Ohio Resource Center
Lessons
Pizza Pi: Work Force
Discipline
Mathematics
9, 10, 11, 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. Activity sheets guide students step by step through the basic process. Homework problems, extension problems, and problem solutions are included. Teacher materials are available only through Key Curriculum Press, but the essence of the lesson is incorporated in the student activity sheets. (sw/js)

Common Core State Standards for Mathematics
High School - Algebra
Reasoning with Equations and Inequalities
Represent and solve equations and inequalities graphically
HSA-REI.D.12
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
D.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
F.
Solve and graph linear equations and inequalities.
H.
Solve systems of linear equations involving two variables graphically and symbolically.
4.
Extend the uses of variables to include covariants where y depends on x.
6.
Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems.
7.
Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.
9.
Solve linear equations and inequalities graphically, symbolically and using technology.
3.
Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.
6.
Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.
6.
Solve equations and inequalities having rational expressions as coefficients and solutions.
7.
Solve systems of linear inequalities.
10.
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
11.
Solve real-world problems that can be modeled, using systems of linear equations and inequalities.
9.
Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution).
Mathematical Processes Standard
Benchmarks (8–10)
B.
Apply mathematical knowledge and skills routinely in other content areas and practical situations.
F.
Use precise mathematical language and notations to represent problem situations and mathematical ideas.
Benchmarks (11–12)
J.
Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation.
Principles and Standards for School Mathematics
Algebra Standard
Represent and analyze mathematical situations and structures using algebraic symbols
Expectations (6–8)
explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;
Expectations (9–12)
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases;
use symbolic algebra to represent and explain mathematical relationships;
Use mathematical models to represent and understand quantitative relationships
Expectations (6–8)
explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;
model and solve contextualized problems using various representations, such as graphs, tables, and equations.
Expectations (9–12)
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases;
use symbolic algebra to represent and explain mathematical relationships;
identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts;
draw reasonable conclusions about a situation being modeled.
Connections Standard
Recognize and apply mathematics in contexts outside of mathematics
Representation Standard
Use representations to model and interpret physical, social, and mathematical phenomena