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1-001-S-MandMDeathAndImmigration
30 May 2015 | | Contributor(s):: Brian Winkel
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, collect data, estimate parameters, and compare their model prediction with their actual data. There is a video of one run of the main simulation in...
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1-001B-S-MAndM-DeathImmigrationMystery
27 Jun 2016 | | Contributor(s):: Brian Winkel
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...
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1-001d-S-HotelPopulationDecay
03 Jul 2019 | | Contributor(s):: Dina Yagodich
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.
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1-002-S-Tossing
11 May 2015 | | Contributor(s):: Brian Winkel
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 ...
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1-003-S-CollegeSavings
12 May 2015 | | Contributor(s):: Brian Winkel
We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.
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1-003-S-Text-IntroNumericalMethods
10 Jan 2019 | | Contributor(s):: Brian Winkel
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.
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1-004-S-MicroorganismImmigration
30 May 2015 | | Contributor(s):: Brian Winkel
We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.
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1-005-Text-S-NavigatingNumericalMethods
31 Mar 2019 | | Contributor(s):: Corban Harwood
This technique narrative guides a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor method. These methods are motivated by velocity...
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1-005B-S-ChemDataCollection
30 May 2015 | | Contributor(s):: Brian Winkel
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...
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1-005C-S-OilSlick
17 Jan 2022 | | Contributor(s):: Jennie D'Ambroise
We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate. This model enlightens students as to how derivatives are used in applications as well as a brief introductory encounter with parameter estimation for a linear,...
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1-006-S-FinancingSavingsAndLoans
31 May 2015 | | Contributor(s):: Brian Winkel
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...
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1-007-S-AntTunnelBuilding
31 May 2015 | | Contributor(s):: Brian Winkel
We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill. SPANISH LANGUAGE VERSION We have placed in Supporting Docs both...
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1-009-S-ICUSpread
02 Jun 2015 | | Contributor(s):: Brian Winkel
We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.
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1-011-S-Kinetics
03 Jun 2015 | | Contributor(s):: Brian Winkel
We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We offer many opportunities to model these chemical reactions with data, some of which comes from...
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1-011A-S-Kinetics
06 Jun 2015 | | Contributor(s):: Karen Bliss
Adapted from 1-11-Kinetics, SIMIODE modeling scenario. We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...
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1-012-S-SublimationCarbonDioxide
03 Jun 2015 | | Contributor(s):: Brian Winkel
We offer data on the sublimation of dry ice (carbon dioxide) with data collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the differential equation, estimate the parameters in...
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1-013-S-Sleuthing
03 Jun 2015 | | Contributor(s):: Brian Winkel
We present several situations in which differential equation models serve to aid in sleuthing and general investigations. One involves initial speed given information about constant deceleration and distance to stop in traffic incident; one involves modeling a steel ball launched vertically and...
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1-014-S-DrainingContainers
17 Mar 2017 | | Contributor(s):: Brian Winkel
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?''
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1-015-S-Torricelli
03 Jun 2015 | | Contributor(s):: Brian Winkel
We model the height of a falling column of water in a right circular cylinder (radius = 4.17 cm) emptying through a small hole on the side of the cylinder. Indeed, in all the videos below where are referred to in this Modeling Scenario the cylinder is a 2 liter soda pop...
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1-016-S-DogDrugs
04 Jun 2015 | | Contributor(s):: Brian Winkel
We offer a problem of determining the necessary drug administration in order to keep a dogsedated with specific information on half-life for an exponentially decaying presence of the drug in the body.