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...
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.
10 Jan 2019 | Technique Narratives
We ask students to develop two numerical methods for solving first order differential equations geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes.
17 Mar 2017 | Modeling Scenarios
We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''
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...
27 Nov 2015 | Modeling Scenarios
We examine plots on the spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.
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...
02 Mar 2016 | Modeling Scenarios
We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...
07 Apr 2016 | Modeling Scenarios
This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.
03 Jun 2016 | Modeling Scenarios
Things float or they don’t. Well, it’s not quite that simple. In this exercise we lead students through applications of several laws of physics to develop and solve differential equations that will predict where in a water column a weight with an attached lift bag will become...
30 Nov 2016 | Modeling Scenarios
This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential...
11 Sep 2016 | Modeling Scenarios
We offer students the opportunity to develop several strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t. We go further...
26 Apr 2017 | Modeling Scenarios
Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...
26 Aug 2017 | Modeling Scenarios
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.
23 Jul 2016 | Modeling Scenarios
We offer students a chance to model a one compartment salt mixing model.
30 Aug 2018 | Modeling Scenarios
We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.
27 Feb 2016 | Modeling Scenarios
There are three videos associated with this Modeling Scenario and all are available on SIMIODE YouTube Channel: Capture-3 YouTube Version SlowMoCapture-1 YouTube Version SlowMoCapture-2 YouTubeVersion and as streaming videos or down loads in this Modeling Scenario under the Supporting Docs Tab...
15 Aug 2017 | Modeling Scenarios
We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.
26 Nov 2016 | Modeling Scenarios
We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out. First, we review the principles and derivation of the applicable physics in...
22 Nov 2016 | Modeling Scenarios
We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.