__Cover Letter__

The central problem in this unit is Baker's Choice. Bakers wanted to know how many plain and how many iced cookies they should make to earn the maximum profit. There are constraints on the amount of cookie dough, icing, oven space, and preparation time. One mathematical skill needed to solve this problem is interpreting word problems. Students must be able to understand the constraints described in the problem before they can write inequalities to represent them. They get practice with this skill in the first homework assignment and first POW ( A Simpler Cookie and The Broken Eggs). Also in order for student so be able to write equations necessary to solve the Baker's Choice linear programming problem they must be familiar with defining variables. The second homework assignment High School Numbers allows them to practice using variables that have been defined to write and solve algebraic expressions. Next students receive practice working with inequalities in a classwork assignment. Since students must write and graph inequalities, this activity is crucial to them understanding the central problem. Students also practice working with inequalities in Picturing Cookies and Inequality Stories. In Picturing Cookies Part I, students graph inequalities that they have written based on given constraints. Next student complete Picturing Cookies Part II where they build upon what they learned about graphing inequalities in Part I to graph multiple inequalities on the same plane. This is how the feasible region is created in the Baker's Choice problem.

Once students understand how to define variables, write equations and inequalities, and construct a feasible region by graphing inequalities they are ready to attempt linear programming problems. Each subsequent linear programming problem, beginning with Profitable Pictures, is a bit more challenging than the previous one. As the weeks progress, the problems contain more constraints and fewer to no hints or outlines of steps to help them solve the problem. Students must use what they have learned from working on and reflecting up previous problems. Finally, students solve the Baker's Choice problem, which is the most difficult of all the linear programming problems in the unit. However, students have gradually been given the mathematical skills required to solve this problem.

Once students understand how to define variables, write equations and inequalities, and construct a feasible region by graphing inequalities they are ready to attempt linear programming problems. Each subsequent linear programming problem, beginning with Profitable Pictures, is a bit more challenging than the previous one. As the weeks progress, the problems contain more constraints and fewer to no hints or outlines of steps to help them solve the problem. Students must use what they have learned from working on and reflecting up previous problems. Finally, students solve the Baker's Choice problem, which is the most difficult of all the linear programming problems in the unit. However, students have gradually been given the mathematical skills required to solve this problem.