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    Modeling Scenario
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    1-125-DiceyPopulation-ModelingScenario
    We offer students an opportunity to generate data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the...
    simulationimmigrationdeathdice
    Modeling Scenario
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    1-015-Torricelli-ModelingScenario
    We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.
    dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver
    Modeling Scenario
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    1-142-WaterBottles-ModelingScenario
    This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or use data included in the student version.
    data collectionexperimenthalf-lifeNewton's Law of Coolingwater bottle
    Modeling Scenario
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    1-047a-CondensationOptimization-ModelingScenario
    We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
    simulationdataoptimizationenergycondensationbest fitcostsum of scquare errors
    Modeling Scenario
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    1-101-ClassMMDeathImmigration-ModelingScenario
    We offer students an opportunity to generate unique data for their team on a death and immigration model using m&m's and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters.
    simulationimmigrationdata collectiondeath
    Modeling Scenario
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    1-111-SpreadOfInformation-ModelingScenario
    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with a separable linear first order differential...
    datalogisticracismprejudicemisinformationmemesspreaddisinformationinformationliesGoogle Trendscoinspennies
    Modeling Scenario
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    3-099-PullBack-ModelingScenario
    We guide students through the development of an empirical model for the velocity and distance traveled of a simple pull-back toy. Students can record videos and extract data using their own pull-back toy or use data included.
    dynamicspull-back toy
    Modeling Scenario
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    3-100-Ripcord-Toys-ModelingScenario
    This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct experiments or use videos to collect data.
    dataphysicsdynamicsdata collectionrollingslippingripcordtoy
    Modeling Scenario
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    1-013-SleuthingWithDifferentialEquations-ModelingScenario
    We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
    projectile motionaccelerationNewton's Law of Coolingspeeding
    Modeling Scenario
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    4-035-ParEstSteadyState-ModelingScenario
    Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the parameters and estimate these parameters
    driversteady statesum of square errors
    Modeling Scenario
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    1-017-DiseaseSpread-ModelingScenario
    Using a grid and m&m candies, we simulate the spread of disease. Students conduct the simulation and collect data to estimate parameters (in several ways) in a differential equation model for the spread of the disease.
    Modeling Scenario
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    1-001B-DeathImmigrationMystery-ModelingScenario
    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
    m&mMystery Novelsimmigrationexperimentdeath
    Modeling Scenario
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    1-054-GrowthInFarmland-ModelingScenario
    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple...
    fittingfarmfarmland
    Modeling Scenario
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    1-028-SouthernSweetIcedTea-ModelingScenario
    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.
    dataNewton's Law of Coolingteasweet tea
    Modeling Scenario
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    1-073-WaterExitBottle-ModelingScenario
    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container.
    datawaterflowTorricelli's Lawbottle
    Modeling Scenario
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    1-005B-ChemDataCollection-ModelingScenario
    A chemistry graduate student is 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 note the times.
    kineticslaboratoryorder of reactionchemical reactionchemical datainfusion
    Modeling Scenario
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    1-037-CommonColdSpread-ModelingScenario
    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.
    diseasecommon coldresidence hall
    Modeling Scenario
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    1-141-MMGameRevisited-ModelingScenario
    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen M&M falling M up when tossed).
    Probabilitystochastic processesBayesian methodsprobability distribution
    Modeling Scenario
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    1-107-ClothDry-ModelingScenario
    We build a mathematical model for the rate of drying in a wet cloth while hanging in air. A model can be based on underlying physical principles (analytic) or based on observations and reasoned equations, but no physical assumptions (empirical).
    dryingclothevaporation
    Modeling Scenario
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    4-023-MysteryCircuit-ModelingScenario
    Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors.
    filterscircuitRLC circuitKirchhoffvoltagegaindriver