Let’s Leap into Math to Learn Leap Year Calculations!

March 2, 2016


Cindy Bryant
Thursday, March 3, 2016 - 11:45am

This past Monday, February 29, was Leap Day. You may think that Leap Day is added to the calendar every four years, creating a Leap Year, but it’s more complex than that and requires a bit of math to calculate.

How Do I Calculate Leap Year?

As it turns out, February 29 is not added to the calendar every four years. While it’s true that all non-century years that are divisible by four are leap years, this just doesn’t hold true for century years.

The best way to calculate whether a particular year will include the extra leap day is to first see if the year can be divided by four. If it can’t, then it isn’t a leap year. If it is divisible by four, then check to see if it is also divisible by 100. If it isn’t divisible by 100 then it will be a leap year. If it can be evenly divided by 4 and 100 (such as 2000), then check to see if it is divisible by 400. If it is, then that is a leap year. If it is not, such as 1900, then it is not a leap year. Leap Year calculations require a lot more than you had originally anticipated, don’t they?

The History behind the Calculations

The reason for all this extra calculation is because the Solar System doesn’t take an exact number of days to orbit the sun to keep the seasons on schedule according to the intended calendar. 

It was Julius Caesar’s astronomer, Sosigenes of Alexandria, who suggested the 365-day calendar, the Julian calendar, with an extra day (leap day) every four years. But, by the 16th century the Julian calendar was ten days behind the solar calendar. 

To correct this error, in 1582 Pope Gregory XIII (hence the Gregorian calendar) fine-tuned the calendar to ensure it stayed in line with the Earth’s movement around the sun and moon by ordering the advancement of the calendar by ten days and omitting leap year three times every four hundred years.

There are numerous legends and folklore related to Leap Year. For example, Sadie Hawkins Day is synonymous with February 29 and is the day when women can ask men to marry them. According to Irish legend or history, St. Brigid struck a deal with St. Patrick to allow women to propose to men every four years. Couples that marry during leap year are thought to have bad luck, according to Greek and Ukrainian folklore. And in Scotland, it’s considered unlucky for someone to be born on Leap Day.

But, quite honestly, it may be the opposite! Statistically speaking, about one in 1,461 births are “leaplings,” babies born on February 29. Worldwide, there are between four and five million leaplings and an estimated 200,000 in the United States. The odds of being born on a leap day are very low compared to being born on any other day of the year, or one in 365 days. I think that these leaplings are lucky because they beat the low odds of being a leap day baby, and also because they get to choose whether they celebrate their birthday on February 28 or March 1 during off-leap years.

On Which Day of the Week Were You Born?

Leaplings, like all of us, know the date that they were born; but there’s a good chance that they may not know the day of the week that they were born. It would be easy to just do a quick Google search for the day or a 100-year calendar to find out, but that would take all the fun and mathematics out of it! As a teacher, I found that all my students always enjoyed doing the math first and then confirming their calculations online. But, even if you already know the day of the week, it can still be fun to check the date and confirm it with some simple mathematics.

There are many different ways to calculate the day of the week on which you were born, but the method that I made this chart from uses the Key Value Method. Click the chart below to view the PDF!

The math doesn’t have to stop once everyone has calculated and confirmed the day of the week they were born. There’s a wealth of data that can be collected, graphed, and analyzed related to day of birth.

Math in Your Everyday

Several years ago, I created a two-week unit of study entitled “Calendar Capers” which included a look at the history of the calendar, having my approximately 120 sixth grade students calculate their day of birth and then having each student graph their birthday by placing a star (red for girls and blue for boys) on a large “A Star is Born” graph to determine the day of the week most sixth graders were born. The data provided ample opportunities to explore mean, median, mode, and range.

To incorporate more real-life data collection and reporting, I had the students determine the day of the week that most babies were born at our local hospital during the past year using data provided by the hospital’s obstetrics department. Groups of students were assigned a month for the previous year to create monthly graphs that were then used to create a large graph for the entire year. The final large graph was then given to the local hospital to display.

These activities are just one way for students to apply mathematics to everyday life and see how it can be used. To maximize opportunities for learning and doing mathematics, it’s beneficial for students to participate in a variety of learning activities using an array of different tools.

Online Math Tutoring

One tool that can serve in assessing mastery and aiding students in learning mathematics is LearnBop, a highly adaptive online math program for grades 4–12 and an exclusive partner of Fuel Education. Every incorrect answer becomes a learning opportunity, and its math tutoring program allows students to learn from mistakes with custom feedback and then try again. If a student makes a mistake or asks for help, the automated tutoring system breaks down the problem and guides the student. The one-to-one interactive platform offers hints, visuals, and videos for each student to self-pace in order to gain mastery before moving on to the next concept. 

So, what are you waiting for? Leap into mathematics today!

About the Author

Cindy Bryant is the director of learning at LearnBop in charge of overseeing projects and activities that relate to learning, instruction, and effectively implementing LearnBop, an online math program for grades 4–12. Prior to joining the LearnBop team in 2013, Cindy was a classroom teacher for 25 years, served as a member of the NCTM board of directors, was the former director of Missouri K–12 Mathematics, and was named a Presidential Awardee.  

Read an online math tutoring success story.


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