Ohio Resource Center
Lessons
National Debt and Wars
Discipline
Mathematics
9, 10, 11, 12
Professional Commentary
Students collect information about the national debt, plot the data by decade, and determine whether an exponential curve is a good fit for the data. Then student groups determine and compare common traits and differences in changes in the national debt during three war eras: the Civil War, World War I, and World War II. The lesson uses graphing calculators to interpret the data, but spreadsheets can also be used. Activity sheets, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included. (author/sw)

Common Core State Standards for Mathematics
High School - Functions
Construct and compare linear, quadratic, and exponential models and solve problems
HSF-LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
1. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
2. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
3. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (8–10)
G.
Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.
6.
Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
B.
Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.
J.
Describe and interpret rates of change from graphical and numerical data.
Benchmarks (11–12)
A.
Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
3.
Identify functions as linear or nonlinear based on information given in a table, graph or equation.
16.
Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern.
5.
Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.
10.
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
Principles and Standards for School Mathematics
Algebra Standard
Understand patterns, relations, and functions
Expectations (6–8)
identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
Expectations (9–12)
analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;
Analyze change in various contexts
Expectations (6–8)
identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
Expectations (9–12)
analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;
approximate and interpret rates of change from graphical and numerical data.