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You Don’t Need a Toga to Learn Roman Numerals
The Roman number system is both a base 10 and hieroglyphic character system at the same time. This is always a good system to teach children. It helps to dress the part and have a day couch when introducing this topic. It is amazing how a bit of theatrics can make learning something seen as “weird” or “geeky” memorable. Those teaching in a module style learning environment can link history, literature, politics and any other aspect of human learning together with this unique and still used number system. One still can find Roman numerals as the copy write date on movies and TV shows.
Most of mankind’s Mathematical knowledge was based on counting. It is only recently when we replaced hieroglyphic characters with symbols that assume values by a devised place arrangement. We invented symbols because we had to count. It’s not as though we were sitting around in our dirt floor huts with an oil lamp computing the distances between stars or even just doing multiplication tables. We were counting the number of eggs the hens laid that day and trying to figure out what we could exchange for them.
This was mankind’s lot. We had to know what we owed relative to the limited supplies available for barter. We had to know a relative value for what we owned. So, most of our existence was counting. In fact some of our early symbols were based on common everyday items. We invented many different symbols that stood for individual to large amounts. Unfortunately these symbols were not based on placement value. This made doing even addition and multiplication a difficult process.
The Roman hieroglyphic number system is a bridge between the old counting hieroglyphs and the newer symbol placement value system. Fortunately, Roman numerals can be reproduced in a Word document using a modern keyboard. You don’t even have to know what the special keystroke is to find special characters. This is one very good reason learning to use Roman numbers is an ideal number system to study. Not only is this another way for students to learn addition and multiplication in a now untraditional method to supplement current methods it is also a way to keep alive our roots. It is a way to understand how ancient peoples viewed their world.
Roman numerals are base 10. This removes a stumbling block from the learning process. You would have glassy eyes on even your brightest student’s faces if you tried to use Babylonian Base 60 hieroglyphs and system. The Roman number system is enough of a challenge for younger students.
These ancient Mathematical techniques should not be forgotten. They developed as mankind learned and developed. It is a natural process. I see this process of solving in students today. They had no idea that the techniques they were using were as old as man.
Students need to be able to grasp just exactly what a number is. We rush many students too quickly into the rarefied ethers of modern symbolism. We need to slow down and let children learn numbers the same way we did as a new conscious species. That is why including these old methods of understanding should be included in our modern world.
Understanding How to Use the Roman Number System
Numbers were arranged so that the symbol for the largest value was furthest left. The next largest value symbol comes to the right of the first symbol. Keep adding symbols until the symbol with the smallest value is furthest right. XXIII is 2 tens and 3 ones to a loyal Roman citizen or 23 in our modern language. LXI would be 50 and 10 and 1 or simply 61.
A smaller symbol to the left of a larger valued symbol was a shorthand technique used in a specific way. IV means 1 less than 5 or 4 = IIII. XC means 10 less than 100 which would be LXXXX or 90. Romans would technically have written this as LXL instead of LXXXX. These people did not put more than one smaller symbol before another. They did not write XXC which could be interpreted as 2 tens less than 100. No, they would write 80 as LXXX. Shorthand went so far, otherwise it becomes just as hard to figure out what number one intended than if there wasn’t a short hand technique.
Adding with Roman Numerals
Adding two Roman numbers together is not much different than how we do it today. One still adds the smallest elements together first and progresses to the larger. I always found that it was just as easy to put everything all together and then replace unacceptable combinations with the proper ones. For example let’s add CXLVII and LXXXVII. I first replace the XL with an unapproved XXXX to avoid later confusion. Our problem becomes CXXXXVII + LXXXVII = CLXXXXXXXVVIIII. The first thing I notice is that LXXXXX is another C. So our first simplification becomes CCXXVVIIII. The next thing I notice is that VV is really X. Our second simplification becomes CCXXXIIII. The last thing I notice is that IIII is usually written as IV. Our addition reduces down to CCXXXIV. As you can see addition just becomes a matter of replacing poor symbols notation with a more concise group of hieroglyphs much as one would arrange their loot when playing Monopoly.
Another way to add two Roman Numbers together is this way. It uses a borrowing/replacing system sort of similar to subtraction methods today. Using this way lets the scribe reduce his symbols in one step instead of the three it took me earlier.
CXL V II
+ L XXX V II
So the IIII = IV
2 V’s = X
2 L’s = C
The one X to the left of the C cancels 1 X on the right of C.
That means we end up at the same place CCXXXIV.
Multiplying with Roman Numerals
Multiplying is a bit harder. I recently posted a hub about how the Egyptians multiplied. Because the Roman numeral system is not quite like our own Base 10 numeral system it is best to multiply like the Egyptians. This method was ancient by the time of the Romans. It was known to be infallible. I imagine this way was the method used by the Romans too.
Let’s multiply XXII by XXXI. This works out to look like this
I = XXXI
II = LXII
IV = CXXIV
VIII = CCXLVIII
XVI = CDXCVI
Since XVI + IV + II = XXII then the proper right hand sum is CDXCVI + CXXIV + LXII = DCLXXXII
A Final Plea
I hope you get an idea that thinking out of the box. All Mathematicians solve problems differently. I spend as much time reading through the logical process for how a student solves a problem as I do any other part of the teaching process. Teaching students to solve problems the way they understand them is part of the process. Yet, I never discourage any student their own method. Plus I like to learn new methods myself. It helps me to understand more fully what it is we do when we solve a similar problem. That’s what it is I feel it means to be a teacher.
I want to encourage you to teach your students methods and processes for solving problems that may not be the direct sterile symbolic way we have come to distill down to the modern basic level. I want to encourage you to take the time to show students alternate ways of thinking. I challenge you to teach students how we as a species once processed information. We need this variety. We need to include ancient methods so that students can “feel” or actually count objects the way we used to do. It is more than just preserving past knowledge. It must have been easily understood if we used the same methods for thousands of years. Some people need to have alternate processes for the proverbial lightning bolt to strike.