# Math Students Collaborating Nationwide, Even Worldwide!

There are middle school projects that gain impact through collaboration with students outside your own classroom, such as estimating the average amount of water used per person per day. This problem takes on deeper relevance when averages are compared to those of classrooms around the country and the world. Other projects, such as finding the circumference of the Earth, require data input by geographically distant schools.

To connect with and collaborate with classrooms interested in the same project, you can make use of online sites, even though you work in an offline classroom. You need Internet access to register for the project (free registration!), to find suggested teaching procedures, and to submit and retrieve data from other schools. But you can be offline while teaching the lessons, collecting and analyzing data, and presenting results.

The Internet-based projects below are excellent samples of what’s available online for the offline classroom. If you know of similar projects, please share via this blog!

In this project, students share information about water usage with other students from around the country and the world. Based on data collected by their household members and their classmates, students determine the average amount of water used by one person in a day. Students must develop a hypothesis, conduct an experiment, and present their results.

If your school is located among rural roads, you and your students can collect roadkill data in your community for analysis and compare your data to other areas participating in the project. The site provides a detailed protocol for monitoring and reporting roadkill, a method of reporting data through the web, and access to data collected by all participants. The project crosses many disciplines, including environmental science education and data analysis.

The International Boiling Point Project

Students around the world boil water to discover what influences its boiling point. Is it room temperature, elevation, volume of water, or the heating device used? All you have to do is boil a bit of water, record a bit of information, and send it along to the site for inclusion in the database of results.

In the course of the project, students learn about Eratosthenes and his experiment, and then do a similar experiment themselves by collaborating with other schools. They learn the “why” of the measurements they’re taking, collect the data as precisely as possible, and submit their findings to the central site. By collaborating with a classroom in another state or even another country, they actually determine a good estimate of the Earth’s circumference. The site provides detailed instructions, activities, and reference materials.

# What’s the Average?

Students often answer with the formula: “Add all the numbers together and divide, etc.” with no strong idea of what “average” means. Few adults, in fact, distinguish among the measures of central tendency: mean, median, and mode, but tend to lump them into a general idea of “what’s typical” of the data. Not a bad place to start, but insufficient for understanding the wealth of statistics that overwhelm us in today’s world.

The first activities here immerse students in working with mean, median, and mode both visually and interactively. They will be confronted constantly with the differences among the three concepts of average. The second set offers problems to challenge them to use these statistics in problem situations, such as finding how average temperature changes with distance from the equator.

Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how these statistics change (or, in some cases, how they don’t change).

Understanding Averages
Written for the student, this tutorial on mean, median, and mode includes fact sheets on the most basic concepts, plus practice sheets and a quiz. Key ideas are clearly defined at the student level through graphics as well as text.

Plop It!
Users click to easily and quickly build a bar graph and view how the mean, median, and mode change as entries are added to the graph. An efficient tool for viewing these statistics visually.

Comparing Properties of the Mean and the Median Through the Use of Technology
Seven points appear on a number line, 0 to 400. As students move one or more of these points along the line, the effects on the mean and median are immediately displayed. Questions challenge students to explore these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other?

Working hours: How much time do teens spend on the job?
This activity challenges students to interpret a bar graph (showing only percentages), to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance! A full solution sets out the math in detail. Related questions ask students to calculate averages for additional data sets.

The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students learn to collect, organize, and interpret data. Classrooms can participate in the project each spring and each fall. You will find project information, lesson plans, and implementation assistance at the site.

Train Race
In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Players extend their basic understanding of these statistics as they try to find the most reliable train for the trip. Students can select one of three levels of difficulty. There are tips for students as well as a full explanation of the key instructional ideas underlying the game.

# Getting Dirty With Data

Data overwhelms our modern lives. How to make sense of the numbers in newspaper stories, in campaign speeches, in scientific experiments? Statistics offers tools to help us organize and interpret data. Even at the middle school level, students can work with statistics in real-world situations, whether actual or simulated. To actually apply statistics to real questions, nothing answers like a class project. Students can get their hands on messy, raw data. Collecting and analyzing data, displaying their findings and reaching conclusions — these may be your students’ best mathematical experiences of the school year!

