Reading and writing Roman numerals
The seven symbols, the addition rule, subtractive notation, and reading Roman numerals in the real world
About three lessons of 45 to 60 minutes
You already read Roman numerals every day, you just might not notice
Roman numerals look old-fashioned, but they never really went away. They are on the clock in the hallway, on the copyright line at the end of a movie, in the name of a king or queen, and in the name of the Super Bowl. Once you know the seven symbols and two rules, you can read every standard Roman numeral from 1 to 3999.
Unlike the numbers you write every day, Roman numerals do not use place value at all. There is no ones column or tens column, just symbols added together or, in six special cases, subtracted. That is what makes this topic different from anything else in this unit's grade range, and also what makes it fun: it is really a small, closed puzzle with only seven pieces.
- The numbers on a clock facemany clocks print IIII instead of IV for 4; visual balance with VIII is one common explanation for this traditional clockmaker's form
- The front pages of a booka preface or table of contents is often numbered in lower-case Roman numerals (i, ii, iii) before the main chapters start at page 1
- The names of monarchs and popesQueen Elizabeth II is read 'the second', and Pope John Paul II is read the same way
- The Super Bowlthe NFL introduced Roman numerals with Super Bowl V and applied them to the earlier games; Super Bowl 50 was a one-year exception that used '50' instead of L
What students will be able to do
Students will recall the value of each of the seven Roman numeral symbols, apply the addition rule for symbols written largest to smallest, apply the subtractive rule for the six subtractive pairs, and convert whole numbers from 1 to 3999 to and from standard Roman numerals, including numbers that require combining both rules.
- I can recall the value of each of the seven Roman numeral symbols: I, V, X, L, C, D and M.
- I can add symbols written largest to smallest to find the value of a Roman numeral.
- I can name the six subtractive pairs and use them to write numbers like 4, 9, 40 and 90.
- I can convert a whole number into a Roman numeral, and a Roman numeral into a whole number, even when both rules are needed in the same numeral.
- I can explain why Roman numerals have no symbol for zero.
Standards this unit teaches
- Year 3 Maths: MeasurementUK National Curriculum (England)Read analogue clocks with Roman numerals
Statutory requirement (Department for Education, "National curriculum in England: mathematics programmes of study", updated 28 September 2021, Year 3, Measurement): pupils should be taught to tell and write the time from an analogue clock, including clocks using Roman numerals from I to XII.
- Year 4 Maths: Number and place valueUK National Curriculum (England)Read Roman numerals to 100
Statutory requirement (Department for Education, "National curriculum in England: mathematics programmes of study", updated 28 September 2021, Year 4, Number and place value): pupils should read Roman numerals to 100 (I to C) and understand that numeral systems changed over time to include zero and place value.
- Year 5 Maths: Number and place valueUK National Curriculum (England)Read Roman numerals to 1,000
Statutory requirement (Department for Education, "National curriculum in England: mathematics programmes of study", updated 28 September 2021, Year 5, Number and place value): pupils should read Roman numerals to 1,000 (M) and recognise years written in Roman numerals.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
- Place valueknowing what a digit is worth in our number system makes it clear why Roman numerals work in a completely different way
- Comparing numbersdeciding whether one symbol is bigger or smaller than its neighbour is exactly what drives the subtractive rule
- Additionthe addition rule is literally adding the value of each symbol in a Roman numeral, largest to smallest
Words to teach and display
- Roman numerals
- a number system that uses the letters I, V, X, L, C, D and M instead of digits
- Symbol
- one of the seven letters used to build a Roman numeral
- Additive notation
- writing symbols largest to smallest and adding their values, such as VIII = 5 + 1 + 1 + 1
- Subtractive notation
- writing a smaller symbol directly before a larger one to mean subtract, such as IV = 5 - 1
- Place value
- a base-ten system where a digit's value depends on its position, the system Roman numerals do not use
Teach it: symbols, rules, then practice
This is a rules-and-symbols topic, not a concrete-pictorial-abstract build like fractions or place value: there is no physical model to construct, only seven symbols and two notation rules to learn correctly and then apply in both directions. Teach the symbols first as memorised facts, then the addition rule, then the narrower subtractive-pair rule, before mixing both directions of practice and reading real examples.
1. The seven symbols and their values
Start by teaching the seven symbols as memorised facts, not something to work out. There is no shortcut here, students simply need I=1, V=5, X=10, L=50, C=100, D=500 and M=1000 to be automatic before any rule makes sense.
Point out the pattern in the values: 1, 5, 10, 50, 100, 500, 1000. Each jump multiplies by 5, then by 2, then by 5, then by 2, and so on. Seeing that pattern makes the sequence far easier to hold in memory than seven unconnected facts.
