## Resources

###### Applied Filters

##### Resource Type

Modeling Scenario Technique Narrative Potential Scenario Article or Presentation Free Online Textbook General Resource Sample Syllabus Assessment Rubric or Guide SCUDEM EXPO

##### Differential Equation Type

ODE PDE Difference Delay Integral First Second Higher Linear Nonlinear System Constant Coeff Homogeneous Nonhomogeneous Other

##### Technique

Boundary Value Problems Eigen Methods Exact Equations Fourier Series Initial Value Problems Integrating Factor Laplace Transform Linear Algebra Matrices Numerical Methods Parameter Estimation Qualitative Behavior Separable Separation of Variables Series Substitution Methods Theory (general) Undetermined Coefficients Variation of Parameters Other

##### Qualitative Analysis

Equilibrium Stability Attractor Phase Plane Graphical analysis Eigenvalue analysis Parameters Other

##### Application Area

Chemistry Economics Engineering Humanities Life Sciences Mathematics Modeling (general) Physics Social Sciences Other

##### Course

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

##### Course Level

Introductory Upper Level Graduate High School Other

##### Lesson Length

Portion of one class period One class period Multiple class periods One term (semester or quarter) One year Other

##### Technology

Derive Excel GeoGebra Maple Mathematica MathCad MatLab Octave Python R SAGE Calculator None Other Desmos

##### Approach

Directed Flipped Guided Open-ended Discussion Develop model Other

##### Skills

Data collection Data analysis Programming Statistics Other

##### Key Scientific Process Skills

Reading research papers Reviewing prior research Asking a question Formulating hypotheses Designing/conducting experiments Predicting outcomes Gathering data/making observations Analyzing data Interpreting results/data Displaying/modeling results/data Communicating results Translating into mathematics

##### Assessment Type

Assessment of individual student performance Assessment of student groups/teams Assignment Exam/quiz, in class Exam/quiz, take home Homework Answer clicker-type question(s) Answer essay question(s) Answer fill in the blank question(s) Answer multiple choice question(s) Answer short answer question(s) Answer true/false question(s) Create a concept map Create a diagram, drawing, figure, etc. Create a website Create graph, table etc. to present data Design an experiment or research study Design/present a poster Give an oral presentation Informal in-class report Interpret data Order items (e.g. strip sequence) Participate in discussion Peer evaluation Post-test Pre-test Produce a video or video response Respond to metacognition/reflection prompt Self evaluation Solve problem(s) Written assignment: One minute paper Written assignment: Brochure Written assignment: Essay Written assignment: Figure and or figure legend Written assignment: Report Written assignment: Literature review

##### Pedagogical Approaches

Think-Pair-Share Brainstorming Case Study Clicker Question Collaborative Work One Minute Paper Reflective Writing Concept Maps Strip Sequence Computer Model Physical Model Interactive Lecture Pre/Post Question Guided inquiry/investigation

##### Vision and Change Core Competencies - Ability

Create and develop models Use quantitative reasoning Design simulations Tap into interdisciplinary study Communicate and collaborate with mathematics community Communicate and collaborate with other disciplines Understand the relationship between material and society

##### Principles of How People Learn

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

##### Bloom's Cognitive Level

Foundational: factual knowledge & comprehension Application & Analysis Synthesis/Evaluation/Creation

##### Includes clear efforts on Issues

Diversity Equity Inclusion Enhancement of all

Modeling Scenario

##### 1-038-Ebola-ModelingScenario

Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
population dynamics
data analysis
exponential growth
Ebola
logistic
epidemic

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...
resistance
Flight
Rocketry
mass
Newton's Second Law of Motion
thrust
Free Body Diagram
apex
rocket

Modeling Scenario

##### 1-078-MonodGrowthModel-ModelingScenario

Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
bacteria
nutrient cycles
growth
Monod
consumption

Modeling Scenario

##### 1-031-CoolIt-ModelingScenario

We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...
Spanish
Newton's Law of Cooling
cooling

Modeling Scenario

##### 1-005-OilSlick-ModelingScenario

We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.
model fitting
spreadsheets
Spanish
derrame de petrÃ³leo
datos
expansiÃ³n
oil slick

Modeling Scenario

##### 1-007-AntTunnelBuilding-ModelingScenario

We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill.
Spanish
hormiga
tÃºnel
ant
tunnel

Modeling Scenario

##### 1-008-HangTime-ModelingScenario

We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion ``hang-tune.''
gravity
hang tim
Newton's Second Law of Motion
jump shot

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...
data
difference equations
parameter estimation
continuous
epidemic
discrete
boarding school

Modeling Scenario

##### 3-065-UpDown-ModelingScenario

We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity
Newton's Second Law of Motion
velocity
motion
apex

Modeling Scenario

##### 1-145-FastPitch-ModelingScenario

We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.
Measurement
resistance
air resistance
baseball
pitcher
fast

Technique Narrative

##### 1-015-DimensionlessVariables-TechniqueNarrative

This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
linearization
dimensional analysis
time scale
scaling
dimensionless variables
spatial scale

Technique Narrative

##### 7-006-LaplaceTransformBirth-TechniqueNarrative

We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
Transformations
power series

Technique Narrative

##### 5-012-LinearSystemConjecture-TechniqueNarrative

Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
discovery learning
conjecture
solution
substitution

Technique Narrative

##### 2-005-LinearizeItAll-TechniqueNarrative

Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
computation
error
Torricelli's Law
data fitting
linear approximation

Technique Narrative

##### 1-001-SepartionOfVariables-TechniqueNarrative

We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
solutions
strategy
method
applications