Junk Mail
No one is immune from receiving junk mail, but just how much of it is really finding its way to your address? In this simple activity, data collection and analysis are a key part of a project to learn about the importance of recycling. For one week, students count and record the number of pieces of junk mail received in their homes. The display and organization of the data can be modified to address the data and statistics topics the class is working on.

Numerical and Categorical Data
In this unit of three lessons, students formulate questions that can be addressed with numerical and categorical data. They then collect, organize, and display relevant data to answer those questions. As they collect categorical data, they consider how to word questions and how to record and display the data. As they collect numerical data, they focus on how to obtain measurements and how to represent and analyze the data by describing its shape and other important features. The final lesson examines specifically the differences in representing and analyzing categorical and numerical data.

Population Growth
This series of activities explores the mathematical and environmental aspects of population growth. How fast is the population growing? Has it always grown at this rate? Are the populations of different countries growing differently? How can we predict the population in the future? How will a growing population impact the environment? Using archived census and demographic data as well as up-to-the-minute population estimates from the U.S. Census Bureau, students will learn how to model population growth and study the implications of a changing population.

Boil, Boil, Toil and Trouble: The International Boiling Point Project
Be part of an annual event: Enroll your class in this free Internet-based collaborative project. Students discover which factors — room temperature, elevation, volume of water, or heating device — have the greatest influence on boiling point. Students boil water, record their data, and send it via email to be included in the site’s database of results. After gathering the data, activities focus on analyzing the compiled data to find answers to questions about how and why water boils.

# Give Us Our Daily Math

Middle schoolers may not easily see the connection between data analysis problems invented for the classroom and math problems encountered in their daily lives. You will spark their interest in data analysis by showing them its value in finding solutions to real problems in many settings — from buying a soda to taking after-school jobs to understanding weather reports. When you introduce data analysis to middle school students, you are exposing them to applications that correlate with the NCTM Principles and Standards: creating and reading graphs, calculating statistics, and, above all, solving real-world problems.

Working Hours: How Much Time Do Teens Spend on the Job?
This activity challenges students to interpret a bar graph to determine the average number of hours teenagers work per week. A hint suggests that students assume that 100 students participated in the survey. Interesting statistics about the hourly wages and annual salaries of various occupations are given.

Does It Make a Difference Where You Shop?
In this online activity, your students compare soda prices from two stores using data displayed on a scatterplot graph. Students are shown how the line y = x can be used to analyze the data and draw a conclusion. Further problems involving scatterplots compare car mileage and the performance of NBA players.

The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students can participate in the project each spring, April-June. You will find project information, lesson plans, and implementation assistance.

New York Times Daily Lesson Plan: Mathematics
These lesson ideas from the New York Times offer suggestions for ways to draw on real-world issues and statistics to develop lessons in mathematics. Each lesson idea includes a description of the activities along with handouts and questions for discussion. Links to related Times articles provide an interactive aspect to each of the lesson entries.

# Math in Spring and Summer Sports

In the springtime, some middle school students enjoy outdoor sports much more than they enjoy their math classes. Why not use two of these popular sports to our advantage in the classroom? The following problems with baseball and track themes challenge students to exercise some of the skills they learn in the middle school curriculum.

What Is Round, Hard and Sold for \$3 Million?
This activity challenges students to determine which is worth more today: Babe Ruth’s 1927 home-run record-breaking ball or Mark McGwire’s 70th home-run ball that sold in 1999 for \$3 million. Compound interest is the main topic.

Who’s On First Today?
In this activity, students use hits and at-bat statistics to determine which of two baseball players has a better batting average.

Fun with Baseball Stats
In this lesson plan, students use baseball cards to convert statistics to decimals, fractions and percentages. Then, they use their statistics in playing a game. Activity sheets can be downloaded.

Can You Run As Fast As a Car?
This activity asks the student to determine if Florence Griffith-Joyner moved faster than a car traveling 15 miles per hour when she ran 10 meters at a record-breaking 0.91 seconds during the Seoul Olympics. Along with the answer, students will find a description of how to make unit conversions and other problems related to conversions of units of measure for volume, distance, currency, and temperature.