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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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.

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.

Decimals – Multiplication and Division

These resources offer practice in operating on decimals and, moreover, opportunities to think about the processes of multiplication and division. As stated in the NCTM Focal Points, students should make sense of these procedures, become fluent in performing them, and be able to apply them in solving problems. I believe these sites, as a whole, offer practice in both understanding and problem solving.

If you have ideas to offer, please share them with your colleagues.  Just add your comments below.

Learning about Multiplication Using Dynamic Sketches of an Area Model
In this applet, a rectangle represents the familiar area model of multiplication. By changing the height of the rectangle, students can explore the effect of multiplying a fixed positive number, in this case 3, by decimal numbers greater than 1 and less than 1. The visual is powerful!

Too Big or Too Small?
Scroll down to Activity 3: Exploring the Effect of Operations on Decimals. Through playing the cleverly crafted game presented here, students explore the effect of operations on decimal numbers. They begin with the number 100 as they enter a maze. For each segment chosen on the maze, the student calculates the assigned operation and number; for example, “+ 1.2” or “x 0.8.” The goal is to choose a path through the maze that results in the largest value at the finish.

Decimals
This site has explanatory lessons and interactive practice on most aspects of decimals, including multiplying decimals and dividing them. A good set of materials for self-tutoring or review. 

Find the Cost of Meat per Week at a Zoo
In a multi-step, NAEP assessment item, students must determine how much a zoo spends each week on meat to feed the animals. The site links to the scoring guide, sample student responses, and data on how well grade 8 students did on this multiplication/division problem. Only 13% solved it correctly!

Where’s the (Decimal) Point? asks students to explain clearly how they know where to put the decimal point in multiplication and in division of decimals. Students must think beyond the “rules” to the “whys.” I suggest these problems as challenges for older middle school students who are ready to stretch their thinking to the level of generalizing arithmetic.


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 11/16/2011.

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.


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 12/07/2011.