Roman numerals are not a place-value system. A digit's value in our number system depends on its position (the 3 in 300 is worth more than the 3 in 30), but a Roman symbol is always worth the same amount wherever it appears. That single difference explains almost everything else in this unit.
What number does VIII represent?
- List the symbols in order: V, I, I, I.
- Each symbol is the same size or smaller than the one before it, so the addition rule applies: add every value.
- 5 + 1 + 1 + 1 = 8.
Answer: VIII = 8.
- What is the value of X? Of C?
- Why is a Roman symbol always worth the same amount, unlike a digit in our number system?
2. The addition rule: largest to smallest, add
Teach the first and simpler rule: when symbols are written from largest to smallest, left to right, add every symbol's value together. Most Roman numerals a student meets early on, like VIII or XVI, use only this rule.
Model a few examples on the board, always reading left to right and keeping a running total: XVI is X (10), then V (5), then I (1), so 10 + 5 + 1 = 16.
In standard notation, I, X, C and M may repeat up to three times in a row, while V, L and D do not repeat. Three I's in a row is fine (III = 3), but a fourth I is replaced by a subtractive pair, which is exactly where the next rule takes over.
What number does CLXVI represent?
- List the symbols in order: C, L, X, V, I.
- Every symbol is the same size or smaller than the one before it, so add all five values.
- 100 + 50 + 10 + 5 + 1 = 166.
Answer: CLXVI = 166.
- Why can XVI just be added straight across, left to right?
- What is the biggest number you can write using only three X's and the addition rule?
3. Subtractive notation: the six pairs
Now teach the exception that makes Roman numerals more than repeated addition. When a smaller symbol is placed directly before a larger one, it is subtracted from it instead of added. This only ever happens for six specific pairs, and the rule for which pairs are allowed is narrow and worth teaching precisely.
The six subtractive pairs are IV = 4, IX = 9, XL = 40, XC = 90, CD = 400 and CM = 900. Every one of them is a single small symbol placed immediately before a single larger symbol.
The rule is deliberately narrow: only I, X and C are ever used to subtract, and each one only subtracts from the next one or two symbols above it. I only comes before V or X (never L, C, D or M). X only comes before L or C (never D or M). C only comes before D or M. The symbols V, L and D are never used to subtract from anything, and a subtractive symbol is always a single letter, never two, so a numeral like IIX for 8 is not valid.
Write 90 as a Roman numeral.
- 90 is 10 less than 100.
- X (10) is one of the three symbols allowed to subtract, and C (100) is one of the symbols X is allowed to subtract from.
- Write the smaller symbol before the larger one.
Answer: 90 = XC.
- Why is 99 written XCIX and not IC?
- Which three symbols are ever used to subtract, and why do you think it is only those three?
4. Combining addition and subtraction
Bigger numbers need both rules working together. The reliable method is to break the number into place-value-style chunks, thousands, hundreds, tens and ones, convert each chunk on its own using the addition or subtraction rule, then write the converted chunks in order from largest to smallest.
Take 44 as a small example: break it into 40 and 4. Forty is the subtractive pair XL, and 4 is the subtractive pair IV, so 44 = XLIV, one subtractive pair after another.
The same method scales up to every number in this unit's 1 to 3999 range, which is exactly what the worked example below shows for a four-digit year.
Write 1994 as a Roman numeral.
- Break 1994 into place-value chunks: 1000 + 900 + 90 + 4.
- Convert the thousands: 1000 is the addition case, a single M.
- Convert the hundreds: 900 is the subtractive pair CM (100 before 1000).
- Convert the tens: 90 is the subtractive pair XC (10 before 100).
- Convert the ones: 4 is the subtractive pair IV (1 before 5).
- Write the four converted chunks in order, largest first: M, then CM, then XC, then IV.
Answer: 1994 = MCMXCIV.
- Break 2024 into its place-value chunks before converting it. What are the four chunks, and what happens to the hundreds chunk?
- Why does breaking a number into chunks first make a long conversion easier?
5. Reading Roman numerals in the real world
Finish by reading real examples, so the rules connect straight back to places students actually encounter Roman numerals outside of a maths lesson.
Clock faces often number 1 to 12 in Roman numerals, I through XII. Many traditional clocks print IIII rather than IV for 4. This centuries-old clockmaker's form has several proposed explanations; visual balance with VIII on the opposite side of the dial is one common explanation, not a settled fact.
A book's front matter, the pages before Chapter 1 such as a preface or table of contents, is traditionally numbered with lower-case Roman numerals (i, ii, iii), switching to ordinary numbers once the main chapters begin.
