Discipline: Mathematics

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....

Discipline: Mathematics

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....

Discipline: Mathematics

Professional Commentary: This site shows how to represent rotations, reflections, expansions, compressions, and shears using standard matrices. An applet allows students to explore the connection between entries in the matrix and the effect of the transformation geometrically....

Discipline: Mathematics

Professional Commentary: This tutorial reviews some of the basic definitions relative to matrices, such as trace, transpose, identity matrix, and inverse of an invertible matrix. Elementary algebraic operations on matrices are also reviewed, including sum, difference, scalar multiple, product, and determinant....

Discipline: Mathematics

Professional Commentary: This site illustrates in general, and then with detailed examples, how to solve a system of equations using Gaussian elimination. Applying elementary row operations to the augmented matrix for the system of equations, the student can reduce the matrix to row-echelon form, from which the solution of the system, or the nonexistence of a solution, can...

Discipline: Mathematics

Professional Commentary: This lesson on cryptology from the National Security Agency, "America's Codemakers and Codebreakers," is accessible to a wide range of students. The 34-page lesson material begins with a discussion of shift transformations and letter frequencies, techniques of code analysis that middle school students can easily understand and enjoy....

Discipline: Mathematics

Professional Commentary: Students read an antifreeze chart to determine the necessary mix of antifreeze and water for protection against various temperatures. Students then numerically analyze a particular cooling system to determine how much fluid to drain and replace with antifreeze to get the desired percentage concentration of antifreeze....

Discipline: Mathematics

Professional Commentary: Land has been donated to River City. Students must decide how to split the land use between development and recreation in a way that will minimize the cost to the city of the necessary improvements, while adhering to restrictions agreed on by the River City Council....