A MATHEMATICAL FINISH FOR 1976Author(s): HELEN CUNNINGHAMSource: The Mathematics Teacher, Vol. 69, No. 8 (DECEMBER 1976), pp. 688-690Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27960662 .

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A MATHEMATICAL FINISH FOR 1976

Mathematical decoding to celebrate the nation s 200th birthday.

By HELEN CUNNINGHAM

University of Louisville

Louisville, KY 40208

THOMAS Jefferson, Benjamin Franklin, 1776, the thirteen colonies, and the Decla ration of Independence with its fifty-six signers have become quite familiar to stu dents in this Bicentennial year. No longer is

July 4, 1776, considered just the first na tional holiday, but it has become a mean

ingful event as well, which involved many ideas and many people. Students' knowl

edge of the early history of the United States has increased during this year of cel ebration.

Mathematics teachers can capitalize on students' newly acquired historical knowl

edge of, and interest in, 1776 and can create

exciting activities involving numbers and events of that year. A Bicentennial code can be designed that will be a springboard for various drills. In the example given, well known facts are used. After working with an exciting Bicentennial code, students en

joy making others of their own. Older pu pils will create more difficult and challeng ing codes.

Equations from the code can be used to check assigned values and determine un known ones. The total number of equations given might be seven, four, thirteen, or

another number associated with 1776. In this example, every letter of the code except

W is used in thirteen equations.

1. 2. 3. 4. 5. 6. 7.

BK = F

Q + U = AH =

2 =

H + I = G AE = L M + J = M

8. DV2 = S R 9. BD = X

10. + A =

11. Z + U = F 12. C + K =

13. DN = Y

Since this code is designed for use in addition and multiplication excercises, val ues for the vowels are small. The intended uses of the code, the mathematical back

ground of the pupils, and the time available should determine the structure of the code.

Students like to find the value of their names in a code. This could lead them to

finding the sum of the values of the letters in their names. From lists containing stu dents' names and their code values, activi ties can be designed to label primes, com

posites, palindromes, multiples of a

specified number, or factors of 1776, 56, or another Bicentennial number. Name-code values can be combined with 1776,13, or 56 for addition, subtraction, or multiplication problems.

To incorporate the early history of the nation, the teacher can use names of patri ots, signers of the Declaration of Independ ence, colonies, events, or places of 1776 in

interesting exercises. For example, let each student select the names of several signers and guess which will have the largest value

by addition. After those calculations are

made, the code value of the colony repre sented by the signers can be combined with the value of the signers' names in a variety of problems. For example, a student who selects Richard Henry Lee and George

Wythe from Virginia and uses this example code will probably guess that George

Wythe's name has the larger value, since it contains W. The sum of 347 for Richard

Henry Lee can be used with George Wythe's value of 1959 in a subtraction, ra

tio, or percentage problem. Using those values with 120 for the colony of Virginia's sum can result in excercises involving sub

traction, addition, and multiplication. A variety of problems using the code

688 Mathematics Teacher

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A Bicentennial Code

A = The number of original colonies with thirteen letters in their names.

= The number of the month in which the Declaration of Independence was

adopted. C = The number of original colonies. D = The number of original colonies hav

ing names beginning with "New." E = The number of persons on the com

mittee that drafted the Declaration. F = The number of signers of the Decla

ration.

G = The number of letters in the name of the colony where the Declaration

was signed. H = The number of letters in the first

signature of the Declaration. I = The number of sentences in the first

paragraph of the Declaration. J = The number of times the name of

George III appeared in the Declara tion.

= The number of letters in the day of the week on which the Declaration was adopted.

L = The number of letters in the name

of the person who wrote most of the Declaration.

M = The century in which the Declara tion was written.

= The number of letters in the name

of the elder statesman on the com

mittee that drafted the Declaration. O = The day of the month on which the

signing of the Declaration is cele

brated. = The age of Thomas Jefferson in 1776.

Q = The age of Benjamin Franklin in 1776.

R = The year during the 1700s in which the Declaration was signed.

S = The number of years designated by "bicentennial."

= The sum of the digits of the year in which the Declaration was written.

U = The number of white stripes in the

Grand Union Flag of 1776. V = The number of letters in the last name

of the commander of the Continental

Army. W = The year the colonies declared their

independence. X = The sum of the letters in the last

names of the Declaration signers who

later became president of the United States.

Y = The sum of the number of the month,

day, and the digits of the year in

which the Declaration was adopted. = The number of years after 1776 that

two Declaration signers died on

July 4.

with historical material and Bicentennial numbers will enliven drill work:

PAUL REVERE + 1776 BOSTON X 13 PHILADELPHIA X 56 INDEPENDENCE -r 7

(234 + 1776) (252 X 13) (133 X 56) (119-5-7)

Problems such as BELFRY + LAN

TERNS or TEA X PARTY + INDIANS will inspire students to suggest others that reflect events or facts of history that interest or amuse them.

Division problems can be designed using

code values. Examples can range from

simple one-digit divisors to more difficult ones. Abbreviations of the names of the colonies or initials of patriots can be used as divisors. Their values can be calculated

by addition or multiplication, depending on the letters involved. Dividends can in

clude names of signers, places, events, or

quotes from that famous year, 1776. Creative students will design statistical

work with code values. Calculations of the

mean, mode, and median, as well as graph ing, can use historical information for de

termining values.

December 1976 689

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When students find working with codes to be exciting, they will challenge each other with problems. For instance, "Which motto has the greater code value: 'CO

LONISTS, UNITE NOW' or TIGHT FOR FREEDOM'?" Creative ideas will evolve as students use the codes.

As the Bicentennial year draws to a close, capitalize on students' historical knowledge and their interest in codes. Make routine drill more exciting with varied uses of a Bicentennial code. End 1976 with a mathe matical bang!

(Answers to "Bicentennial Code Values"

appear on p. 645.)

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690 Mathematics Teacher

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