## Monday, February 29, 2016

### Leap Year Math

Perhaps you've heard that this year 2016 is a leap year. How do we know that?

We use the figure 365 for the number of days in a year.

In actuality, the number is closer to 365.25. To compensate for this discrepancy, every four years we have what is called leap year.

In leap years, a day is added to February. Normally February has 28 days.

However, every 4 years, we give February 29 days to  help synchronize the calendar year with the solar year, or the length of time it takes the earth to complete its orbit about the sun,  about 365.25 days.

A leap year has 366 days. The year 2016 is a leap year with 366 days. So the month of February will have 29 days.

Because 365.25 is not exact, three leap years are dropped every 400 years.

These are the end-of-century years that are not evenly divisible by 400.

These rules only apply to the Gregorian calendar currently used by American and European countries.

Several other calendars are used by Asian countries.

Here's a formula we can use to find out if a year will be a Leap Year:
 Leap Years are any year that can be evenly divided by 4 (such as 2012, 2016, etc.) except if it can can be evenly divided by 100, then it may not be (such as 2100, 2200, etc.) except if it can be evenly divided by 400, then it is (such as 2000, 2400, etc.)

In other words:
1. Divide the year by 4. If there is no remainder (so it divides evenly), it may be a leap year.
2. Divide the year by 100. If there is no remainder, then it may NOT be a leap year.
3. Divide the year again, by 400. If there is no remainder, it is a leap year.

Both 1600 and 1700 are evenly divisible by 4. However, 1700 was not a leap year because 1700 is not evenly divisible by 400.

Can you determine which of these years were leap years? The answers appear below.

1960            1930             1836              1862

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1960 and 1836 are both divisible by 4 and 400. 1960 is also divisible by 100. So both 1960 and 1836 are leap years.

## Tuesday, February 9, 2016

### Celebrating e-Week in the Math Classroom

Although it may not be as well known as Pi, e is also an irrational number that is roughly equivalent to 2.7.

The first few digits are: 2.7182818284590452353602874713527. It's decimal expansion never terminates.

So the week of February 7 is the logical time to celebrate e in all its variations.

Your students may have used e in exponential and logarithmic functions.

It is an expression that is used in the study of compound interest. It is often called Euler's number after Leonhard Euler, who proved that e is an irrational number.

The number e is a mathematical constant.

Let your class have fun celebrating e-Week with egg-shaped candy, enchiladas, edible snacks, effervescent drinks, etc.

You may want to have your students read the poetry of ee cummings or Edgar Allen Poe, watch a clip from the E! Network or ESPN, read an e-book, do some of their work on electronic devices, listen to music with earbuds, do some math problems that use e or 8 or any number that begins with "e."

Let your students email a math problem to a classmate, create an elaborate story problem, do some Excel Math Stretches (brainteasers from your Teacher Edition), or do anything else you can think of that relates to e!

Your students could find the dimensions of the Eiffel Tower, use an encyclopedia (electronic or hard copy), discover some fun math facts about the earth or England, play a game of crazy eights, dress up in clothes from the 80s, and find cookie recipes with and without eggs.

Then let your students write as many math problems as they can with the numbers 8, 11, 80 - 89, or any numbers that contain the letter "e".

Challenge them to solve problems with exponents, add a list of eight (or eleven) numbers and then do it again keeping track of their best time.

Have your students write a note of encouragement to one of their favorite teachers or to their parents. Use the comment box below to share your e-Week activities. Have fun!
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