Leadership Program
Exploring Discrete Mathematics

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Lesson Ideas
Created by: Judy Ann Brown LP '92Materials: Copy of New Year's Magic Worksheet, Pencil, Scrap Paper
Object of the lesson:
Follow the directions to find the sum of 6 cells in the magic array.Content/Procedure:Give each student a copy of the New Year's Magic Worksheet.Enrichment: Suzanne Alejandre's Web Unit Magic SquaresIf students follow the directions correctly they will have one number circled in each row and column. The sum of the circled numbers will be 1998.
After students compare their answers with those found by others in the class they should be encouraged to look for patterns. Consider how the array would need to be changed to produce the answer 1999 or 2000.
For more information on how the magic array was created see The Math Behind The Magic.
Mathematical Content:
The material in this lesson addresses the following NCTM Standards:
Teacher Comments:
 Erica Voolich LP'94: When I do this with my students it is for the Jewish New Year in the Fall (since I teach at a Jewish school), but I spend most of the class having the students figure out why it works and building their own. The 7th graders can follow the algebra involved in a "proof" and can see it work with numbers.
Other Resources:
 Voolich, Erica, "Magic Squares," The Elementary Mathematician, Volume 8, Number 4, (Fall 1994).
For more information, please send mail to Judy Ann Brown, judyann@forum.swarthmore.edu
Web page created Wednesday, December 10, 1997
updated Friday, December 10, 1999