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We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare their model prediction with their actual data.
We describe a number of different faculty efforts and resources related to this Modeling Scenario including several in Spanish.
There is a video of one run of the main simulation in this Modeling Scenario on YouTube.
We also present a very helpful narrative about experience in using this material from John Thoo, Yuba College, Marysville CA USA, who used this material in his course work.
We have placed at our YouTube website a video produced by Dina Yagodich, Frederick Community College, Frederick MD USA. Dina walks her students through the by hand solution of the resulting differential equation model, m'(t) = - 0.5 m(t) + 10, with initial population level y(0) = 50. We also offer the video, "diff eq lecture m and m" here. Featured are by hand solution, Matlab solution with attention to command details, and desmos plotting.
Additionally, PROF Arati Nanda Pati of the University of St. Thomas, Houston TX USA offers, " . . . a report prepared by the students based on the first day of the classes on how to collect data using M&M’s and then model with differential equations."
SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODE-SPANISH.cls. Names will be 1-1-S-M&M-DeathImmigration-StudentVersion-Spanish and 1-1-T-M&M-DeathImmigration-TeacherVersion-Spanish.
Further Spanish Language Resources
PROF Norma Miller, Universidad Tecnológica de Panamá, Panama City PANAMA has shared with us her lesson material she is using in her differential equations course in Spring 2020. We have placed the following Spanish language files in Supporting Docs for this Modeling Scenario.
Simulación muerte e inmigración de m&m's - parte experimental.docx and pdf version. This is the Word and pdf versions of experimental part of the Project (first 3 pages of complete Project; to be given first).
Simulación muerte e inmigración de m&m's - completo.docx and pdf version . This is the Word and pdf versions of the “complete” Project (to be given after experiments are completed and Excel file has been discussed with the students).
Aspectos teóricos - Simulación muerte e inmigración m&m's.docx and pdf version. This is the Word and pdf versions of the theoretical part of the Project (to be gone through with the students or given as a separate handout).
Ajuste de parámetro de experimento 1 con Solver.xlsx This is an Excel file with sample data for death only experiment. Sheet 2 is same as sheet 1 only that Solver was applied to the data. This is to be worked through with students as some may not be familiar with Excel.
Student models for experiment 1: EcDif 04-15 Proy1-parte1 Modelos de estudiantes
Discrete model for experiment 1: EcDif 04-15 Proy1-parte2 Modelo discrete
Discrete model for experiment 1 compared to student data: EcDif 04-15 Proy1-parte3 Modelo discreto vs los datos
Continuous model for experiment 1: EcDif 04-15 Proy1-parte4 Modelo continuo solución
Modeling change, from discrete to continuous model for experiment: EcDif 04-15 Proy1-parte5 Modelando el cambio
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