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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Think Globally and Locally, Mathematically

Student Explorations in Mathematics, formerly known as Student Math Notes, is an official publication of the National Council of Teachers of Mathematics (NCTM) and is intended as a resource for grades 5-10 students, teachers, and teacher educators. Each issue develops a single mathematical theme or concept in such a way that fifth grade students can understand the first one or two pages and high school students will be challenged by the last page. The content and style of the notes are intended to interest students in the power and beauty of mathematics and to introduce teachers to some of the challenging areas of mathematics that are within the reach of their students.

The teacher version includes additional information on world poverty as well as instructional ideas to facilitate classroom discourse. The student guides are available for free download (see below) but the teacher’s guides are only available with NCTM membership.

In the following activities from the May 2011 and September 2011 issues of the magazine, students use histograms and make comparisons between different country groups, then create graphs that compare these differences in many ways and consider how each of these displays might be used. In part 2, students consider important information about world poverty by using measures of central tendency and box plots. Students analyze data and use a hands-on manipulative to interpret and understand box plots, including the connection between percentiles and quartiles.

Part 1: Hunger at Home and Abroad (May 2011)
World Poverty Data can be downloaded here.

Part 2: Poverty at Home and Abroad (September 2011)
World Poverty Data can be downloaded here.


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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.

Math and Baseball

The baseball season is just warming up and the playoffs are around the corner. Why not bring “America’s Pastime” into the math classroom? The following problems challenge students to exercise some of the skills they learn in the middle school curriculum.

Baseball Fantasy
These two activities from PBS Mathline have pairs of students act as co-managers of a baseball team. Each pair receives a pack of baseball cards. They compute and analyze the key statistical data of the given players, make decisions on who they want to keep and who they want to trade, arrange their lineups, and play simulated games. Students use the key statistical data to construct individual player spinners, determine the line up, and play a simulated baseball game. The ultimate goal is to be the manager of the winning team of the Fantasy Baseball World Series.

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.

Come to the Middle School Portal 2: Math and Science Pathways online network to discuss this and many other topics and connect with colleagues!


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 11/29/2011.

BIG Numbers

Those BIG numbers fascinate, don’t they? I’ve watched 5th and 6th graders gathered around the teacher just to hear more about the size of a million, or even a billion. Ths article, Thinking Involving Very Large and Very Small Quantities, shows how we, as adults, often fail to comprehend such quantities. The article begins: “Intuitively a million is a lot more like a billion than ten is like one hundred, because our intuition has some grasp of ten and one hundred, but we have little grasp of what millions and billions involve. Fortunately, there is often a way to make intelligent decisions involving big quantities. Use arithmetic!” Topics here, which can generally be dealt with through just multiplication and division, include national finances, terrorism, airplane crashes and lotteries among others.

For your own classroom, I’ve looked for problems that may open discussion to large numbers. Please share your finds with your colleagues by posting comments.

How Much is a Million?
This lesson focuses students on the concept of 1,000,000. It allows them to see first hand the sheer size of 1 million while at the same time providing them with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. The lesson, which involves solving an equation, can easily be adapted for pre-algebra middle school students.

Too Big or Too Small
This unit features three activities, but I’m recommending only the first of these. Here students explore whether one million dollars will fit into a standard suitcase. If so, how large would the suitcase need to be?  How much would it weigh? Figuring out real answers to these questions can promote number sense.

Making Your First Million
In this activity for grades 4-6, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that will enable them to develop the concept of very large numbers.

The MegaPenny Project
This site illustrates the magnitude of large numbers by showing and describing arrangements of large quantities of U.S. pennies. It begins with 16 pennies that measure one inch when stacked and one foot when placed in a row. The next visual shows a thousand pennies, and in progressive steps the site builds to a quintillion pennies. All pages have tables at the bottom listing the value of the pennies on the page, size of the pile, weight, and area (if laid flat).

One Grain of Rice
Beginning with the famous story of the village girl trying to feed her people, the lesson involves students in the mathematics of exponential growth. Students work collaboratively to come up with a bargaining plan to trick a raja into feeding the village using algebra and estimation. The complete activity includes the development of an exponential equation, but just following the growth of the number of rice grains throughout the story gives a good introduction to exponential growth. Questions for students and ideas for assessment are provided.

Finally, from the Figure This! collection, developed especially for middle school students, come these short but interesting problems on working with large numbers. Each question contains a hint on how to get started and a complete mathematical set-up on how to solve it.

How Fast Does Your Heart Beat?
If you started counting your heartbeats at midnight on January 1, 2000, when would you count the thousandth beat? The billionth?

How Much is Your Time Worth?
Would you rather work seven days at $20 per day, or be paid $2 for the first day and have your salary double for every day of the week

How Much Water Do You Waste?
If the faucet leaks 2 drops every second for a week, how much water goes to waste—enough to fill a glass, a sink, or a bathtub?

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 4/09/2012.

Decimals—Adding and Subtracting

Do you find that your middle school students still become confused with decimals? Not unusual! The resources here offer support in explaining the concepts underpinning addition and subtraction of decimals, in particular, place value. They also include demonstrations of addition and subtraction and opportunities for practice. The goal for students, as stated in NCTM’s Focal Points, is to develop fluency with computing, solving problems, and making reasonable estimates. I hope these resources will visually and interactively engage your students, helping them toward that goal. 

If you have found other digital resources that have helped your own teaching of this topic, please take a moment to share with your colleagues. Just leave a comment below! 

Builder Ted
This interactive game deals with place value in decimals, necessary to understanding addition and subtraction. In the game scenario, students help Builder Ted by placing numbered bricks on a ladder in numerical order. At the first level of difficulty, all numbers are positive, but the two higher levels include negative numbers as well. If a number is placed incorrectly, all the bricks immediately fall and the player begins again.  

Place Value
The user can type in any number, such as 3601.076, or let the computer choose a number. As the student passes the mouse over each digit in the number, its place value is shown. Also, how to say the number is given, plus a short exercise asking the student to identify the digit in, say, the thousandth position.

Fractions, Decimals, and Percentages
Especially appropriate for tutoring or even review, the site introduces decimals (reading, writing, and comparing) and then offers examples and practice in operating with decimals.

Base Block Decimals
With this virtual manipulative, students can explore the meaning of place value and grouping as they add and subtract decimals. The base blocks can represent negative as well as positive numbers with one to four decimal places. Students exchange and group the blocks as needed to solve the problems created by either the student or the computer. All material is available in Spanish and French as well as English, including instructions for using the manipulative, information about bases and place value, and suggested questions for classroom use.

Decimals
This site offers bare-bones explanations of decimal topics and interactive practice. In the long list of topics are adding and subtracting decimals as well as adding and subtracting money. The computer sets the problem and gives immediate feedback to the student’s response. The bottom of each lesson page contains timed exercises.


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 11/29/2011.