A behavior over
time graph (BOTG) is used to show what happens to something over time. Whether it
is changes in the stock market or changes in the sea level, every graph tells a
story. This lesson helps students understand BOTGs. STELLA modeling and simulation
software, allows students to create models and run simulations of systems over time.
The results of simulations are displayed using visual representations such as BOTGs.
Word problems typically give students
a lot of trouble. They have difficulty understanding what is important in the problem
and in translating the words into mathematical equations. In this lesson, students
use STELLA modeling and simulation software to create a visual representation of
a problem involving a class trying to raise money by making school T-shirts.
In this lesson,
students use the basic building blocks of STELLA modeling and simulation software
to create a visual representation of a problem whereby two boys are trying to save
money for an iPod. Graphs showing different saving and spending patterns help students
understand the structure of linear functions.
This lesson expands
upon the Linear Functions lesson by introducing interest rates into an iPod savings
plan. Using STELLA modeling and simulation software, students create a visual representation
of the population dynamics of Malawi to better understand the differences between
linear and exponential functions.
This lesson introduces students to Newton's Law of Cooling through
a scenario driven model titled "Coffee with the President and the Prime Minister".
Students are able to explore Newton's Law by manipulating temperature differentials
and container insulating capacity.
This lesson explores the concepts
behind a simple pendulum. Investigate what effect, if any, string length, initial
displacement, and pendulum ball mass have on the amplitude, period, and frequency
of the pendulum's motion. Students can also see how the variables of simple harmonic
motion are related
This lesson uses
the "Virtual Bungee Jumping" model to explore the physics of a mass-spring system.
Students can manipulate mass and spring constant (number of bungee cords) and see
the resulting graphs of position vs. time, position vs. velocity, and restoring
force vs. position. In the extended experiments section, initial displacement and
force of gravity can also be manipulated.
The following activities
use STELLA to simulate filling or emptying a rain barrel with water. They were written
by Dr. Edward Gallaher and Diana M. Fisher, author of
Modeling Dynamic Systems: Lessons for a First Course to prepare students
for understanding a model used by medical researchers to study drug assimilation
in the human body.
This lesson uses the STEP function in STELLA to explore what happens
to the volume of water in a rain barrel if you increase/decrease the rate of water
flowing into it. Similarly, the PULSE function is used to simulate the impact of
dumping a bucket of water into a barrel at a specific time.
This lesson focuses on how water
drains out of a rain barrel. Students explore the use of different-sized spigots
to see the impact on the time it takes to drain the barrel.
Combining concepts from the previous two activities, this lesson
guides students to understanding the dynamics of steady state. What impact does
increasing or decreasing the flows have on the time it takes for the level of water
in a rain barrel to remain constant?
Building on the previous activity, this lesson explores what happens
when the outflow of one rain barrel flows into a second barrel.
How does the volume of water in the first barrel affect the volume in the second?