MATHEMATICAL MODELING

MATHEMATICAL MODELING: 

MATHEMATICAL MODELING

Example: Industry : 

Example: Industry First jetliner to be digitally designed, "pre-assembled" on computer, eliminating need for costly, full-scale mockup. Computational modeling improved the quality of work and reduced changes, errors, and rework .

Example: Climate Modeling: 

Example: Climate Modeling

PowerPoint Presentation: 

What is a Mathematical Model? 1 Models are abstractions of reality! 2 Models are a representation of a particular thing, idea, or condition. 3 Mathematical Models are simplified representations of some real world entity can be in equations or computer code are intended to mimic essential features while leaving out inessentials 4 Mathematical models are characterized by assumptions about: Variables (the things which change) Parameters (the things which do not change) Functional forms (the relationship between the two)

Mathematical Modeling?: 

Mathematical Modeling? Mathematical modeling seeks to gain an understanding of science through the use of mathematical models on HP computers. Mathematical modeling involves teamwork

Modeling Cycle: 

Problem Formulate Compute Interpret Validate Report Modeling Cycle meaningful problem based in a context students care about.

What are the “favorite” careers dreamed of by 4th grade students?: 

What are the “favorite” careers dreamed of by 4th grade students? You gave the assignment, they collected the data, and on the next slide is what they came up with:

PowerPoint Presentation: 

Number of Students SMP ???

Questions we could ask…: 

Questions we could ask… What was the most popular career chosen by 4th grade students? What was the least popular career chosen by 4th grade students? Which career was chosen by 55 students? List the careers chosen by the 4th grade students from most to least popular. Which career was chosen by 65 students? How many students chose a medical career? SMP ???

Modeling in the Common Core: 

Modeling in the Common Core Descriptive Modeling Describes or summarizes phenomena in a compact form. E.g., Graphs of observations such as of global temperature & atmospheric CO 2 over time. Analytic modeling Seeks to explain data on the basis of deeper theoretical ideas, but with parameters that are empirically based. E.g., exponential growth of bacterial colonies follows from a constant reproduction rate.

Modeling in the Common Core: 

Modeling in the Common Core Models devised depend on a number of factors: How precise an answer do we want or need? What aspects of the situation do we most need to understand, control, or optimize? What resources of time & tools do we have? What are the limits of our mathematical, statistical, & technical skills, & our ability to recognize significant variables & relationships among them. Is this a life or death situation? What do we care the most about? Do we have more than 1 period? What technology is available? Is this a 3rd grade class? Algebra I? precalculus? AP Statistics?

Summary: 

Summary Modeling can be done from Kindergarden through the Calculus. Modeling crosses all domains of mathematics Modeling integrates all of the standards of mathematical practice. Modeling takes a situation in the real world, removes it from the real world and places it in mathematics, solves it, then replaces it in the real world to see if the mathematical solution fits.

Mathematical Modeling Test: 

Mathematical Modeling Test Modeling in mathematics refers to which of the following (there can be more than one correct answer.): Answer: It depends on the question being asked !