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Interdisciplinary Lively Application Projects (ILAPs)

Mathematical Association of America
Number of Pages: 

Teachers of mathematics have enjoyed a bonanza of exciting teaching techniques and resources over the last several years. Interdisciplinary Lively Application Projects (ILAPs) is a new book from the MAA, in the same "Classroom Resource Materials" series as Proofs Without Words, She Does Math! (recently reviewed in Read This! by Lynette I. Millett) and Learn from the Masters. It adds another resource to the marketplace of ideas.

There are so many good ideas and great resources that nobody can use all of them. A teacher has to pick and choose to find the ones that fit that teachers own style and curriculum, and also fit the students interests and abilities.

ILAPs are projects in applied mathematics designed to be done in small groups. This book contains eight such projects, followed by six short articles about how to use them in your classrooms. I tried one of them in class this semester, and was quite satisfied with the results. More about that later.

ILAPs arise from a consortium centered at the United States Military Academy. They lie naturally within a spectrum of teaching resources in applications of mathematics, about midway between the relatively structured, but richly diverse UMAP modules and the unstructured problems that appear on the annual MCM (Mathematical Contest in Modeling).

ILAPs present a fairly specific scenario, designing a deck, planning a hike, modeling air pollution, and pose some fairly specific questions that must be answered and issues that must be addressed. They are not as specific as UMAP modules, nor as broad as MCM questions. They are specific enough that any student should realize what the problem is and what has to be done, but general enough that a student can be somewhat creative.

My students worked on an ILAP titled "Decked Out", the problem of designing a deck for the Student Union building. It was one of the easier problems in the book, and required mathematics only up to college algebra and elementary geometry. The students were given some constraints and some costs and asked to design a deck that had three sections, a rectangle, a parallelogram and three quarters of a circle. They had to figure out how big the sections could be and still fit in the allowed area, figure out how much material would be required, and design an arrangement of picnic tables that would fit as many tables as possible. They were required to hand in a report that included:

  • A cover
  • A one page "executive" summary
  • Drawings of the site
  • A bill of materials

The authors estimate that a typical ILAP takes the group 6 to 10 hours to complete. These estimates seem reasonable. I gave my students about two and a half hours of class time to work on the project, and they seemed to more than match that time with work outside class. I was quite satisfied with the quality of their work, particularly the quality of their writing.

Other ILAPs in this book use calculus, differential equations and regression. There are only eight of them here, but there seem to be more on the way.

Some aspects of this book suffer problems from the production process. Diagrams that say they are drawn to a scale of 1"=20 are in fact drawn to a scale of 1"=35. A table of lumber costs that had once lined up nicely was garbled by wraparound when a margin was changed. Topographic maps in the backpacking problem also are scaled incorrectly. Moreover, those maps have been reduced too much to photocopy clearly. Students would not be able to use them effectively in their reports.

The six short articles at the end of the book give some guidance on how to use ILAPs, and how to prepare more of them. Design and testing an ILAP seems to be a big project.

One of those articles, "Technical Report Format and Writing Guide", by Kent Miller, only four pages long, is a real gem. It is a clear, concise description of how to write up a report. Anyone can be a technical writer, just by following these instructions.

You can learn more about ILAPs in one of the MAA Minicourses in Baltimore, "Interdisciplinary Lively Applications Projects."

 Ed Sandifer ( is an avid runner, professor of mathematics at Western Connecticut State University and Contributed Papers Coordinator for the North East Section of

Date Received: 
Friday, June 6, 1997
Include In BLL Rating: 
David C. Arney, editor
Classroom Resource Materials
Publication Date: 
Ed Sandifer
Publish Book: 
Modify Date: 
Friday, November 9, 2007