Additional Math Pages & Resources

Wednesday, December 12, 2012

The 12 Days of Christmas

Since today's date is 12-12-12 and Christmas is fast approaching, I was reminded of the song, The 12 Days of Christmas. Our family has a brightly-illustrated picture book with the song lyrics that we enjoy reading over again this time of year.

The 12 Days of Christmas is a favorite Christmas carol. There are versions with motions that make it a fun counting song to do with children. We start singing it after Thanksgiving and continue through to Christmas, but the twelve day of Christmas actually refers to the 12 days after Christmas. These are the 12 days between Christmas (the day celebrated as Jesus' birth) and Epiphany (when the wise men  arrived at the home of the little child Jesus).

The poem mentions gifts given on each day over a twelve-day period. The letters in parentheses indicate the abbreviation we'll use for each gift:
On the first day of Christmas, my true love gave to me a partridge in a pear tree (p).
On the second day of Christmas, my true love gave to me 2 turtledoves (t) and a partridge in a pear tree.
On the third day of Christmas, my true love gave to me 3 french hens (f), 2 turtledoves and a partridge in a pear tree.
On the fourth day of Christmas, my true love gave to me 4 calling birds (c), 3 french hens, 2 turtledoves and a partridge in a pear tree.
On the fifth day of Christmas, my true love gave to me 5 gold rings (gr, 4 calling birds, 3 french hens, 2 turtledoves and a partridge in a pear tree.
On the sixth day of Christmas, my true love gave to me 6 geese a-laying (gl), 5 gold rings, 4 calling birds, 3 french hens, 2 turtledoves and a partridge in a pear tree.
On the seventh day of Christmas, my true love gave to me 7 swans a swimming, 6 geese a-laying, 5 gold rings, 4 calling birds, 3 french hens, 2 turtledoves and a partridge in a pear tree.
On the eighth day of Christmas, my true love gave to me 8 maids a milking (m), 7 swans a swimming, 5 gold rings, 4 calling birds, 3 french hens, 2 turtledoves and a partridge in a pear tree.
Now that you get the idea, we can skip ahead to the gifts given on the twelfth day:
On the twelfth day of Christmas, my true love gave to me 12 drummers drumming (dd), 11 pipers piping (pp), 10 lords a leaping (ll), 9 ladies dancing (ld), 8 maids a milking (m), 7 swans a swimming (s), 5 gold rings (gr), 4 calling birds (c), 3 french hens (f), 2 turtledoves (t) and a partridge in a pear tree (p).
The first day the true love gives a gift of a partridge in a pear tree. The second day's gifts include another partridge and tree plus two turtledoves. The third day brings yet another partridge and pear tree, two turtledoves, and three french hens. By the end of the 12 days, the poor lover has received 12 partridges in pear trees, 22 turtledoves, 30 french hens, etc.  It sounds like a zoo (literally). Can you figure out the total of each item given by the end of the 12-day period?

Each day, a new gift is given, plus all the gifts from the previous day are given once again. We can put together a mathematical equation to represent the total gifts, using the abbreviations shown above for each gift: 12p + 11(2)t + 10(3)f + 9(4)c + 8(5)gr + 7(6)gl + 6(7)s + 5(8)m + 4(9)ll + 3(10)ld + 2(11)pp + (12)dd


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Now back to our twelve days of Christmas math. The first number indicates the days the gift was given (12 days for the partridge, 11 for the turtledoves, etc.) and the number in parentheses indicates the quantity of that gift given each day (1 partridge, 2 turtledoves, 3 french hens, etc.) Over the 12 days of Christmas, the true love would give:
12 partridges and pear trees
22 turtledoves
30 french hens
36 calling birds
40 gold rings
42 geese laying eggs
42 swans
40 maids and cows
36 lords
30 ladies dancing
22 pipers with pipes
12 drummers with drums

Notice the pattern. There are 12 each of partridges and drummers, 22 each of turtledoves and pipers. So the easiest way to count the gifts is to add the first half of the list and then multiply it by two:
12 + 22 + 30 + 36 + 40 + 42 = 182
182 x 2 = 364
There are a total of 364 gifts given in this song (not counting the additional items such as pear trees, drums, pipes, cows, etc.)

If you'd like to hear a new slant on this old favorite, you might enjoy "The 12 Days After Christmas" written by Frederick Silver in 1968. It begins, "The twelve days after Christmas, my true love and I had a fight. And so I chopped the pear tree down and burned it just for spite!" Listen to the Desert Chorale perform the song:

Then download the sheet music (http://www.musicnotes.com/sheetmusic/mtdFPE.asp?ppn=MN0089151) for a fee and sing it through yourself for a good laugh (you can even transpose it to the key of your choice).

Whichever version you prefer, take some time to enjoy this once-in-a-lifetime day of 12-12-12. Sit back, relax, and read one of the following books about twelve:
The Twelve Days of Christmas
The Gershwins and Me: A Personal History in Twelve Songs
Twelve Angry Men
Polar Bears Past Bedtime (Magic Tree House #12)
Twelfth Night
The Labours of Hercules: Twelve Hercule Poirot Mysteries
The Twelve Tribes of Hattie
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