Mathematics: Modeling Our World (MMOW) Course 3

The Mathematics: Modeling Our World curriculum is founded on the principle that mathematics is a necessary tool for understanding the physical and social worlds in which we live. This is not the same as saying that mathematics can be applied. Rather, important questions about the “real world” come first and serve to motivate the development of the mathematics. Thus the contextual questions “drive” the mathematics.

Mathematics: Modeling Our World derives mathematical concepts from real-life situations rather than illustrating skills, after the fact, with examples. As students discover a variety of ways to solve a problem, they not only learn mathematics and content in other curriculum areas but they also learn how to organize and analyze data, make predictions, prepare and present reports, and revise their predictions based on new information.

In the first Chapter, The Geometry of Art, students work within the context of the world of art as they use mathematics to create and analyze perspective representations of three-dimensional objects. Four basic elements of perspective drawing are examined: overlapping, diminution, convergence, and foreshortening.

In Chapter 2, Fairness & Apportionment, students explore fairness while trying to solve the problem of dividing an estate fairly among heirs when an estate contains objects that cannot be sold. Another real-life problem involves trying to allocate a limited number of computers among several schools. Students are also introduced to several existing methods of apportionment of the Chaptered States House of Representatives. They are asked to analyze those methods for strengths and weaknesses and challenged to suggest their own algorithms for fair allocation along with mathematical measures of fairness for testing them.

The two main real-life situations providing the context for Chapter 3, Sampling, are analysis of public opinion and the estimation of wildlife populations. As part of the work of the Chapter, students conduct their own public opinion poll, write the poll questionnaire, select a sampling design, administer their survey, compile the data, analyze the results, and write a report.

In Chapter 4, Mind Your Own Business, students are faced with the challenges and dilemmas involved in the management of a small manufacturing business. They use mathematics to answer many pressing questions that real businesses face including: How are price and sales related? Which price will maximize profits? What happens when a business must conform to a relatively fixed market price? How does a small business decide whether expansion is feasible and will be profitable?

Chapter 5, Oscillation, is multi-contextual with four major contexts that dictate the mathematics covered: amusement rides (ferris wheels and carousels); planetary motion (seasonal changes in temperature and daylight due to the earth’s motion, as well as the changes in the moon’s appearance due to its motion about the earth); sound (music); and seasonal power usage (the periodic nature of electrical usage).

Chapter 6, Feedback, models several different situations from various contexts. In each situation the underlying structure is that of interacting quantities, though that is not always immediately obvious. The Chapter progresses from the analysis of sales data for a new product, to examining the spread of jokes and diseases, to the modeling of interacting species.

In Chapter 7, Modeling Your World, students first work within the context of modeling projects created by other students. After critiquing those models, they apply what they have learned to modeling projects of their own choosing set in contexts of particular interest to them.

 Chapter 1 The Geometry of Art LESSON ONE Keep It In Perspective LESSON TWO Drawn to Scale LESSON THREE Vanishing Point LESSON FOUR The Right Space LESSON FIVE The View From the Edge LESSON SIX Foreshortening Chapter Summary
 Chapter 2 Fairness & Apportionment LESSON ONE Heir Today, Gone Tomorrow LESSON TWO More Estate Division LESSON THREE Apportionment: The Unfairness of Fairness LESSON FOUR Other Methods LESSON FIVE Measuring Unfairness Chapter Summary
 Chapter 3 Sampling LESSON ONE It’s All in the Question LESSON TWO Experience Counts LESSON THREE Say It With Confidence! LESSON FOUR Selective Service LESSON FIVE The Results Are In! LESSON SIX Tag, You’re It! Chapter Summary
 Chapter 4 Mind Your Own Business LESSON ONE So, You Want to Be in Business LESSON TWO Who’s Minding the Store(room)? LESSON THREE Changing Assumptions LESSON FOUR Slow Growth Chapter Summary
 Chapter 5 Oscillation LESSON ONE Life’s Ups and Downs LESSON TWO A Sine of the Times LESSON THREE Connections LESSON FOUR Fade Out LESSON FIVE Now We’re Cookin’ Chapter Summary
 Chapter 6 Feedback LESSON ONE What Lies Ahead LESSON TWO Another Model LESSON THREE It’s Going Around LESSON FOUR An Ecological PushMe-PullYou Chapter Summary
 Chapter 7 Modeling Your World LESSON ONE The Modeling Process LESSON TWO Analyzing Mathematical Models LESSON THREE Modeling Our World LESSON FOUR Creating Your Model Chapter Summary

Course 3 of the Mathematics: Modeling Our World (MMOW) curriculum offers additional resources to supplement the text:

Teacher's Edition CD-ROM

The embedded teacher materials are designated by two kinds of icons that are also color-coded.

A note icon opens a popup window when the cursor moves over it. Whether the entire note fits in the popup depends on the individual settings.

There are two types of notes embedded in the teachers files:

Yellow teaching notes that are relatively short and contain no figures or equations.

Short answer sets that contain no figures or equations. Usually these are answers for discussion/reflection questions or short activities.

The second type of icon is a pin that indicates an attachment. The attachment opens in a second window when the icon is doubled-clicked.

There are three types of attachments embedded in the teachers files:

Yellow teaching notes that contain figures or equations.

Answer sets for most activities and individual work exercises.

Support materials: assessment problems, handouts, transparencies, and supplemental activities.

Calculator and computer software

Calculator and computer software written specifically for Mathematics: Modeling Our World (MMOW). With software programs for each allows students to explore real-world themes with the same tools used by scientists, technicians, and business people. The software includes graphing calculator programs, specialty computers, spreadsheet template, data sets, and geometric drawing utility sketches.

DVD Video

Video segments accompany each and are used to motivate students as they begin a , or to provide additional information for a specific problem.

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