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An Introduction to Mathematical Modeling

Grade Focus
Grade 11, Grade 12
Age Level
16, 17
Subject
Math
Technology Integration Activity
Discovering the Internet, Imaging, PowerPoint Presentations, Video Productions
Estimated Time of Completion
3 - 4 weeks
Author: Dorothy AuthenticatedPublicUser Last modified: 05/01/2010

An Introduction to Mathematical Modeling

Downloads for this lesson plan

Rubrics for grading (EXE, 15K)

Groupwork Rubric (EXE, 10K)

Introduction

Students will study the process involved in the mathematical modeling cycle.  They will understand the concepts of estimation and the value of significant digits and order of magnitude.  They will use simulations to estimate the outcomes of various types of events and/or problems with a particular focus on Fermi problems, curve fitting, and the recognition of the types and cumulative nature of errors that are inherent in mathematical models.  An introduction to the power of spreadsheet programs as a modeling tool will also be introduced.

Prerequisite Experience

Basic spreadsheet use

Basic internet skills

Use of Powerpoint or other presentation software

Teacher Prep Time

10 - 15 minutes per class to prepare administratively

Project

The final assessment of the unit which will be a creation of a model that will answer the following problem: A Category 5 hurricane is headed towards Hampton Roads.  The latest weather models project that it will make a direct hit the Eastern seaboard at the mouth of the Chesapeake Bay.  How many hours prior to projected land fall should the governor give the evacuation order in order to evacuate Hampton Roads?   Students will use a variety of tools, including Excel, the internet, and Powerpoint in the completion of this final assessment.  Findings will be presented to the group, and possibly to a panel of community leaders at a later date.

Assessment/Grading

Rubrics will be used to evaluate students work on their models. Additionally, weekly quizzes will be used to assess understanding of the vocabulary and principles of modeling.

Time Management Tips

Class Participation "grades" may help to keep students focused, as well as the Groupwork rubrics

I originally only planned for 2 blocks for the students to work on Presentation, but it actually took almost 3 and a half.

Lesson Plan Details

Engage

Students will be introduced to the modeling cycle by giving them the following question to solve in groups of 3 or 4:  “How many people in the world are picking their noses RIGHT NOW?”  Students will have to develop a strategy to answer this and other Fermi problems over the course of the next two weeks.

Explore

As students explore this, and other Fermi type problems, students will be asking themselves the following questions which will lead to the concepts they must know regarding the mathematical modeling cycle.·         What is the best approach to understanding the problem?·         What do I already know and how do I get “there” from here ? ·         What type of data is this?  Where do I go from here?·         Does my conclusion make sense and is it justifiable? ·         What will be the best way to represent my data and my findings?

Explain

As students work through solving these problems, we will discuss the process that they naturally go through such as identifying their assumptions and variables that are important in the problem, using resources (such as the internet) to get required information in order to construct their own solutions, constructing and using formulas to arrive at solutions, and recognizing sources of error and determining acceptable degrees of mathematical error in modeling.

Elaborate

Students will be required to present and defend their answers to the rest of the class. Presentations will range from extremely informal (at the beginning of the unit) towards more formal and professional as the unit continues. The fact that while there are no “right” answers, there are certainly WRONG answers will be stressed, as well as the idea that all answers must be mathematically justifiable and prove-able.

Evaluate

Rubrics will be used to evaluate students work on their models.  Additionally, weekly quizzes will be used to assess understanding of the vocabulary and principles of modeling.

Extend

Students will be introduced to using technology as a modeling tool, specifically Excel.  Students will be shown how a spreadsheet could be created to model both exponential and logistic growth models.  (Students will have explored both of these models in previous math classes, so the focus can be on the use of the software and its tools, including graphing and adjusting data.)   All of the above will lead to the final assessment of the unit which will be a creation of a model that will answer the following problem: A Category 5 hurricane is headed towards Hampton Roads.  The latest weather models project that it will make a direct hit the Eastern seaboard at the mouth of the Chesapeake Bay.  How many hours prior to projected land fall should the governor give the evacuation order in order to evacuate Hampton Roads?  Students will use a variety of tools, including Excel, the internet, and Powerpoint in the completion of this final assessment.  Findings will be presented to the group, and possibly to a panel of community leaders at a later date.