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.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: As a culminating activity to instruction in functions, linear equations, and proportional reasoning, students are introduced to the mathematics of bicycles. Students pair up to investigate bicycle-related relationships, such as wheel diameter and coasting distance or frame tubing size and weight allowances.... 3 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.... 4 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.... 5 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.... 6 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.... 7 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.... 9 A Distant View: Exploring the Principles of Telescope Optics Resource Type: Lessons Grades: Grades 8–12 Professional Commentary: Students see real-life applications of rational functions and the Pythagorean Theorem, as they investigate the essential concepts of how lenses work to magnify vision, and then build simple telescopes to demonstrate their understanding. Discussion questions, suggestions for assessment, additional activities, interdisciplinary connections, and Internet extensions are included in the lesson plan.... 10 NAEP Assessment Item, Grade 12: Solve a quadratic inequality Resource Type: Assessments Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: Students are asked to solve a quadratic inequality. This multiple-choice question is a "hard" test item used in grade 12 in the 2005 National Assessment of Educational Progress (see About NAEP).... |