
3008THangTime
31 May 2015  Modeling Scenarios
We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion "hang time.''We include a Mathematica and a Maple...

1006TFinancingSavingsAndLoans
31 May 2015  Modeling Scenarios
We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...

Teaching Modeling with Partial Differential Equations: Several Successful Approaches
31 May 2015  Articles and Publications
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial...

1005BTChemDataCollection
30 May 2015  Modeling Scenarios
We present a situation in which a chemistry graduate student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not keep track of...

1005ATChemDataCollection
30 May 2015  Modeling Scenarios
We present a situation in which a chemistry graduate student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, she only collects the data at the start and end of a number of ten minute intervals and does not keep track of...

1005TOilSlick
30 May 2015  Modeling Scenarios
We describe a modeling activity for students in which modeling with difference and differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a ...

1004TMicroorganismImmigration
30 May 2015  Modeling Scenarios
We present a modeling opportunity for population death with nonconstant immigration and suggest the use of both discrete and continuous models with a comparison of results.

1001TMandMDeathAndImmigration
30 May 2015  Modeling Scenarios
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare their model prediction with their...

3019TShuttlecockFall
30 May 2015  Modeling Scenarios
We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and...

3016TFallingCoffeeFilters
30 May 2015  Modeling Scenarios
We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.

3013TWhiffleBallFall
30 May 2015  Modeling Scenarios
We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and apply it to our...

3020TChord PathTime
30 May 2015  Modeling Scenarios
Using Newton's Second Law of motion students can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. They come to a nonintuitive conclusion through their analysis, but upon reflection the conclusion does make...

1003TCollegeSavings
12 May 2015  Modeling Scenarios
We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.

1002TTossing
11 May 2015  Modeling Scenarios
We offer students simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential decay fit, difference equation, and differential equation.We add a Hand Out Working Version which can be used in class authored by Rachel ...