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Now with all digital content in Macmillan Learning’s Achieve, For All Practical Purposes emphasizes the connections between contemporary mathematics and modern society. Long a foundational text in the development of the liberal arts mathematics course, its  distinctive style introduces students to real math applications without simply listing equations and asking students to crunch numbers—practice is geared toward understanding what these equations do and what they can reveal. For All Practical Purposes seeks to engage those students who tend to be wary or disinterested in math courses and to show them both the usefulness of these math concepts and the beauty of math as applied in the world around us.

Someone once said that there is no history, only memory. In order to set a historical context for this paper I need to take a trip down memory lane and talk about the beginning of the Mathematical Contest in Modeling (MCM)®. In late 1984, Ben Fusaro came to me with the idea for a modeling competition. I no longer remember the original formulation of the idea, but the basics were there: a team competition for undergraduates who would work on an open-ended problem for an extended period of time and be allowed to use any inanimate resources, assuming they were appropriately cited. In other words, you just couldn’t ask a non-team member how to solve the problem.

A mathematics trail is a walk to discover mathematics. A math trail can be almost anywhere—a neighborhood, a business district or shopping mall, a park, a zoo, a library, even a government building. A free downloadable guide from The Consortium for Mathematics and Its Applications reviews the history of math trails and discusses their attributes, including the practical issues of organization and logistics in setting up and maintaining a math trail. The guide also discusses the mathematical issues in choosing and describing math problems and tasks along a trail and describes a variety of examples. The math trail guide points to places where walkers can formulate, discuss, and solve interesting math problems. Math trails offer opportunities of making and using connections among mathematical ideas, recognizing and applying mathematics in contexts outside of math class, communicating mathematical thinking to others clearly, and analyzing and evaluating the mathematical thinking and strategies of others.