Students use matrices and technology to solve the Meadows or Malls problem, a linear programming problem with six variables. Students who have not done linear programming problems before are advised to begin with The Busing Problem before attempting Meadows or Malls. In Meadows or Malls, students begin by reviewing homework problems in which they relate the solvability of a system of linear equations to the invertibility of the coefficient matrix. The students use graphing calculators to solve linear systems. The final activity of the lesson involves reviewing all of the equations and constraints of the Meadows or Malls problem, refining those considerations, using the graphing calculator to solve the linear systems involving six equations and six variables, and then testing those solutions in the cost equation to determine the best division of land use for the city. The lesson plan includes ideas for assessment, teacher discussion, extensions, additional resources, and a discussion of the mathematical content. The user should first locate the lesson and then access the appropriate video clips illustrating lesson procedures. (author/pk)

This higher order problem context makes use of a common community issue that can easily be adapted to the career-technical situation. It is an ideal candidate for a joint mathematics and career-technical unit that develops concepts for both Agricultural and Environmental Systems and Industrial and Engineering Systems. The basic problem can easily be adapted by teachers familiar with linear mathematical concepts to apply to manufacturing and other situations. Teachers should not allow the complexity of the stated context prevent their use of this unit. The problem can be simplified or developed and presented in such a way that students with any number of different abilities and backgrounds can tackle it. It is an ideal unit for demonstrating the power of mathematics in a problem solving arena. Download the full lesson plan, which includes the complete procedure and materials for duplication.