Letters, Not Numbers: Roman Numerals

Lesson Plan - Get It!

Audio:

In ancient Rome, they used Roman numerals for counting (make sense?).

Roman numerals use seven values for counting. Roman numerals are used in textbooks, football games, clocks, and on statues to represent years. The Roman numeral system is a number system that uses letters instead of numbers to represent values. The list below shows the numerals of the Roman numeral system:

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100
• D = 500
• M = 1,000

One fun way to remember the order of Roman numerals is to remember this sentence:

I Value X-rays. Let's Count the Doctor's Money. The first letter of each word represents the order in which we should remember Roman numerals. The number 0 does not exist in Roman numerals. There is no letter that represents 0.

How to write numbers in Roman numerals

If the value can be represented by one letter, then only that letter is used. For example, to show the value 5, use V, and to show the value 100, use C.

Otherwise, special rules need to be followed. Here are the rules for writing Roman numerals:

Rule 1 When the larger value is written first, followed by the smaller value, then add the values.

Find the value for VII.

The first Roman numeral, V, has a value of 5. The Roman numerals that follow, II, have a smaller value of 2, so add the values:

• V = 5
• I = 1
• I = 1
• 5 + 1 + 1 = 7
• VII = 7

Rule 2 When the smaller value is written first, followed by the larger value, then subtract the values.

Find the value for IX.

The first Roman numeral, I, has a value of 1. The Roman numeral that follows, X, has a larger value of 10, so subtract the values:

• I = 1
• X = 10
• 10 - 1 = 9
• IX = 9

Rule 3 The capital letters I, X, C, and M are the only letters that can be repeated. Think of these values as powers of 10.

• I = 1
• X = 10
• C = 100
• M = 1,000

If you wanted to represent the value of 100, you would use C. The letter L cannot repeat. Even though L=50, you cannot use LL to represent 100. Only the Roman numerals I, X, C, and M, can be repeated.

Rule 4 The letters, I, X, C, and M cannot repeat more than three times in a row.

XIII would mean 10 + 1 + 1 + 1, which is 13.

VIII would mean 5 + 1 + 1 + 1, which is 8.

If you wanted to show the value 9, you would use the subtraction method. IX means to take 1 away from 10 to get 9.

XX means 10 + 10 = 20.

XXX means 10 + 10 + 10 = 30.

But how would you write 40? It cannot be XXXX because you cannot repeat the letter more than three times, so you will need to use the subtraction method.

XL means 50 - 10, which equals 40.

If we have larger numbers, the same rules apply:

• LX = 60
• LXX = 70
• LXXX = 80

How would you write 90? Discuss with an adult or teacher.

You cannot write LXXXX, so you would write XC, which is 100 - 10 = 90.

Roman numerals can be used to represent years. How would you write the year 1969 in Roman numerals?

Break it into smaller pieces. Since the numbers represent numbers in a base ten system, break the number into the following:

• 1000 + 900 + 60 + 9
• 1000 = M
• 900 = CM, showing that 100 less than 1,000 is 900.
• 60 = LX, 50 + 10
• 9 = IX, showing that 1 less than 10 is 9.

Now, write the Roman numerals in order to represent the number broken into smaller pieces:

MCMLXIX.

Before moving on, watch How to Read Roman Numerals, from Socratica Kids, to see more examples. After the video, discuss these questions with an adult or teacher:

• How are Roman numerals used differently from our number system?
• How would you show the value 80 using Roman numerals?

Prepare to practice identifying and writing Roman numerals in the Got It? section with some interactive activities and games.