Baseball: A Tool for Middle and High School Math

Baseball, perhaps more than any other major sport, is a game of numbers.  The sheer number of games (162 in the major league schedule) leads to a large amount of statistical information. Students who understand baseball better than math may understand many mathematical concepts without realizing it. For these students, harnessing the connection between baseball math and classroom math topics can prove to be an effective teaching strategy.

While the applications among younger grades are straightforward (batting averages equate with fractions, etc.), it is in high school that the real interesting connections can be made. The field of sabermetrics involves advanced statistical interpretations of baseball. As a result of sabermetrics, new baseball statistics have been created, statistics that are far more complex than earned run average (ERA) or batting average. This includes statistics such as WAR (wins above replacement), WHIP (walks and hits per innings pitched) and the Pythagorean Expectation Statistic (used to predict a team’s performance over a season). The generation of these formulas is an engaging way to teach algebra. The use of sabermetrics in baseball is the foundation behind the best-selling book Moneyball by Michael Lewis, which was also made into a movie starring Brad Pitt.

Baseball can be used to teach statistics. One of the primary applications of sabermetric data is the comparison between players between different eras.  Was Barry Bonds a better homerun hitter than Babe Ruth? The answer is that it depends on how you consider the question. Barry Bonds had the most home runs in his career as well as the most home runs in a single season ever. However, his achievement is less than Babe Ruth in terms of his t-score ranking. In other words, the Babe Ruth was more standard deviations above the median home run totals for the era he played in than was Barry Bonds.

There are games online that emulate baseball based on mathematical algorithms.  Whatifsports.com is a “historic fantasy sports website” that allows competitive play based on baseball player’s performance history, with statistics “normalized” to average performance. Sabermetrics are utilized extensively in fantasy baseball. In an advanced baseball math lesson, students would be expected to justify their drafting and roster moves in statistical terms. Since this is a fun activity and baseball is primarily a summer game, this is a great method to keep students thinking about math while on break, and could help fight academic summer slide.

An earlier Math Hub blog looked at the connection between math and baseball as focused on elementary education. Could we extend the use of baseball to middle and high school algebra and statistics lessons? Share your thoughts here.

Making Math Relevant

The web sites Worldometers and USA Right Now provide real time statistics on the world and the United States.  These web sites are not only mesmerizing to watch but can also serve as sources to help math educators create contemporary word problems that engage students in the math curriculum. 

Both sites include a Media category where users can view how many emails and tweets sent, how many cell phones sold, and how many items “Googled” thus far on the given day.  Consider how many tweens and teens would find this type of information relevant to their own lives!

Worldometers, named one of the best free reference web sites of 2011 by the American Library Association, also provides opportunities to raise significant issues in fields such as Government and Economics, Health, Energy, and Food.  For example, educators can create meaningful word problems through global data on the amount of forest lost this year, the number of people without access to safe drinking water, and the number of deaths caused by smoking cigarettes this year.  Beyond word problems, educators can encourage students to use the data in practical ways, such as creating a school-wide anti-smoking campaign or raising money to build a fresh-water well in a third world country.

Check out the web sites and find data that will engage your students!

Math Activities: The Numbers of Major League Baseball

Last weekend marks one of my favorite times of the year – the opening games for Major League Baseball. I always find the winter months to be a bit boring because I can’t watch my favorite team, the New York Yankees, play ball each evening. Of course, you can imagine that there’s more to the baseball season than just balls and strikes. Like so many things that I am passionate about, I always look for the math in baseball. Finding mathematical connections to students’ interests will lead to more successful lessons and more motivated students. There are so many possible math activities using baseball statistics, but it’s up to you to be sure the math involved is appropriate for each student’s ability level.

