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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.

data Spanish tank column of water aperture Torricelli's Law Conservation of Energyt Solver water flow Excel Solver

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3-103-PullBackCars-ModelingScenario

This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.

modeling dynamics hands-on toy pull-back car pullback

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1-001-MM-DeathAndImmigration-ModelingScenario

We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!

simulation immigration death Spanish dats Winkel Brian Winkel

Modeling Scenario

1175

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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.

data physics dynamics data collection rolling slipping ripcord toy

Modeling Scenario

947

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366

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1-030-EyeModel-ModelingScenario

We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina.

retinal surgery Akaike Information Criterion Spanish sum of square errors surgery retiona ophthalmology eye intraocular gas bubble

Modeling Scenario

376

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186

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3-043-BallisticModeling-SpongeDart-ModelingScenario

The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.

projectile motion air resistance ballistics dimensional analysis Newtonian mechanics sponge dart Nerf gun Nerf dart Buckingham's Theorem

Modeling Scenario

499

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1-012-Sublimation-Modeling Scenario

We offer data on the sublimation of dry ice (carbon dioxide) 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...

sublimation dry ice

Modeling Scenario

123

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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

170

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1-042-KoolAid-ModelingScenario

Students run experiments involving concentrated solution of drink powder flowing from upper to lower tank, initially filled with plain water. They make qualitative observations about the intensity of the color in the tanks, record data, and build...

concentration compartment tanks KoolAid

Modeling Scenario

124

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1-043-CoolingUpAndDown-ModelingScenario

We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.

temperature oscillation Newton's Law of Cooling cooling thermostat air conditioner

Modeling Scenario

184

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1-001s-StochasticMDeathImmigration-ModelingScenario

We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.

simulation data logistic immigration stochastic death fitting

Modeling Scenario

145

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1-001d-HotelPopulationDecay-ModelingScenario

You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel. Before you run the simulation in MATLAB, answer some questions.

simulation logistic exponential decay fitting

Modeling Scenario

126

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1-046-GoingViral-ModelingScenario

Students participate in a simulation of the spread of a viral disease in the classroom and model the process with a logistic differential equation. The simulation uses random numbers and the entire class participates.

simulation mathematical model data logistic random number generator fitting random process

Modeling Scenario

112

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1-001c-PopulationDecayThenSome-ModelingScenario

You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel.

simulation occupancy population hotel

Modeling Scenario

122

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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.

simulation data optimization energy condensation best fit cost sum of scquare errors