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Exploring Data

Lessons on the Web

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High School Lesson Plans on the Web

Acid Rain Simulation - Louie Beuschlein
A two-day unit plan that incorporates some decision-making ideas from statistics into the science classroom. No previous experience with statistical analysis is required. The NCTM Statistics Standard is taken into account in this lesson by having students make use of sampling to back up a claim and by having students design (with teacher assistance) a statistical experiment to study a problem.

The "Birthday Problem," An Introduction to Mathematica - Louie Beuschlein
This AP Statistics unit introduces students to Mathematica and to the Monte Carlo method of solving probability problems. Using Mathematica's random-number-generating capability along with its ability to work with lists, students can use the computer to simulate the birthdays of any number of people and find approximate but reliable solutions to the "Birthday Problem."

Buffon's Needle - An Analysis and Simulation - George Reese
Buffon's Needle involves dropping a needle on a lined sheet of paper and determining the probability of the needle crossing one of the lines on the page. The probability is directly related to the value of pi. Reese presents an analytical solution to the problem along with a program written for Macintosh computers for simulating the needle drop in the simplest case scenario in which the length of the needle is the same as the distance between the lines.

The Cereal Box Problem - A Lesson in Expected Value - George Reese
FREE INSIDE! Collect all six!! How many cereal boxes would you expect to buy to get all the prizes? includes an online simulation.

Chi-Square - Amar Patel
An amusing lesson about statistics, in particular the chi-square statistic. The material in this lesson helps students to understand statistical terms such as expectation, significance, and chi-square. Requires Excel.

Data Analysis Project: Honors Functions, Trigonometry, and Statistics
A computer project by students at the Kent School. Based on UCSMP's Functions, Trigonometry and Statistics, the purpose was to learn how to do a statistical analysis and communicate the results. Students found information and data on the Internet, and results include background information, uni- and bi-variate data presentation and analysis, and conclusions. See NBA Draft Picks, German Traffic Safety, and Ice Cream Consumption.

Descriptive Statistics - Introduction (Central Tendency, Variation) - Jay Hill
This branch of statistics lays the foundation for all statistical knowledge, but it is not something that you should learn simply so you can use it in the distant future. Descriptive statistics can be used NOW, in English class, in physics class, in history, at the football stadium, in the grocery store.

Descriptive Statistics - Introduction (Mode, Median, Mean, Range) - Chris Povich
A lesson plan that uses Jay Hill's Introduction to Descriptive Statistics to aid in understanding and applying measures of central tendency, variability, and correlation.

Distribution Curves - Anne McCall
This lesson examines the properties and calculations associated with a distribution curve, which is basically the shape of a data set when displayed on a histogram. Although it focuses on Normal distribution curves, it is important to be familiar with the shapes of all three major types of distribution curves.

Earthquakes - John Meseke
Students graph earthquake data and use the information for decision making. This lesson uses the data set of the number of earthquakes from 1900 to 1989 with a magnitude of 7 or greater.

Exponential Fit: Running to Conclusions - Ed Malczewski
This lesson explores the process of finding the best fitting exponential curve to sets of data. It requires Internet access, a bag of Skittles, and Microsoft Excel.

Gender Issues through Chi-square Experiments - Chris Povich
Your group has been created as an investigating committee for the local school board, which has been discussing gender issues within mathematics and society. You have been appointed to observe three teachers teaching in the district to see if there exists any bias towards calling on one gender more than another... Each group is responsible for creating a paper on their findings, and students are responsible for explaining their Chi-square test, calculations, and conclusions.

Graphs and Stories - Malcolm Swan, The Language of Graphs
"Most students leave school knowing how to plot a graph from a table of numerical values, but far fewer are competent at interpreting graphs. But in the real world interpretation is more important than plotting. This WWW page is about graph interpretation - the skill of putting a story to a graph. "

Guessing Correlations - John Marden
You see four scatter plots and four correlation coefficients. Your task is to match them up.

Hare and Tortoise Game - Chris Povich
Each turn consists of three moves. The player rolls a die a total of three times per turn; after each roll, the player's marker is moved one place to the left if the number on the die is odd and one place to the right if it is even. Students calculate probabilities of landing on different positions, and use Resampling Stats software to write a program that will model the hare/tortoise game.

