Pascal's Triangle   Leadership Program

Exploring Discrete Mathematics
in the Classroom

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The Twelve Days of Christmas
and Pascal's Triangle

stocking Created by: Judy Ann Brown LP '92
stocking Materials: A copy of Pascal's triangle, colored pencils
stocking Object of the lesson:
stocking Content/Procedure:

Pascal's Triangle 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
 
Pascal's Triangle 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
    ...
 
Pascal's Triangle 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
    ...
 
Pascal's Triangle 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.

stocking Mathematical Content:

stocking Other Resources:

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

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