What a powerful question! And it's one commonly posed to math teachers all over the world. Need help with an answer? Here are a few to consider.
Suppose you're asked the question about a piecewise function. Let's start with the standard definition: "a combination of two or more functions, each represented by different intervals within the domain." That may sound a bit obscure to the average high school student, but what if you put it into perspective? The IRS tax bracket can be modeled by a piecewise function. Each function is determined by the amount of tax owed, and the domain is represented by the taxable income intervals. Help students learn more with the Piecewise-Defined Functions Lesson and discover how the IRS tax bracket can be written using these functions.
Speaking of the IRS, did you know that it uses the Consumer Price Index (CPI) to adjust income thresholds, deduction amounts, and credit values? The CPI represents the percent change (per month) in prices paid by urban consumers for goods and services. Using the Consumer Price Index Data, students can analyze and compare the indexes for each month between 2003 and 2015. Need more data? Data Depot gives students access to 180+ real-world data sets.
Many real-world situations can be modeled by exponential growth or decay. For example, the spread of disease can be modeled by exponential growth. Our lesson on The AIDS Epidemic: Analyzing the Data lets students graph exponential functions and (as the title asserts!) analyze data. Students first review the history of the acquired immune deficiency syndrome (AIDS) and examine the number of reported cases in the U.S. from 1982 to 1996. With that background, they investigate whether splitting the time frame of a data set affects the accuracy of data interpretation. How? By plotting the data, determining the exponential model that best fits that data, and calculating the rate at which the disease spread.
Got six minutes to discuss quadratic functions? Real-World Examples of Quadratic Functions is an audio tutorial that answers this question: “When are quadratic functions used in the real world?” The tutorial can spark whole-class discussions, or students can use it individually. Students first review the basics of quadratic functions and their graphs. They then use quadratic functions to maximize the area of a garden, using a specific number of tiles, to determine the whether a ball will make it over the left field wall (the Green Monster) at Boston's Fenway Park and also to determine whether a meteorite created a crater. The tutorial concludes with a short quiz to check students’ knowledge.