Mathematics: Modeling Our World (MMOW) Course 2

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.

For example, in the first chapter, Gridville, students are challenged to find the optimum placement for a fire station. This leads to development of the absolutevalue function and a new kind of geometry. Throughout the , the role of mathematics and the role of commy values are considered together in the search for the “best” location.

In Chapter 2, Strategies, students learn about game theory as they solve problems in the contexts of a wide range of situations—including the strategies needed to win a simple matching game, the international political strategy involved in the Cuban Missile Crisis of 1962, and the economic strategies employed by everyday business competitors and investors.

In Chapter 3, Hidden Connections, students are immersed in finding optimal solutions to such real-life problems as finding the most economical way to plan a trip, the fewest time slots needed for meetings or activities, and a stable way of matching partners. All these settings lead to a common descriptive structure, a new kind of graph, which turns out to be geometric rather than algebraic.

Chapter 4, The Right Stuff, challenges students to define “efficiency” as they examine ways to package soft drink cans with the goal of optimizing either the use of package space or packaging material. They then move on to apply their skills to the problem of designing a package to hold melons of more than one size. These problems lead to the development of many ideas in the study of Euclidean geometry.

In Chapter 5, Proximity, students are challenged with several engaging contextual problems: estimating rainfall in the state of Colorado, estimating the volume of water in a lake, drawing school attendance boundary lines, choosing a location for a restaurant, and locating archaeological dig sites. Again, the mathematical result is the development of geometric concepts.

In Chapter 6, Growth, students work within such real-life contexts as deciding on appropriate limits on home construction, tracking the accumulation of money in a savings account, determining the proper dose of a medicine, monitoring available space in existing landfills, and developing the mathematics of sequences and series.

In Chapter 7, Motion, the study of motion evolves from understanding some of the mathematics involved in planning successful car and motorcycle stunt jumps. As they use motion detectors to collect distanceversus- time data on moving objects, including themselves, students model four different stunts during the : two near-collision stunts, one intentional “collision,” and a ramp-to-ramp jump. Out of these experiments and designs comes an in-depth understanding of quadratic functions and their properties.

English, speech, international policy, history, environmental science, family and consumer sciences, economics, medicine, and a host of other content areas are brought into the mathematics classroom as various issues and problems are solved by students in the context of real-world experiences.

 Chapter 1 Gridville LESSON ONE In Case of Fire LESSON TWO Linear Village LESSON THREE Absolute Value LESSON FOUR Minimax Village LESSON FIVE Return to Gridville Summary
 Chapter 2 Strategies LESSON ONE Decisions LESSON TWO Changing Your Strategy LESSON THREE Changing the Payoffs LESSON FOUR Optimal Strategies LESSON FIVE Optimal Strategies Revisited LESSON SIX Games That Are Not Zero Sum Summary
 Chapter 3 Hidden Connections LESSON ONE Connections LESSON TWO Procedures LESSON THREE Minimum Spanning Tree Algorithms LESSON FOUR Coloring to Avoid Conflicts LESSON FIVE Traveling Salesperson Problems LESSON SIX Matching Summary
 Chapter 4 The Right Stuff LESSON TWO Designing a Package LESSON THREE Technological Solutions LESSON FOUR Getting the Facts LESSON FIVE Packaging Spheres Summary
 Chapter 5 Proximity LESSON TWO Neighborhoods LESSON THREE Rainfall LESSON FOUR A Method of a Different Color LESSON FIVE Digging for Answers Summary
 Chapter 6 Growth LESSON ONE Growing Concerns LESSON TWO Double Trouble LESSON THREE Finding Time LESSON FOUR Sum Kind of Growth LESSON FIVE Mixed Growth Summary
 Chapter 7 Motion LESSON TWO Falling in Line LESSON THREE It Feels Like Fall LESSON FOUR What Goes Up Must Come Down LESSON FIVE The Grand Finale Summary

Course 2 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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