Ohio Resource Center
Lessons
Discipline
Mathematics
10, 11, 12
Professional Commentary

Students narrow their choice of college by following a process used to determine locations of airports, power plants, and medical facilities. Multi-Attribute Utility Theory is a structured methodology that handles tradeoffs among multiple and often competing objectives. Students identify key variables, create measures of the variables, collect data on the measures, scale the data, estimate weights for the variables, and compute a weighted sum. Activity sheets guide students step by step through the process. Also included are extension activities, homework problems, complete solutions to activities and problems, and a video discussing the value of the mathematical ideas. 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
Standards for Mathematical Practice
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP2
Reason abstractly and quantitatively.
CCSS.Math.Practice.MP4
Model with mathematics.
High School - Number and Quantity
Quantities
Reason quantitatively and use units to solve problems.
HSN-Q.A.1
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
HSN-Q.A.2
Define appropriate quantities for the purpose of descriptive modeling.
Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (11–12)
D.
Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases.
9.
Use vector addition and scalar multiplication to solve problems.
Measurement Standard
Benchmarks (11–12)
B.
Apply various measurement scales to describe phenomena and solve problems.
Data Analysis and Probability Standard
Benchmarks (11–12)
A.
Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators.
D.
Connect statistical techniques to applications in workplace and consumer situations.
11.
Examine statements and decisions involving risk; e.g., insurance rates and medical decisions.
2.
Transform bivariate data so it can be modeled by a function; e.g., use logarithms to allow nonlinear relationship to be modeled by linear function.
Mathematical Processes Standard
Benchmarks (11–12)
C.
Assess the adequacy and reliability of information available to solve a problem.
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
Number and Operations Standard
Compute fluently and make reasonable estimates
Expectations (9–12)
develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
Measurement Standard
Understand measurable attributes of objects and the units, systems, and processes of measurement
Expectations (9–12)
make decisions about units and scales that are appropriate for problem situations involving measurement.
Data Analysis and Probability Standard
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Expectations (9–12)
understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable;
Problem Solving Standard
Solve problems that arise in mathematics and in other contexts
Connections Standard
Recognize and apply mathematics in contexts outside of mathematics