# Collecting and Analyzing Real Data

Data collection and analysis can be an avenue into meaningful mathematics, science, and problem-solving skills needed by students in the twenty-first century. And an answer to the student question, Why do we have to study math? can be found when teaching mathematics with a real-world statistics approach. Below are digital teaching resources that demonstrate how data and statistics are a vital part of learning mathematics in a meaningful context. The resource activities are often interdisciplinary, which makes them time-consuming to prepare, as additional expertise is often needed. But the payoffs can be huge: student engagement, in-depth learning, and a real-world context for learning mathematics.

One approach is to look at situations in your community or larger world issues and have the students frame questions to investigate. Students may develop a passion for scientific inquiry when a topic can be analyzed with numbers. Requiring quality work and including a component about sharing results with the community will add value to an interdisciplinary contextual learning experience. Teachers may want to enlist a community person to provide additional expertise. Whether thinking small activity or big project, be ready to be surprised at what the data analysis reveals!

Analyzing Numeric and Geometric Patterns of Paper Pool
Look out, pool sharks! Begin the study of data and statistics with this super student exploration where data are collected and analyzed while students apply mathematical topics studied in grades 6 and 7: factors, multiples, rectangles, and the meaning of being relatively prime. In the Paper Pool applet, a ball is hit from the lower left-hand corner of a grid-lined pool table at a 45-degree angle. Students modify the size of the rectangular pool table and observe how the ball always travels on diagonals of the grid squares. After gathering and organizing data, students look for patterns to predict the corner pocket into which a ball will fall and the number of side hits the ball makes as it moves on the table to a corner pocket. The goal is to determine how the number of hits, final pocket, and number of squares crossed depend upon the relative lengths of the sides of the pool table. Sounds like fun, doesn’t it?

Junk Mail (a mini project)
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.

WWW—Wonderful Web Weather
Just how on-target are those weather forecasters we watch and listen to? In this webquest, students work in groups to track online weather reports for several locations over the course of three days and determine the accuracy of forecasts. Students develop an understanding of how weather can be described by measurable quantities, such as temperature, wind, and precipitation as they find and compare weather data found on the Internet, chart and graph data, and present their conclusions about forecasting. This straight-forward activity is suitable for students who are just beginning their work with data and statistics.

The Global Sun Temperature Project
With this free online collaborative project, students measure the temperature and record the minutes of sunlight for one week. Data are collected on the web site, and average daily temperatures and amount of sunlight are compared. Students draw conclusions about how the distance from the equator influences temperature. If you like this collaborative project, be sure to check out Down the Drain: How Much Water Do You Use?, another collaborative data project from the Center for Innovation in Engineering and Science Education (CIESE).

The Gulf Stream Voyage
If ocean travel is your passion, this site offers a way to spend time at sea without ever leaving your classroom. Here is a science project that uses actual data to help students investigate the science and history of the Gulf Stream. Math students can greatly benefit from the opportunity to collect data and draw conclusions based on the data. In the lesson called Current Now, students use real-time data and satellite images to determine how the Gulf Stream moves in the course of a year. In another activity, students use data about water temperature obtained from ships and buoys to determine the course of the Gulf Stream.

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. Student activities focus on analyzing the compiled data to find answers to questions about how and why water boils.

Backyard Birding—Research Project
Birds are everywhere, and here are ideas for creating a data collection project. Work with a science teacher and, possibly, an industrial tech teacher to expand this multiweek activity into a cross-curricular project to help students see how data analysis can support an understanding of nature.

Population Growth
These nine online lesson/activities investigate population growth and its impacts. Students use archived census and demographic data from the U.S. Census Bureau to model population growth and examine how population change affects the environment. Teachers will want to carefully review this resource to choose the activities most appropriate for their students’ mathematics background. Linear, quadratic, and exponential functions are used in some lessons.

# Linking Math to Real Problems

Why bother with statistics in middle school? One answer: data analysis is one of the NCTM Standards and an 8th grade Focal Point. But even more important, in my experience, is that statistics links math to real problems.

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!

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. Their goal is to find the most reliable train for the trip.

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. You will find project information, lesson plans, and implementation assistance at the site.

Down the Drain: How Much Water Do You Use?
In this Internet-based collaborative project, your 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 will 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.

