The Problem:
Search the web for data sets that might be represented by each of the following families of functions: linear, quadratic, exponential, and logarithmic. Create a web page where you briefly discuss and provide links to each of these sources. Then choose one of these data sources to explore further. Create (and provide a link to) an excel worksheet in which you show and discuss the data in at least three different forms (numeric, algebraic, and graphic). Explore and discuss ways that you could use this data with your students.
The Strategy:
We're going to do a lot of web surfing. Our best bets are probably government numbers, such as population stats, employment rates, and economic numbers. We could also try weather stats, such as temperature readings, rainfall readings, and daylight hours. We may also want to try prices of various products, such as gasoline, movie tickets, vehicles, or CDs. Sports data is probably a good bet as well, since sports people tend to keep stats on everything! If we're still stuck, we can always try searching for "data sets" and we'll probably get to a data library or some university's statistics department....
Exploration:
Logarithmic Data:
Click here for Data Source
These data are from the United States Swimming Web Site. Specifically, we're looking at the National Age Group Short
Course Record Times for the 50-yard and 100-yard Freestyle Swimming Events over time (as the age group increases).
I figured this would give me a nice logarithmic function, since I have experience with swimming and know that your
times improve quite a but when you're younger, but tend to level off when you get older. This makes for a nice negative
logarithmic function. You can see a graph of the data on this spread sheet.
Exponential Data:
Click here for Data Source
These data are from a US Governement Web Site and show the Consumer Price Index over time. Specifically, we're
going to look at the Average CPI over time. The CPI is related to the inflation rate, so I figured it would give a nice
exponential function. You can see a graph of the data on this spread sheet.
Linear Data:
Click here for Data Source
These data come from a Data Library at Oregon State and show some population stats for Gwinnett County, GA, which
is where I live. Specifically, we're going to look at the population of males, age 80-84, over a period from 1990 to 1996.
The data ended up being pretty linear, rather than exponential like I had expected.
You can see a graph of the data on this spread sheet.
Periodic Data:
Click here for Data Source
These data come from a World Climate Web Site and show the average temperature in Atlanta, GA, which is the large city nearest
where I live. Specifically, we're going to look at the average temperature, in Fahrenheit, by month, over the course of the year.
Typically, temperature tends to increase over the first portion of the year, top off around July or August, and decrease over the second
portion of the year. This would repeat each year, giving us a periodic function. You can see a graph of the data on this spread sheet.
Conclusions:
For an in-depth look at the Exponential Data Set, you can view this spread sheet. These data could be used quite effectively with students, regarding the discussion of functions which model real-world behavior. All four of these data sets contain data collected from a real-world situation which does, in fact, model a mathematical function. Making connections between mathematics and the real world is an important concept for students so that they see the relevance of mathematics in the world in which they live. Specifically, the data could be used to help students understand line (or curve) of best fit as well as linear, quadratic, exponential, and logarithmic correlation. This activity could easily be expanded to include other families of functions, including periodic and higher-degree polynomial.