The Hermit's Epidemic - Jay Hill
Expected value has very practical applications. Despite the somewhat unrealistic nature of the Hermit Problem, it can show how expected value can be used in the study of infectious diseases. This project tracks the spread of a disease on a desert island with hermits on it. It uses the internet, a computer program (written in Future Basic), and other student activities to explore the concept of expected value (i.e. How many hermits do we expect to get the disease?).

Houston Area Real-Time Traffic Report - Susan Boone
Students calculated the time needed to travel a distance given the rate of speed; data were collected using "real-time" traffic maps of the greater Houston area and over a period of one week, one month, and one school year, traffic patterns were studied at various times of the day. At the completion of the study students wrote a report and sent their results via email.

INDY 500 - Susan Boone
Students research information via the Internet to find the mean and median speed for the Indianapolis 500. Rates per lap are calculated, as well as the length of each lap.

Linear Regression - Amar Patel
Crickets move their wings faster in warm temperatures than in cold temperatures. Therefore, by listening to the pitch of their chirps, it is possible to tell the temperature of the air. A table gives the recorded pitch (in vibrations per second) of a cricket chirping recorded at 15 different temperatures - what if someone asked you what the temperature was, but you couldn't use a thermometer? Could you use the crickets? This lesson explores notions of relations between two variables, with many problems and activities to aid learning and classroom discussion.

M&M - Chris Povich
"M&M's" Plain Chocolate Candies come in six colors: blue, brown, green, orange, red, and yellow. Predict which color of "M&M's" will occur most in the bag. Why did you predict these colors? A lesson that addresses probability through M&M's and the graphing calculator.

For M&M data, see the History/FAQ from "M&M's" Studios.

Min-Max Temperatures - John Meseke
Students use the predicted minimum and maximum temperatures for various cities throughout the U.S. to calculate averages.

Pop Clock - Susan Boone
Data collection, problem solving, research skills, and interpolation of data. Students review the Census Bureau's home page on the Internet and gather data regarding trends in population. They study these data and make predictions on future populations, comparing their results with the information available on the Internet.

The Probable Pen in the Cereal Box - Michael Cornell
How many boxes of cereal do you have to buy until you have received six pens of different colors? A cooperative classroom project during which participants calculated the expected value of a simple probability problem via experimentation.

Standard Deviation, Part 1 - Barbara Christopher
Students will use the Internet to find statistical data for investigations that use the mean, standard deviation, and percentage error; calculate the standard deviation of monthly temperature means; and draw conclusions from the standard deviations and percentage error of these means.

Standard Deviation, Part 2 - Barbara Christopher
A followup to Standard Deviation, Part 1. Students will use the Internet to gather temperature data from 3 cities; calculate the standard deviation and percentage error of the gathered temperatures; and prove or disprove a hypothesis on the basis of these statistics.

Temperature of a Point on a 2-D Plate - Ed Malczewski
A problem that arises often in physics and engineering is to find the temperature at any point on a two-dimensional object which is held at a constant temperature at each edge. In this lesson students find the temperature using statistical methods. The lesson includes a program that will run on Resampling Stats, and a graphical Macintosh application program simulating the random walk.

Variance and Covariance -Ed Malczewski
How Much Money Do Baseball Players Really Make? Are the salaries of the majority of baseball players consistent with the public belief that they make too much money? Variance, a measure of the spread of data, can help us answer this question.

Weather Plots - John Meseke
Looking at graphs of temperature and humidity, students determine that the two graphs are inversely proportional. The data set consists of two curves of the flow of the temperature and the percent humidity for seven days at Boulder, Colorado. It can be used by having students look at the relation between temperature and humidity, studying the two curves, and formulating a relation between them.

What's the City Mileage of a Typical American Car? - Ed Malczewski
Students analyze the data and find an average for the mileages of American cars, exploring the bootstrap method of analysis. An Excel tutorial is provided.

What's Up with the Weather? - John Meseke
A lesson that looks at the maximum temperature for one month for two cities, Denver and Chicago, using the CLIMVIS Interactive Visual Data Center at the National Weather Service.

The World Series Problem - Jay Hill
In order to determine the champion of Major League Baseball in the U.S. and Canada, the winners from the National League and the American League play the "World Series." The Series consists of seven games. If a team wins four out of the seven games, they are the champions. Of course, all seven games are not played if a team has already won four. How many games do you expect will be played before a team wins four games and becomes the champion? This project uses the internet, a computer program (written in Future Basic), and other student activities to explore the concept of expected value.

Questions? Write to the workshop facilitators.

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Math Forum * * * * 1 February 2001