Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students discover the algorithm for solving linear programming problems and gain conceptual understanding through a real-world problem and graphing calculator applications. A 12-page activity packet, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included.... 2 Movement With Functions 3: Road Rage Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds to the cars crashing.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students use algebra or geometry software to discover that the height at which guy wires supporting two vertical poles cross does not depend on how far apart the poles are. This counterintuitive result can lead to conjecturing and testing hypotheses as to what factors determine the height at which the wires cross.... 4 The Busing Problem: Linear Programming Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: Students solve two linear programming problems. The first one, Researching Research Papers, involves three variables; the second, The Busing Problem, involves four variables.... 5 Meadows or Malls?: Using Matrices to Solve Systems Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: 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.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–11 Professional Commentary: This activity focuses on having students create and solve systems of linear equations in real-world settings. By solving a system of two equations in two unknowns, students find the equilibrium point for supply and demand.... 7 Jurassic Oil: Fuel Blending Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students are asked to minimize cost while maintaining certain criteria in the blending of two distinct types of gasoline. Students use the graph of a system of linear inequalities to solve this linear programming problem geometrically.... 8 Cutting Times: Trimming Losses Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students are asked to minimize waste for a local newspaper, which must cut 48-inch rolls of paper into 25- and 21-inch rolls. Students use the graph of a system of linear inequalities to solve this linear programming problem geometrically.... 9 High Step Shoes: Product Mix Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students are asked to maximize profits for an athletic shoe company that produces two kinds of shoes. This is the kind of product-mix problem that occurs whenever a company produces more than one item.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students are asked to minimize the labor costs of hiring different numbers of workers for different shifts at different hourly wages in a pizza shop. Students use the graph of a system of linear inequalities to solve this linear programming problem geometrically.... |