My favorite lessons dealing with baseball and mathematics are those that help students understand decimals. One of the most common uses of decimals in the “real world” is in describing baseball batting averages. We see numbers like .305 or .240, but do the majority of baseball fans know what these numbers really mean? It’s a great topic to delve into, because it will help the students better understand the game and what a batter has to do to improve his average. At the same time, it will help students understand the value of decimal numbers. While the batting average is the most familiar statistic that uses decimals, similar studies can be completed using a batter’s on-base or slugging percentage. Another great activity is to help students determine a team’s winning percentage by dividing the number of wins by total games played. It might even be fun to have a student track a player's or team's statistics for an extended period of time.

If you take one look at the Major League Baseball site, you will see a plethora of statistics that students are able to work with. And because teams play almost every night, the statistics change daily, so there’s never a shortage of math to be completed! So go ahead, take baseball from the field into the classroom. I’m sure that your students will have a ball!

March Madness or Math Madness??

Just this morning, I began filling out my bracket for the annual NCAA Basketball Championship pool. While not everyone is a fan of basketball (myself included), it seems that almost everyone participates in a March Madness pool. I think it’s because there are so many possibilities that even the most skilled sports analyst can’t possibly pick every winner. So, anyone can do a little educated guessing and end up victorious. As I began making my selections, I thought about all of the possible combinations of tournament winners. Then, I glanced at the given odds and began analyzing those numbers. Before long, I realized that I was doing all sorts of math that I hadn’t before recognized.

As it turns out, there is a lot of math evident in the NCAA tournament. We all know that getting kids excited about math and helping them connect to the concepts is one of the biggest battles that math teachers face. And here I am sitting at my kitchen counter looking at some of the most interesting math problems I’ve seen – and as I mentioned, I don’t even like basketball. Imagine the excitement of a middle-school student when they realize that this yearly event can help them learn math!

So, where is the math? Well, it depends on the level of your students, but how about just asking them to figure out the number of different completed brackets that are possible? Or, what about finding the probability that a team will end up in the “Sweet Sixteen”, “Elite Eight”, and so on. Then, think about the odds...which team has the greatest odds? The worst odds? As the tournament commences, you could have students track points of a particular team or a particular region, or even individual statistics of teams or players. Do a little internet research, and you’ll find all sorts of activities related to math and the NCAA basketball tournament. I even found a web quest which covers lots of the categories of math lessons that I mentioned.

Remember, you don’t always have to follow the book or create fictitious mathematical scenarios for your students. Think about what’s going on in their everyday lives and I’ll bet you can come up with some interesting contexts for math problems. This is just one topic that is sure to have many of your kids excited to do the math!

Thanksgiving Activity: A Mathematician's Canned Food Drive

I want to share an activity that helps students understand the importance of community involvement but also helps them practice important math concepts. I used this activity in the weeks leading up to Thanksgiving, but it is one that can be meaningful at any time of the year. Many schools hold can drives to collect food for needy families. However, I decided to put a different spin on my can drive by including daily math activities to help get students more involved.

Students were asked to bring in non-perishable canned goods over a 2-week period. While participation was not mandatory, I found that most of my students were eager to donate. Each day, my class spent time counting the number of cans that had been collected and graphing the data. Students decided to create three different types of graphs: a line graph, a stacked bar graph, and a line plot. Each graph displayed the information in a different manner and we used the graphs to discuss appropriate data displays. I also had students estimate the weight of particular cans (I had to “hide” the weight on the label) and then they weighed the cans to check the accuracy of their estimates. At the end of the project, we also found the total weight of all cans that were collected! Next, I had students find the volume of some of the cans, and I had them find the difference between the volumes of the largest collected can and the smallest. Finding the volume of a cylinder was a new concept for my students, so it required a bit of guidance, but they loved using the rulers to measure the cans and it required them to measure precisely. 

Some other ideas I had but did not use included students looking at the labels to investigate surface area, converting between measurements, and finding the unit price of some of the items. The activities that you can choose are dependent on the level of your students. Overall, though, I found that students enjoyed this because it got them more involved and interested in the charity activity. Typically, students just drop a can off and forget about it. With this activity, they were excited to create graphs, measure the “new” largest can each day, and they were helping their community at the same time!

 

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