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1. 27 Jun 2016 | Modeling Scenarios

We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice. Collected data on generation or iteration and population  is then...

2. 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 ...

3. 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...

4. 30 May 2015 | Modeling Scenarios

5. 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...

6. 24 Jan 2016 | Modeling Scenarios

This activity is structured as a letter from a company seeking assistance with a mathematical problem. The students will act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use...

7. 04 Jun 2015 | Modeling Scenarios

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.  We work to build our model of random events which...

8. 25 Jun 2016 | Modeling Scenarios

We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea.  We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.

9. 07 Apr 2016 | Modeling Scenarios

This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.

10. 22 Jun 2016 | Modeling Scenarios

We offer raw data collected from two thermometers used in the smoking process of Southern barbecue.  One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat.  This data can be used to model and predict the amount...

11. 24 Dec 2015 | Modeling Scenarios

This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking and fishing plan in a lake.  The mixture is of two species of fish, one being the current sole...

12. 26 Aug 2017 | Modeling Scenarios

We consider modeling the attempt of an air conditioner to cool a room to a "constant'' temperature.

13. 15 Dec 2018 | Modeling Scenarios

We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

14. 14 Aug 2017 | Modeling Scenarios

The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.

15. 08 Aug 2019 | Modeling Scenarios

In this paper we present (for educational purposes) simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations from the present Earth climate to an ice age or a ``Venus type of climate.'' The models are accompanied by Matlab...

16. 31 Aug 2019 | Modeling Scenarios

Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom).  Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.  Finally, students solve the...

17. 31 Aug 2019 | Modeling Scenarios

Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom).  Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.  Finally, students solve the...

18. 12 Nov 2016 | Modeling Scenarios

19. 12 Nov 2016 | Modeling Scenarios

We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both cases. Furthermore, we seek to determine the size...

20. 17 Aug 2016 | Modeling Scenarios

The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario. In the first part of the activity, students will read a description of a method used to rate chess players. From the verbal...