### Linear Inequalities and Linear Programming

Saul Gass (1970). An Illustrated Guide to Linear Programming. Published by McGraw-Hill, New York.

The Interactive Mathematics Program Year 2 text includes a complete unit on linear programming entitled Cookies, pp. 301–375. One particularly useful section within this unit occurs on days 22–27 of the suggested schedule. Here students are led through the process of creating their own linear programming problems.

The Interactive Mathematics Program is an NSF-funded curriculum. For ordering information, see It's About Time: http://mathimp.org/curriculum/index.html

### Solving Systems of Equations

At the Insights for Algebra 1 Web site, the lesson entitled “Left Hand, Right Hand” offers an interesting activity that asks students to collect data on the time it takes them to write letters first using their right hand and later their left hand. Students then enter their data into TI graphing calculators and find lines of best fit for each set of data. In groups, students discuss their results and determine the meaning of intersection points between their lines. They then consider the three scenarios for solving systems of equations with respect to the activity—when there is one solution and the two lines intersect at a point, when the two lines are parallel, and when two lines coincide. (In this activity, if the two lines coincide, then the student is ambidextrous!) This lesson plan can be found at: www.learner.org/channel/workshops/algebra/workshop3/lessonplan1b.html

ExploreLearning has created a Gizmo™ with an accompanying activity that models a cat and mouse race. The speed that each travels (slope) as well each animal’s starting point (y-intercept) are specified and the user simulates the race to determine whether the cat catches the mouse (the point of intersection). Students can change parameters (such as speed and starting point) to gain a clear understanding of the situation and the mathematical model. ExploreLearning Gizmos™ can be accessed at www.explorelearning.com. This particular activity is found at www.explorelearning.com/index.cfm?method=cResource.dspExpGuide&ResourceID=108.

“Illuminating Elimination”: www.pbs.org/mathline

COMAP/HistoMAP, Module 20: Optimality Pays: An Introduction to Linear Programming, by Jeganathan Sriskandarajah. Published by COMAP, Inc., 1992.