## Resources

#####
Resource Type (97)

Modeling Scenario(95) Technique Narrative(1) Article or Presentation(1)

#####
Differential Equation Type (97)

ODE(90) PDE(4) Difference(15) First(59) Second(27) Higher(3) Linear(46) Nonlinear(39) System(22) Constant Coeff(23) Homogeneous(33) Nonhomogeneous(23)

#####
Technique (97)

Boundary Value Problems(3) Eigen Methods(2) Initial Value Problems(78) Integrating Factor(6) Laplace Transform(2) Numerical Methods(13) Parameter Estimation(45) Qualitative Behavior(7) Separable(21) Separation of Variables(26) Undetermined Coefficients(2) Other(2)

#####
Qualitative Analysis (97)

Equilibrium(15) Stability(10) Phase Plane(7) Graphical analysis(51) Parameters(57) Other(10)

#####
Application Area (97)

Chemistry(4) Economics(5) Engineering(21) Humanities(1) Life Sciences(24) Mathematics(4) Modeling (general)(69) Physics(48) Social Sciences(12)

#####
Course (97)

Precalculus(1) Calculus 1(1) Calculus 2(48) Calculus 3 (multivariable)(2) Differential Equations(95) Modeling(90) Other(1)

#####
Course Level (97)

Introductory(93) Upper Level(84) Graduate(1) High School(82)

#####
Lesson Length (97)

Portion of one class period(49) One class period(47) Multiple class periods(9) One term (semester or quarter)(1) Other(1)

#####
Technology (97)

Excel(28) GeoGebra(1) Maple(2) Mathematica(55) MatLab(11) Octave(1) Python(4) R(1) SAGE(1) Calculator(1) None(9) Other(18)

#####
Approach (97)

Directed(6) Guided(91) Open-ended(5) Discussion(2) Develop model(4)

#####
Skills (97)

Data collection(49) Data analysis(70) Programming(5) Statistics(3) Other(20)

#####
Key Scientific Process Skills (313)

Reading research papers(2) Reviewing prior research(23) Asking a question(298) Formulating hypotheses(265) Designing/conducting experiments(55) Predicting outcomes(97) Gathering data/making observations(74) Analyzing data(125) Interpreting results/data(141) Displaying/modeling results/data(139) Communicating results(115) Translating into mathematics(6)

#####
Assessment Type (96)

Assessment of student groups/teams(2) Assignment(1) Homework(89) Give an oral presentation(1) Informal in-class report(1) Solve problem(s)(1) Written assignment: Essay(2) Written assignment: Report(86) Written assignment: Literature review(1)

#####
Pedagogical Approaches (85)

Case Study(4) Collaborative Work(5) Computer Model(5) Physical Model(3) Guided inquiry/investigation(74)

#####
Vision and Change Core Competencies - Ability (96)

Create and develop models(94) Use quantitative reasoning(84) Design simulations(25) Tap into interdisciplinary study(16) Communicate and collaborate with mathematics community(2) Communicate and collaborate with other disciplines(5) Understand the relationship between material and society(1)

#####
Principles of How People Learn (95)

Motivates student to learn material(90) Focuses student on the material to be learned(90) Develops supportive community of learners(3) Leverages differences among learners(2) Reveals prior knowledge(4) Requires student to do the bulk of the work(2)

#####
Bloom's Cognitive Level (84)

Foundational: factual knowledge & comprehension(2) Application & Analysis(83) Synthesis/Evaluation/Creation(2)

#####
Includes clear efforts on Issues (0)

###### Applied Filters

Modeling Scenario

##### 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.Article or Presentation

##### SIMIODE Spring 2024 Webinars - Insightmaker

We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).Modeling Scenario

##### 1-027-StochasticProcesses-ModelingScenario

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.Modeling Scenario

##### 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.Modeling Scenario

##### 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.Modeling Scenario

##### 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.Modeling Scenario

##### 6-005-InsectColonySurvivalOpt-ModelingScenario

We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.Modeling Scenario

##### 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...Modeling Scenario

##### 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 Scenario

##### 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!Modeling Scenario

##### 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...Modeling Scenario

##### 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.Modeling Scenario

##### 6-001-Epidemic-ModelingScenario

This paper presents real-world data, a problem statement, and discussion of a common approach to modeling that data, including student responses. In particular, we provide time-series data on the number of boys bedridden due to an outbreak of...Technique Narrative

##### 2-001-NumericalMethodsComparisons-TechniqueNarrative

This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.Modeling Scenario

##### 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.Modeling Scenario

##### 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...Modeling Scenario

##### 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.Modeling Scenario

##### 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.Modeling Scenario

##### 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