100 People: A World Portrait Detailed Statistics
You’ve heard the idea before: What if the whole world were represented by 100 people? It is mind-boggling, for example, to realize that 61 would be from Asia and only 5 from North America. This page gives a full list of the data collected, links to a lesson plan and to commentary on the statistics. Excellent for an interdisciplinary project!

If you’d like to focus attention on measures of central tendency, these last two sites help explain the mean and the median though interactive online practice.

Plop It!
Users click to easily and quickly build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. An efficient tool for viewing these statistics visually.

Comparing Properties of the Mean and the Median Through the Use of Technology
This interactive tool allows students to compare measures of central tendency. As students change one or more of the seven data points, the effects on the mean and median are immediately displayed. Questions challenge students to explore further the use of these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other extreme?

Join your colleagues in discussing these and other middle school issues at the Middle School Portal 2 (MSP2) social network. Hope to “see” you there!

# Let’s Go to a Math Fair!

How could we organize a math fair? And what kinds of projects would our students present? I’m not thinking here of projects that would be judged, as in a science fair, but rather investigations and activities that would engage middle school students and be presented for the whole school as well as parents. One idea comes from a 7th grade class at Frisbie Middle School in Rialto, California.

Multicultural Math Fair
Ten activities for the fair, each based on a different cultural heritage, are well described in both Spanish and English. Included here are tips on how to set up a math fair as well as student handouts and free software for specific activities, such as the Tower of Hanoi. You will also find links to resources for related activities, such as studying symmetry and patterns in Navajo rugs. A unique teacher-created site!

If you are looking for more project ideas, here are some I think would make great fair presentations and involve students in learning sound math:

Pascal’s Triangle
Here are three ways to explore the famous triangle: by finding patterns and relations within the triangle, solving a pizza toppings problem in Antonio’s Pizza Palace, or working with an interactive web unit. The set of three investigations could work well as one fair project.

The Noon Day Project: Measuring the Circumference of the Earth
In the course of this online project, students learn about Eratosthenes and his experiment, do a similar experiment by collaborating with other schools, and analyze and reflect on the collected data to determine the accuracy of their measurements and what they learned. The project provides detailed instructions, activities, reference materials, online help, and a teacher area.

The Data Library
This web site contains an extensive list of ongoing data-sharing projects that would work well as fair projects. It also offers a great set of links to data on population, baseball stats, minimum wage, etc., excellent for students working on any statistics project.

Polyhedra in the Classroom
A set of activities developed for middle school students on aspects of polyhedra. The teacher-creator, Suzanne Alejandre, includes not only instructions for each activity but also assessment suggestions and her mathematical objectives for the unit.

Down the Drain
This Internet-based collaborative project allows students to 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. They then compare this to the average amount of water used per person per day in other parts of the world. Students publish reports, photos, or other work for the fair presentation.

# Pandemics and Their Numbers

Everywhere our students are hearing about the HINI influenza. Their interest offers an opportunity to co-teach with a science teacher in an investigation of what we know and don’t know about this pandemic. The New York Times has created an interdisciplinary lesson Pandemic Panic: Researching the 2009 Influenza A (H1N1) Pandemic that asks students to inquire into the current influenza as advisers from multiple perspectives and to share factual information they learn with their classmates and school communities.

The lesson opens with students considering “what we know” and “what we want to know.” The investigation begins as student groups take on such roles as “health advisers” or “economic advisers” or “historical advisers.” “Statistics advisers” could be added, in my opinion. What do the numbers tell us? FluView from the CDC 2008-2009 Influenza Season Week 38 ending September 26, 2009, gives great graphs of several types, some with an over-abundance of information that students will have to sort, select, and make sense of for themselves and their classmates. Statistics and percentages are topics that take on real meaning here.

If the class becomes interested in other diseases that have affected the world, they could research such epidemics as yellow fever. To get them into the story, look into Yellow Fever and the Reed Commission. They could research the number of victims over time and create a timeline from when the disease first reached the present United States up to the discovery of how to control it. A google search on “number of victims from yellow fever” brings up a few good sources, such as an August 10, 1879, article from The New York Times and another from September 24, 1897. Fascinating! But students will need to find other resources as well—encyclopedias and other books, offline as well as online.

If the information found is sufficient, they could calculate rates of change over the course of different decades. Were there times when the disease rates rose more quickly? When they did not change at all? You could explore with them the concept of the slope of a line, what it actually tells us. Your students will find that numbers tell interesting stories!

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# 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.