Leadership Program Exploring Discrete Mathematics in the Classroom

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 Created by: Judy Ann Brown LP '92
 Materials: Student Worksheet, Price Data, Calculators
 Object of the lesson:

Find the total cost of the items in the song, "The 12 Days of Christmas."

 Content/Procedure:

This project is designed to be used as a warmup activity during the 12 days preceding Christmas.

On the first day give the students a copy of the student worksheet. Post the price of the first gift.

Students should understand that they will need to purchase a partridge in a pear tree for each of the 12 days. On the chart students will enter 12 for the number of days given, 12 for the number of gifts needed, the price of one gift item posted by the teacher, the cost of this gift (12 x price), and the total to date.

On the second day 2 turtledoves are given. This gift is given for 11 days, and so 22 doves are needed (2 x 11 = 22). The price of the gift (a pair of turtle doves) is posted by the teacher, and the students then calculate the cost of this gift (22 x price of one dove or 11 x the price of a pair of doves). The total to date will be the sum of the cost for days 1 and 2.

 Teacher Comments:

• Chris Ruda LP'97: I presented the Twelve Days with a concentration on the pattern (n^2+n)/2......and Pascal's triangle. I teach fourth grade inclusion in Dade County Public Schools, Miami, Florida.
• Cathy Micheals LP'97: Love the lesson and my 5th graders really got into a lot of adding and multiplication algorithms.
  Bonus: I'm having the class do a 20-foot-long graph of all the gifts. It's incredible to watch the cooperation going on. Mrs. Micheals needs 2 more French hens, how many lords do we still need?, etc. When it is done we will post it in the hall and add a lot of estimation and computation questions for the school to answer. I'll take a digital picture after vacation and send it to you for posting. The kids and I are having a ball, and it's art, math, graphs, combinatorics, and all wrapped into one bundle.
• Patrick Carney LP'91: Thanks for the posting on the 12 Days. By the way, you mention giving them one a day -- what I did last year was use it in a class studying spreadsheets. I gave students all of the material and they had to create a spreadsheet which figured total number of gifts, total cost, number of gifts each day, gifts to date, amount each day, amoungt to date, etc. From that one little column you provide, we milked it for all sorts of data -- including my favorite -- if she returned them one per day starting the day after Christmas, when would she finish?
• Sue Chapman LP'97 Here are some more activities related to the 12 Days of Christmas.

  From "Celebrate with Mathematics" by Winnie Peterson, Teaching Children Mathematics, November 1994
  The author made Christmas trees of increasing size to illustrate each of the triangular numbers (these numbers represent the cumulative number of gifts given each day of the twelve days of Christmas) She used green balloons stapled onto a bulletin board, but I think I'll try green pattern blocks or die-cut ornament shapes and have students create the trees themselves. She also had groups of students make paper chains with green and red links showing different patterns, including a pattern of triangular numbers. Other students had to decode the patterns shown in the chains.

  Also "Investigating Probability and Patterns with The Thirteen Days of Halloween" by Maryann Wickett, Teaching Children Mathematics, October 1997
  Students investigated the probability of drawing a given gift out of a bag containing all the gifts given over 12 days. The gifts were represented by different colors of unifix cubes. Students made predictions, conducted probability experiments, recorded their data, and looked at patterns in their results.

 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.