify Abstract Concepts n Extend Classroom ‘Wet-Lab’ Experiences n Reveal Misconceptions

9. Hunting the Black Bear Garrett County, Maryland The black bear population is increasing. Bears have caused accidents on I-70. They forage for food in neighborhoods. The Department of Natural Resources wants to know if hunting should be resumed. What should the quota be?

10. The Black Bear Model

11. Model Results

12. The Dangers of Tailgating Montgomery County, Maryland You are driving on I-95 in rush hour traffic. You learned the two-second rule in Driver’s Education, but drivers cut in front of you if you leave that much space. What is a safe separation distance?

13. The Tailgating Model

14. Tailgating Scenario

15. Scenario Results

16. Carbon Cycle Objectives n Model the components and processes which form the carbon cycle. n Identify the characteristics of a system in equilibrium. n Identify feedback loops in a system. n Illustrate the effects of a disturbance to a system in equilibrium.

17. Mauna Loa Data

18. Carbon Cycle Model

19. Carbon Cycle Output

20. Enzyme Model Objectives n Determine the parameter values which result in optimum performance for an enzyme. n Use a simulation to extend understanding of enzyme reaction rates. n Apply the results of the model to real world situations.

21. Enzyme Model

22. Enzyme Model Output

23. Enzyme Model Analysis

24. The Flow Investigation The buret shown can represent many real world situations - a reservoir formed by a dam, a bathtub, drugs entering and exiting your body. Each system is affected by inflow and outflow rates. Use the buret to investigate the characteristics of those rates.

25. The Flow Model

26. Model Output

27. Contact Information n Susan Ragan - Center Director – sragan@mvhs1.mbhs.edu n Maryland Virtual High School – 51 East University Blvd. – Silver Spring, MD 20901 – http://mvhs.mbhs.edu301-649-2880