TITLE: ROMAN NUMERALS
AUTHOR: BESS KUZMA, ST.PIUS X SCHOOL,
AURORA, COLORADO
GRADE AND SUBJECT AREAS: This material is appropriate
for grades 5-8, but could be adapted to the needs of
older or younger students. Though it is designed for
math, it might be supplementary study for history or
world cultures.
OVERVIEW: Roman numerals are no longer an essential
component of math, but need to be considered as a part
of our cultural heritage.
PURPOSE: Students are fascinated by the "secret code"
aspect of Roman numerals. It can easily be integrated
into a study of addition and subtraction, or world
number systems.
OBJECTIVES:
1. Recognize Roman numerals as such when students see
them.
2. Identify each symbol and what it stands for in
Arabic numbers:
I - 1
V - 5
X - 10
L - 50
C - 100
D - 500
M - 1000
3. Generally understand the source of each symbol.
(See background information under RESOURCES)
4. Be able to transfer Roman numerals into Arabic
numbers.
5. Be able to write the correct Roman numerals for
Arabic numbers.
6. Have an appreciation for the historical value of
Roman numerals, how they were used in the Roman
Empire, and why they are no longer commonly used.
ACTIVITIES AND PROCEDURES:
1. Discuss the history of Roman numerals, using
charts, photos, pictures, or whatever resources
are available.
2. Have students make individual charts, showing each
symbol and its equivalent in Arabic numbers.
3. Discuss the addition/subtraction aspects of the
system, and have the students practice. Give each
student 20-30 toothpicks, (the flat type), and
form the Roman numerals for given Arabic numbers.
For example, you might start with 106. Have the
students make this,( CVI ), then have them change
it to 206,( CCVI ), then 266, ( CCLXVI ) then 466,
( CDLXVI ) etc,etc.
4. Have students write Roman numerals of family
members' birth years, or the number of students in
the school, or other large numbers of interest to
them.
5. Let each student bring in an example or picture of
Roman numerals (book preface paging or chapter
numbers, watch or clock, building erection date,
statue or monument, outline topic numbers, etc.)
6. Read books, articles, and encyclopedia entries
about Roman numerals. Library skills could easily
be incorporated.
RESOURCES/MATERIALS:
BACKGROUND:
Roman numerals were developed around 500 B.C. at
least partially from primitive Greek alphabet symbols
which were not incorporated into Latin. Using
predominantly addition, they are read from left to
right.
The symbol "I" for 1 was derived from one finger.
Five fingers held up indicated five of whatever was
being counted. The "V" then was the hand outstretched
vertically with the space between the thumb and first
finger forming the "V".
Originally the Greek letter "X", or "chi", meant
50, but in monument transcriptions it is easy to trace
the original symbol's change to "L", and "X" came to
mean 10. Another theory for "X" is that ten 1's were
written in a row, and then crossed out with an "X" to
simplify counting. Then the "X" alone became a
shorthand version of 10. Yet another idea is that "V"
looks like the top half of "X", as 5 is half of 10, and
other scholars think that "V" doubled with an
upside-down "V" meant 5 times 2, or "X". "C",
indicating 100, came from the Latin word "centum", a
hundred. (Also century, centennial, etc.) "M" is from
"mille", a thousand. Larger numbers, like 5,000, are
shown by putting a small bar called a "vinculum" above
the "V" symbol, indicating multiplication by 1,000.
Until fairly recently a commonly used Roman
numeral for 1,000 was "CI backwards C", derived from
the Greek "phi", or "I" superimposed on "O". Half of
this symbol, "I backwards C", led to "D" for 500, half
of 1,000.
Generally, decoding Roman numerals is very
straightforward. The largest numeral is at the left,
with descending numerals moving to the right. Numbers
are added as you go, as seen in these examples: CCLXVII
- 200 + 50 + 10 + 5 + 1 + 1 = 267 MMMCCLXXXI - 1,000 +
1,000 + 1,000 + 100 + 100 + 50 + 10 + 10 + 10 + 1 =
3,281 and DCCXVII - 500 + 100 + 100 + 10 + 5 + 1 + 1 =
717.
Rather than continuing to add 1's to make 4 -
"IIII" - or 9 - "VIIII" - subtraction was included in
the computation of the numerals to simplify and shorten
the resulting numbers. Therefore, 4 is shown "IV", or
5 minus 1. The smaller numeral BEFORE the larger one
means subtract. "IX" is 9, or 10 minus 1. 40 is "XL",
50 minus 10; 90 is "XC", 100 minus 10; "CD" is 400, or
500 minus 100; and "CM" is 900, or 1,000 minus 100.
Students can follow the principle that subtraction
takes place ONLY when the smaller numeral is before the
larger one, and involves 4 and 9 in various place
values.
Obviously, the cumbersome aspect of Roman numerals
is one of the main reasons that they have been replaced
by the Arabic system in our daily mathematical lives.
Roman numerals remain important as a part of the
world's cultural past, and a unique way to express
numbers.
REFERENCES: Most encyclopedias have at least some
information on Roman numerals, and several books on
Roman numerals are appropriate for students. Three
suggestions:
"Number Art - Thirteen 1 2 3's from around the
world", by Leonard Everett Fisher, published by
Four Winds Press, NY, is a fairly sophisticated
overview of world numerical systems.
"Signs and Symbols Around the World", by Elizabeth
Helfman, published by Lothrop, Lee & Shepard Co,
NY, has a chapter on numerals of many cultures.
There is a very short section on Roman numerals,
but a great deal of general information about
counting and mathematics applications throughout
the world.
"Roman Numerals", by David A.Adler, published by
Thomas Y.Crowell Co, NY, is a much simpler book,
but suitable for younger students.
TYING IT ALL TOGETHER: Many alternatives are possible,
depending upon allotted time for the unit, relative
importance of the material in the curriculum, and the
age of the students. Actual buildings or monuments
could be visited, reports, games, or testing to
ascertain student achievement are all possibilities.
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John Kurilecjmk@ofcn.org