March Mathness

There are more than nine quintillion (9 x 1018) ways to fill out a 64-team March Madness bracket — and almost 150 quintillion permutations for the 68 college basketball teams in this year’s men’s tournament of the National Collegiate Athletic Association (NCAA).

The Princeton University Press March Mathness blog includes interviews of sports rankings experts, coaches, and mathematicians. Their predictions take the power of mathematical methods of rating and ranking, and bring them to bear on the NCAA hoops tournaments. The blog will also provide updates on the group’s collective performance, and the best method for picking the winner.

Blog posts, which date back to March, 2011, have described how math is used during tournaments, as detailed in Princeton University Press books such as Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football by Wayne Winston and Amy Langville and Carl Meyer’s Who’s #1? [Thanks to the Math Forum for putting this information in their weekly newsletter!]

There are all sorts of ways people fill out their brackets. Google has filled out a bracket based on search volume http://www.google.com/insidesearch/collegebasketball.html. Check back often to see how they’re doing.

We’ve blogged about the integration of math and sports in the past, too – check them out at http://msms.ehe.osu.edu/category/sports/.


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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.
We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/07/2012.

Probability in Real Life

Your students may find it difficult to believe that the concepts of probability really have anything to do with everyday life. If they did, would they still grow up to buy all those lottery tickets? In the Powerball Lottery, the largest in the Unites States, the odds of winning the jackpot are 1 in 195,200,000!

So says the Book of Odds, which offers blogs, articles, and thousands of thoroughly researched odds on accidents and death, daily life and activities, health and illness, relationships and society. Its carefully calculated probabilities range from the odds of being the only one to survive a plane crash, to the odds of having a heart attack, to the odds of having ever eaten cold pizza for breakfast.

Once your students are immersed in these odds, you might like to introduce the Game of Skunk. Playing and analyzing the game engages students in real-world applications of probabilistic thinking as they examine choice versus chance and practice decision-making.

On the purely theoretical level, your class would enjoy meeting the Smithville Families. This lesson explores the probabilities for the births of boys and girls in a large family. The outcome of a coin toss is used to indicate the birth of a boy or girl. And then you might compare the conclusions reached with those found in the Book of Odds.

My prediction is high on your enjoying these resources!


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/21/2011.

Dynamic Math and Science Learning With Simulations

Bob Panoff, executive director of Shodor and CSERD: Computational Science Education Reference Desk is passionate about using computational science teaching methods to stimulate student engagement in learning math and science from grades K to gray!

In a recent article for the Association for Supervision and Curriculum Development (ASCD) entitled “Simulations Deepen Scientific Learning,” he explains the role of simulations in making scientific theory understandable for students. Find out about all of Shodor’s computational projects at http://shodor.org/interactivate.

As an example of how one of the simulations work, click on the following link to see how a disease spreads in a virtual population with the Disease Epidemic Model simulation: http://www.shodor.org/featured/DiseaseModel/.

 

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/05/2012.

Math Starters: Projects to Begin the Year!

If you want to “hook” your class on math right from the start, you may want to consider one of these real-world projects. Students deal with real data in these investigations—collecting, presenting, and analyzing their findings. As they work on the NCTM Data Analysis and Probability Standard, they apply school mathematics in contexts arising outside of mathematics, as recommended in the NCTM Connections Standard.

Down the Drain: How Much Water Do You Use?
In this Internet-based collaborative project, students collect data from their classmates and their household members about water usage. The goal is to determine the average amount of water used by one person in a day. They can share that information with other classes online and compare the average amount of water used per person per day in other parts of the country and the world. The project goes beyond merely collecting data to considering some real questions on wasted water. Information on how to set up the project, how to share data online, and how to publish student findings is included.

Boil, Boil, Toil and Trouble: The International Boiling Point Project
Which do you think has the greatest influence on the boiling point of water: room temperature, elevation, volume of water, or heating device? To answer this question requires input from people all over the world, and this online collaboration allows your students to enter the investigation. They will boil water, under controlled conditions, record information, and post it online. They can analyze the data sent in by others worldwide and reach their own conclusions on what makes a pot of water boil.

Musical Plates: A Study of Earthquakes and Plate Tectonics
In this series of lessons, students use real-time data to solve a problem, study the correlation between earthquakes and tectonic plates, and determine whether or not there is a relationship between volcanoes and plate boundaries. The science and data analysis are more demanding in this project than in the first two, but still within the range of the upper-level middle school student. Four activities, each designed to be used in a 45-minute class period, teach students how to access and interpret real-time earthquake and volcano data. “Real-time” actually does mean data on volcanic and earthquake activity that is going on during the time of your class investigation! Three enrichment lessons follow in this teacher-friendly unit.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/28/2011.