Planning 9
The lesson plan for Grade 8 Math that I have chosen deals with Roman numerals. The lesson objectives are as such:
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.
4. Be able to transfer Roman numerals into Arabicnumbers.
5. Be able to write the correct Roman numerals for Arabic numbers.
6. Have an appreciation for the historical value ofRoman numerals, how they were used in the RomanEmpire, and why they are no longer commonly used.
Roman numerals emerged and were developed around 500 B.C. atleast partially from primitive Greek alphabet symbolswhich were not incorporated into Latin. Using mostly addition, they are read from left toright.
The symbol "I" for 1 was derived from one finger. Five fingers held up showed five of whatever wasbeing counted. The "V" then was the hand held vertically with the space between the thumb and firstfinger forming the shape of a "V".
At first the Greek letter "X", or "chi", meant50, but in monument transcriptions it is simple to track the original symbol's change to "L", and "X" then started tomean 10. Another tangible theory for "X" is that ten 1's werewritten in a row, and then crossed out with an "X" to make counting easier. Then the "X" alone became ashorthand version of 10. Yet another idea is that "V"looks like the top half of "X", as 5 is half of 10, and still other scholars believe that "V" doubled with anupside-down "V" meant 5 times 2, or "X" (which is actually the same the other way around) "C",indicating 100, came from the Latin word "centum", a hundred. (we also find this root in wordscentury, centennial, etc.) "M" is derived from"mille", a thousand. Larger numbers, like 5,000, areshown by putting a small bar called a "vinculum" abovethe "V" symbol, indicating multiplication by 1,000.
Until fairly recently a commonly used Romannumeral for 1,000 was "CI backwards C", which originated fromthe Greek "phi", or "I" superimposed on "O". Half ofthis symbol, "I backwards C", led to "D" for 500, halfof 1,000.
In general, decoding Roman numerals is verystraightforward and does not pose special difficulties. The largest numeral is at the left,with descending numerals moving to the right. Numbersare added as you move in the right-hand direction, 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.
Another principle to remember is subtraction. Rather than continuing to add 1's to make 4 -"IIII" - or 9 - "VIIII" - subtraction was included inthe combination of the numerals to make the resulting numbers simpler and shorter. Therefore, 4 is shown "IV", or5 minus 1. The smaller numeral before the larger onemeans subtract. "IX" is 9, or 10 minus 1. 40 is "XL",50 minus 10; 90 is "XC", 100 minus 10; "CD" is 400, or500 minus 100; and "CM" is 900, or 1,000 minus 100.Students can follow the principle that subtractiontakes place only when the smaller numeral is before thelarger one, and involves only 4 and 9 in various placevalues.
It is obvious that the cumbersome aspect of Roman numeralsis one of the principal reasons that they have been replacedby the Arabic system in our daily mathematical lives. Still, Roman numerals remain important as a part of theworld's cultural past, and a unique way to express numbers, and they should be learned as part of the Math program.
The next task was to come up with four learning aids to facilitate the process for students and make the lesson appealing to them.
Worksheet. Students are given worksheets with Arabic numerals and corresponding Roman numerals – first simple, and then compounded. Following the teacher’s explanation, they follow the patterns of numerals formation and get the idea of converting Roman numerals into Arabic ones.
An instructional game. Students are divided into groups of two to four people. Each team is given a sheet with 10 Arabic numerals and twenty to thirty flat toothpicks. The students’ task is to form Roman numerals out of Arabic numerals listed using the toothpicks. The team, which finishes first and makes no mistakes in converting, wins.
A quiz. A 10-question quiz should contain 5 practical questions on transferring Arabic numerals into Roman ones and vice versa and also some questions of the kind “Where can you spot Roman numerals still used?” (for example, clocks, books, monuments etc.). A question on the history of Roman numerals can be added as a bonus question.
A web site for student use. The site dedicated to Roman numerals is located at the address It contains the rules of Roman numerals formation and also has a handy window, which converts Roman numerals into Arabic ones and vice versa. Thus the students can check their knowledge and train conversion from one numerical system to the other. This page is a part of site dedicated to Roman culture, and there the students can also find a lot of useful and interesting information pertaining to this topic, such as facts about Roman names, Roman virtues and philosophy etc.
References
- OFCN’s Academy Curricular Exchange – Mathematics. Last updated: August 24, 2005. Date accessed: April 22, 2007. <
- Roman Numerals. Last updated: September 15, 2004. Date accessed: April 22, 2007. <