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    Modeling Scenario
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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
    juliaDiffusioninnovationrate of innovationBass modelSolver
    Modeling Scenario
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    3-011-EulerBallThrowing-ModelingScenario
    If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
    codingdragonVectorsEuler's methodball
    Modeling Scenario
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    1-144-HeatCool-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
    temperatureNewton's Law of Coolingcooling
    Modeling Scenario
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    1-128-RocketFlight-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
    resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket
    Modeling Scenario
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    3-063-FallingBuildingIce-ModelingScenario
    We model the fall of a piece of ice which is falling from a high building in New York City.
    resistancefallinggravityiceterminal velocityskyscrapers
    Modeling Scenario
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    1-110-TidePoolSnails-ModelingScenario
    Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the sun heats the water. Students model the tide pool's...
    datasnailstemperatureNewton's Law of CoolingcoolingNewtonwarmingtital pooltide pool
    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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    3-017-StackedCoffeeFiltersFalling-ModelingScenario
    Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.
    dataresistancefalling bodycoffee filterstacked
    Modeling Scenario
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    3-101-SpringMassFirstTry-NoResistance-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.
    frequencymassoscillationundampedspring constantspring\Single Degree of Freedom System
    Modeling Scenario
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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
    population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts
    Modeling Scenario
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    3-013-WhiffleBallFall-ModelingScenario
    We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.
    Akaike Information CriterionresistancegravityFree Body Diagramforcefalling objectWhiffle ball
    Modeling Scenario
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    3-080-PendulumModeling-ModelingScenario
    We lead students through building model for several pendulum configurations in motion and ask students to compare results.
    pendulumperiodlinearization
    Modeling Scenario
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    1-018-LogisticPopModel-ModelingScenario
    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...
    data analysisparameter estimationlogisticCiliate protozoapopulationlimited growthparameciaGause
    Modeling Scenario
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    9-002-GroundWaterFlow-ModelingScenario
    The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
    sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank
    Modeling Scenario
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    1-022-SpreadOfTechnologies-ModelingScenario
    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.
    data analysistechnologylogisticspreadinnovation
    Modeling Scenario
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    1-032-WordPropagation-ModelingScenario
    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.
    Googleexponential growthlanguageword problemsetymologyNgrampropagationJumbo
    Modeling Scenario
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    1-094-SteepingTea-ModelingScenario
    We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration.
    concentrationSurface AreacolorNewton's Law of Coolingteasugar
    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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    3-019-ShuttleCockFalling-ModelingScenario
    We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models.
    resistancegravityFree Body Diagramshuttlecockfallingc object
    Modeling Scenario
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    3-029-FerrisWheelCatch-ModelingScenario
    We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.
    parametric equationsprojectile motioninitial velocityferris wheelcatchcollision