Tags: ordinary

Modeling Scenarios (1-20 of 42)

  1. 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...

  2. 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 ...

  3. 1-005A-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, she only collects the data at the start and end of a number of ten minute intervals and does not keep track of when...

  4. 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...

  5. 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...

  6. 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...

  7. 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.

  8. 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...

  9. 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...

  10. 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...

  11. 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...

  12. 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...

  13. 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.

  14. 1-017-S-DiseaseSpread

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways)  in a differential equation model for the spread of the disease. Students ...

  15. 1-018-S-LogisticPopGrowth

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic  model in these situations. 

  16. 1-019-S-RocksInTheHead

    04 Jun 2015 | | Contributor(s):: Brian Winkel

     We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...

  17. 1-020-S-IceMelt

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer up the claim of a store catalog  that   its ice ball mold allows users to  "... make ice balls that outlast cubes and won't water drinks down."  We ask students to build a mathematical model to defend or contradict this claim.

  18. 1-023-S-RumorSpread

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.

  19. 1-025-S-MixingItUp

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

  20. 1-026-S-Evaporation

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We  ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...