A Lesson Plan for the Teachable Moment: THE TWELVE DAYS OF CHRISTMAS AND PASCAL’S TRIANGLE

Created by: Judy Ann Brown LP '92 | Rutgers university Leadership Program: Exploring Discrete Mathematics in the Classroom | http://bit.ly/RI1P3Q

Materials: A copy of Pascal's triangle, colored pencils  Object of the lesson: Using Pascal's triangle, find the number of items given each day in the song, "The 12 Days of Christmas."

 
Content/Procedure:  

	The first (red) diagonal of Pascal's triangle indicates the numbers of new gifts given on the consecutive days.   1 partridge in a pear tree   2 turtle doves   3 French hens   4 calling birds   5 gold rings   6 geese a-laying   7 swans a-swimming   8 maids a-milking   9 ladies dancing 10 lords a-leapin' 11 pipers piping 12 drummers drumming
	The second (green) diagonal of Pascal's triangle indicates the combined gifts given on the consecutive days.   1 = 1 partridge in a pear tree   3 = 2 turtle doves + 1 partridge in a pear tree   6 = 3 French hens + 2 turtle doves + 1 partridge         in a pear tree 10 = 4 calling birds + 3 French hens + 2 turtle doves         + 1 partridge in a pear tree 15 = 5 gold rings + 4 calling birds + 3 French hens         + 2 turtle doves + 1 partridge in a pear tree ...
	The third (yellow) diagonal of Pascal's triangle indicates the total number of gifts given.   1 = 1 partridge in a pear tree   4 = 2 turtle doves + 1 partridge in a pear tree         + 1 partridge in a pear tree 10 = 3 French hens + 2 turtle doves + 1 partridge         in a pear tree + 2 turtle doves + 1 partridge         in a pear tree + 1 partridge in a pear tree 20 = 4 calling birds + 3 French hens + 2 turtle doves         + 1 partridge in a pear tree + 3 French hens         + 2 turtle doves + 1 partridge in a pear tree         + 2 turtle doves + 1 partridge in a pear tree         + 1 partridge in a pear tree ...
	By the fourth day of Christmas you will have received a total of 20 gifts. Look closely at Pascal's triangle - do you see a Christmas stocking? Continue the pattern and see if you can find the cell in Pascal's triangle that shows the total number of gifts given over the twelve-day celebration. You might want to try out Ken Williams' interactive version of Pascal's triangle on the Web.

 

The material in this lesson addresses the following 1989 NCTM (National Council of Teachers of Mathematics) Standards:
• Standard 1: Mathematics as Problem Solving: [K-4] and [5-8]
• Standard 3: Mathematics as Reasoning: [K-4] and [5-8]
• Standard 4: Mathematical Connections: [K-4] and [5-8]
• Standard 6: Number Sense and Numeration: [K-4]
• Standard 7: Computation and Estimation: [5-8]
• Standard 13: Patterns and Relationships: [K-4]

Other Resources:

• Lancaster, Ron, "Media Clips," The Mathematics Teacher, 88 (9), (Dec. 1995), pp. 748-749.
• Raphel, Annette, "Critical Thinking During the December Holidays," The Arithemetic Teacher, 41 (4), (Dec. 1993), pp. 216-219.

For more information, please send mail to Judy Ann Brown, judyann@ptdprolog.net
Web page originallycreated Wednesday, December 10, 1997
updated Friday, December 10, 1999