Roman Numerals Are Still Alive

We started class looking at some of my pictures from my trip to Rome and Pompeii where we looked at ancient buildings like the Colosseum and the Pantheon to works of art by Michelangelo (the Pieta, the Moses, Christ standing, the Sisteen Chapel’s  Last Judgement and ceiling) and Raphael’s School of Athens (with zoomed snapshots of mathematicians we have studied such as Plato, Euclid, and Pythagorus,  as well as inventions by Leonardo da Vinci. Since the entrance to the Colosseum had a carved LII, we studied the ancient use of numbers.

Roman Numerals were used in Europe until the 18th century and even today in certain applications. Generally the only place we see them today is an alternative way of expressing a given Natural Number such as year, or hour on a clock, a chapter in a book, Olympic number or Superbowl number.

Roman Numerals are not a positional system and contain no symbol of zero. Rather, they are an additive system with each symbol taking on a definite numeric value regardless of where it appears. Actually there six subtractive rules that makes writing a value somewhat more compact that do depend upon position relative to another symbol.

The symbols and their values are:

I = 1

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1,000

We had a very rich discussion in class about why the number 100 is represented by a “C” and why 1,000 is represented by an “M.” Even though there is not a lot of evidence for the origin of the seven Roman numerals, we came up with several examples the of the Latin stem centum (century is a100 years, a dollar has 100 cents, a centipede has 100 legs) which means one hundred and mille (there are 1,000 millimeters in a meter, there are 1000 years in a millennium) which means one thousand. 

Of course, the children wanted to know the origin of the V, X, L, and D, so we came up with some theories of a hand makes a V shape with five fingers and an X is two Vs inverted with one upside down. There is no evidence for this but it was fun to observe the creativity of the children in trying to solve these problems.

The table can be extended to larger values by using the convention that a horizontal bar over a symbol indicates "1000 times:”

I = 1,000

V = 5,000

X = 10,000

L = 50,000

C = 100,000

D = 500,000

M = 1,000,000

For our purpose we will generally utilize values that are sufficiently small to be written without the "barred" symbols.

While a particular symbol takes on a given value regardless of its position, it is customary to write the number from left-to-right with the "largest" symbols first.

A Roman value of, as an example: DCCLXVII

would be:

500 + 100 + 100 + 50 + 10 + 5 + 1 + 1 = 767

The Romans used equivalence rules to shorten these expressions. There was no use for VV since we had X, no use for LL since we had C, and no use for DD because we had M. In all cases, by applying the equivalence rules to shorten the expression by replacing several symbols with one we would get IV to represent 4, IX for 9, XL for 40, XC for 90, CD for 400, and CM for 900. The children found this pattern before I told them by looking at 1, 5, 10, 50, 100, 500, 1000 and subtracting one from each of the last six. 

My challenge page in the first attached document includes a question asking for the largest Arabic number (these are the numbers we use today with the digits 0-9) with the most subtractions without the use of the horizontal bar. It would be MMMCMXCIX for 3,999. 

The largest Arabic number with the most Roman numerals without the horizontal bar would be MMMDCCCLXXXVIII or 3,888. 

I provided several worksheets where they could look at Roman numerals on actual buildings and convert them into Arabic numbers such as the Statue of Liberty with the date July IV, MDCCLXXVI or July 4, 1776, for the date of America’s independence.

Another worksheet allows the children to explore several conversions from Arabic numbers to Roman numerals and vise versa.

Finally, I gave them the attached list of historical events from the year 9 AD to the year 1600 AD and they can convert those to Roman numerals. I have also attached a solution key created by first grade Mathlete, Adrian.