Calendar Math Activities
By Michael Naylor

To view Michael Naylor's article on Calendar Math click here.

Calculate the day of the week (Grades 6-8)
Supply your students with these directions for an algorithm for calculating the day of the week. With it, they can choose any date from 1900 to 2099 and figure out which day of the week on which it fell or will fall. Have them first use it to find out today's day of the week in order to verify that the algorithm works, then they can use it find out on which day of they week they were born, on which day their next birthday will fall or any other day they choose. The algorithm is tricky, requiring some careful calculating and direction following, but some kids can even memorize this procedure and perform it mentally – no small feat!

Algorithm for the day of the week (years 2000-2099):

1. Start with the last two digits of the year and add one-fourth of this number to itself. Ignore any remainders. (This adds extra days to account for leap years.)

   For example: January 12, 2007. Take the number 7 for the year (07), 1/4 of 7 is 1 remainder 3, round down to 1. Add 7 + 1 = 8.

2. If the date is a January or February of a leap year, subtract 1 from the leap year number (since the extra day hadn't happened yet.) In our example, 2007 is not a leap year, so don't subtract anything.
3. Add the "month number" as follows:
   
   
   
   

   January = 6	February = 2	March = 2
   April = 5	May = 0	June = 3
   July = 5	August = 1	September = 4
   October = 6	November = 2	December = 4

   In our example, the current total = 8. Add 6 for January, 8 + 6 = 14.

4. Add the day number. In our example, add 12 for January 12: 14 + 12 = 26.
5. Divide by 7 and take the remainder.

   Example: 26 ÷ 7 leaves a remainder of 5. Another way to think of this is to subtract the greatest multiple of 7 less than the current sum: the greatest multiple of 7 less than 26 is 21, so subtract 21 from 26 to leave 5.

6. The remainder tells the day of the week: 0 is Sunday, 1 is Monday, 2 is Tuesday, etc.

   Example: 5 corresponds to Friday, so January 12, 2007, falls on a Friday.

Using the algorithm for the years 1900-1999:

1. For years starting with 19-, use the same algorithm above but add 1 to the final result.

   Another example: April 16, 1995.

   95 ÷ 4 = 23 (ignore the remainder).

   Add 95 + 23 + 5 (the code for April) + 16 (the day) + 1 (to adjust for 1900s) = 140.

   Dividing 140 by 7 leaves a remainder of 0, which corresponds to Sunday.

   April 16, 1995, was a Sunday.

To view Michael Naylor's article on Calendar Math click here.

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.

January, 2007, Vol.37, No.4