Mathematics

Background Information:

In Chapter 4, we examine algorithms.  An algorithm is a step-by-step method of carrying out a procedure to acheive a desired result.  In this activity, we will explore an algorithm that allows us to find the day of the week on which a particular date occured.  As you know, the day of the week on which a date occurs varies from year to year.  One of the factors that affects the placement of days of the week is whether or not a year happens to be a leap year.  In order to use the algorithm, you will need to know about leap years.

 

As explained on page 176 of your Mathematical Ideas textbook, “In general, if a year is divisible (evenly) by 4, it is a leap year.  However, there are exceptions.  Century years, such as 1800 and 1900, are not leap years despite the fact that they are divisible by 4.  Furthermore, an exception to the exception, a century year that is divisible by 400 (such as the year 2000) is a leap year.”  Since none of the years above are century years, you can use the divisibility by 4 method to determine if a leap year is involved, or, for a full list of leap years from 1800 to 2400, you can visit the Kalendar-365 Leap Years website. Your answer to item 1 is the number of days in the year you chose.

 

Your job is to follow the steps in the algorithm to determine the day of the week on which  one of the following important historical events occured. 

The Bombing of Pearl Harbor – December 7, 1941

Assassination of John F. Kennedy – November 22, 1963

Bicentennial of the United States – July 4, 1976

Y2K – January 1, 2000

Terrorist attacks on the United States – September 11, 2001

 

A Perpetural Calendar Algorithm – developed by Dan Foley, University of New Orleans

The algorithm requires several key numbers.  The key numbers for the month, day, and century are determined by the following tables.

Tables from p. 176 of textbook

The following table contains the steps for the algorithm in the left column and an example in the right column.  The example is the date October 10, 1942.

 

Step 1 Obtain the following five numbers

1.  The number formed by the last two digits of the year

2. The number in the previous step divided by 4 with the remainder ignored

3.  The month key from the table above

4.  The day of the month

5.  The century key from the table above

Example

42

10

1

10

0

Step 2 Add the five numbers from Step 1 63
Step 3 Divide the sum in Step 2 by 7 and retain the remainder 0, because 63/7=9 with no remainder
Step 4 Find the day of the week next to the remainder in the day key table Saturday

 

INSTRUCTIONS:  To get full credit for this activity, choose one of the following historical dates, follow the instructions below.

 

The Bombing of Pearl Harbor – December 7, 1941

 

Assassination of John F. Kennedy – November 22, 1963

 

Bicentennial of the United States – July 4, 1976

 

Y2K – January 1, 2000

 

Terrorist attacks on the United States – September 11, 2001

 

 

1.  Using the date that you chose,  complete the following table.

 

Step 1 Obtain the following five numbers

1.  The number formed by the last two digits of the year

2. The number in the previous step divided by 4 with the remainder ignored

3.  The month key from the table above

4.  The day of the month

5.  The century key from the table above

Results

___

___

___

___

___

Step 2 Add the five numbers from Step 1 ___
Step 3 Divide the sum in Step 2 by 7 and retain the remainder ___
Step 4 Find the day of the week next to the remainder in the day key table _____________

2. Create a post to the Discussion Board with the date you chose as the Subject of your post.

(for example, the subject of your post might be: “Assassination of John F. Kennedy – November 22, 1963″)

 

3.  Copy and paste your table with the steps you followed and the results column into your post.

4.  Submit your post.  Be sure to subscribe to the thread so that you will be notified if anyone replies to your post.

 

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