Problem-Based Mathematics—Not Just for the College-Bound
Mathematics is far more interesting to students when they get to do some real thinking. That is one of the premises of the Interactive Mathematics Program.
Picture this: You're on a planning team, consulting to the city manager. Your task is to come up with a reasonable plan for the use of 550 acres of land recently obtained by the city. The acreage includes a recently closed army base, a 300-acre farm, and abandoned mining land.
Two conflicting parties are interested in the property. The business community is pushing for development schemes, while environmental groups are advocating for recreational space. The two factions have arrived at a partial compromise, which is what you have to work with. They have agreed that
a maximum of 200 acres from the army base and the mining land will be used for recreation, and
the amount of army land used for recreation plus the amount of farm land used for development will together total 100 acres.
Not only are you dealing with opposing factions, but with improvement costs ranging from $50 to $2,000 per acre, depending on which parcel of land is involved and how it will be used. You have to satisfy everyone while minimizing the total cost for improvements. To arrive at a reasonable allocation plan will demand careful analysis and attention to detail.
If you were 16 and in a traditional high school math class, you would be enrolled in Algebra II, perhaps doing one system of linear equations after another.
Instead, it's a whole new ball game. Your task is to solve the city's planning problem. This isn't an extra credit assignment. It's a unit called Meadows or Malls? You're going to be working on it for the next six to eight weeks, learning and using algebra, geometry, and matrix operations.
Don't expect to spend your time memorizing facts. There will be no pop quizzes, and no columns of figures to work on and turn in when the bell rings.
Do expect to be working both in a group and on your own. You'll be dealing with numbers and doing matrix operations on a sophisticated calculator. You'll also be working with words—writing and explaining to the rest of the class how your group arrived at its solution to the problem.
Welcome to Year 3 of the Interactive Mathematics Program, also known as IMP.
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