Turning Multivariable Models into Interactive Animated Simulations Module 2A Modeling Tool: Excel Materials needed for this model: --computer with interface and temperature probe such as Vernier’s LoggerPro, LabPro, and temperature probe) --access to hot water and a cup --Excel --Internet access --Cooling Coffee Excelet version 2 © 2011 Pittsburgh Supercomputing Center 1

Agenda Collect experimental data for the cooling of hot water Analyze and mathematically model the data Examine a multivariable simulation As a group, build an interactive simulation in Excel Explore some possible classroom applications What we are going to do today.

Part I - Objectives Via a temperature probe, collect a class set of data for the cooling of hot water. Using Excel, graph and discover a mathematical model for the data. Need a temperature probe interfaced to computer. Place probe into hot water (80-90o C) and allow data collection as water cools. Need to collect enough data to see temperature leveling out to room temperature.

Any ideas… What type of model fits the cooling data? Try it in Excel. How well did it fit the data? Allow participant to discuss what type of mathematical model might fit the data. Chart suggestions! Allow participants to explore suggested types and record back on success. This is a shifted exponential curve: y = e-kt + constant where the constant is the room temperature (curve levels out to room temperature) So the standard exponential regression will not fit the data very well.

Our final model… What did we need to do to the data to model it? Did we get a perfect fit of the data? Why or why not? To get Excel to model this data, a transformation is needed. The experimental data must have the value of room temperature subtracted form it and then run the exponential regression model on the corrected data. This gives the cooling constant, k. A lack of perfect fit (r2 < 1) is due to experimental error which collecting data. Air currents in the room are a good source of error.

Part II - Objectives Examine a pre-built Excel simulation and consider how it could be used in the classroom. Build an interactive simulation of the model in Excel. Need to have the pre-built cooling coffee excelet available for participant exploration.

Let’s ponder this question What experimental variables might influence the model? Chart possible variables that might influence the model. The list of variables might include: --room temperature --starting initial temperature --type of container --air currents in the room --liquid used

Let’s examine a multivariable simulation of the model Here is a pre-built interactive Excel simulation of Newton’s Law of Cooling – click on the “cool it” tab. Take a few minutes to examine the variables and to think about how you might use this simulation with students. Allow participants to explore cooling coffee excelet – may want to point out the interactive features! Chart ideas about use of this simulation.

Let’s construct a simulation Open a blank Excel worksheet See handout with instructions for the construction of this simulation. We will construct a slightly simpler version that was shown.

Classroom Applications Other experiments that are part of the curriculum? Chart ideas about applications in the classroom.

Summary Collected and analyzed experimental data for the cooling of hot water Developed a mathematical model Explored a pre-built simulation of Newton’s Law of Cooling Constructed an interactive simulation Discussed classroom application of this simulations and others

The big picture… In this module, we collected data, derived a model, and then expanded the model to construct a multivariable simulation. 12