Monarchs and popes who share a name are told apart with a Roman numeral, such as Queen Elizabeth II or Pope John Paul II, both read as 'the second'.
Film and television closing credits often stamp the production year in Roman numerals, for example MCMXCIV for 1994.
The NFL first used Roman numerals for Super Bowl V and applied the names I to IV to the earlier games. Super Bowl 50 was a one-year exception that used the numeral 50 instead of L; the NFL returned to Roman numerals for Super Bowl LI.
A film's closing credits show the copyright notice MCMXCIV. What year was the film made?
- Read the symbols in groups: M, then CM, then XC, then IV.
- M is 1000 (addition case).
- CM is 900 (100 before 1000, subtractive pair).
- XC is 90 (10 before 100, subtractive pair).
- IV is 4 (1 before 5, subtractive pair).
- Add the four values: 1000 + 900 + 90 + 4.
Answer: MCMXCIV = 1994.
- Where have you seen a Roman numeral outside of a maths lesson?
- Why do you think IIII survives on clock faces even though IV is the standard rule everywhere else?
Common misconceptions and how to address them
Misconception4 is written IIII, four ones in a row, instead of IV.
Why it happens: Students learn the addition rule first and simply repeat the smallest symbol to build up to a number, before they know the subtractive rule exists.
How to address it: Teach the 'never four in a row' rule immediately after the addition rule: whenever a symbol would repeat four times, swap to the subtractive pair instead. Mention the one common exception, clock faces, so students are not confused when they see IIII printed there.
MisconceptionA smaller symbol placed before a larger one is always subtracted, no matter how far apart the two symbols are, so 99 could be written IC (100 - 1).
Why it happens: Students learn the general idea, smaller before bigger means subtract, without the extra condition on which pairs are actually allowed.
How to address it: Teach the six subtractive pairs as a fixed, memorised list (IV, IX, XL, XC, CD, CM) rather than a free rule. I only ever subtracts from V or X, X only ever from L or C, and C only ever from D or M, so 99 is written XCIX (90 + 9), never IC.
MisconceptionReading order does not matter, so IX and XI mean the same thing.
Why it happens: Students have not yet internalised that, unlike ordinary addition where order does not change the sum, in Roman numerals the position of the smaller symbol relative to the larger one changes the operation entirely.
How to address it: Contrast the pair directly on the board: IX is I before X, subtract, 10 - 1 = 9. XI is X before I, add, 10 + 1 = 11. Say the rule out loud every time: small-then-big subtracts, big-then-small adds.
MisconceptionRoman numerals can represent zero, or there is some symbol for 'nothing'.
Why it happens: Every other number system students have met, including their own base-ten system, has a zero, so they assume Roman numerals must too.
How to address it: State precisely that the standard Roman numeral system taught here has no symbol for zero and no placeholder because it is not a place-value system. Later number systems introduced zero as both a number and a place-holder. In ordinary modern Roman-numeral contexts, zero is written with our usual digit 0 instead.
MisconceptionAny of the seven symbols can be used to subtract, for example VL for 45 (50 - 5).
Why it happens: Once students learn that a smaller symbol before a larger one subtracts, they overgeneralise the rule to all seven symbols instead of just I, X and C.
How to address it: Anchor the rule to the three symbols that start each x1/x5/x10 group: I, X and C are the only symbols ever used to subtract. V, L and D are never used to subtract; 45 is written XLV (40 + 5), not VL.
Guided practice (with answers)
1. Write 8 as a Roman numeral.
Answer: VIII. Using the addition rule: V (5) + I + I + I = 5 + 1 + 1 + 1 = 8.
2. Write XIV as a number.
Answer: 14. X is 10, then IV (a smaller symbol before a larger one) subtracts to 4, so 10 + 4 = 14.
3. Write 49 as a Roman numeral.
Answer: XLIX. Split 49 into 40 and 9: 40 is the subtractive pair XL (50 - 10), and 9 is the subtractive pair IX (10 - 1), so 49 = XLIX.
4. Write MCMXCIV as a number.
Answer: 1994. M is 1000, CM is 900 (100 before 1000), XC is 90 (10 before 100), and IV is 4 (1 before 5): 1000 + 900 + 90 + 4 = 1994.
5. Write 1776 as a Roman numeral.
Answer: MDCCLXXVI. Break it into chunks: 1000 (M) + 500 (D) + 200 (CC) + 50 (L) + 20 (XX) + 6 (VI).
6. Is IIX a correctly written Roman numeral for 8?
Answer: No. A subtractive symbol is always a single letter, and I can only come before V or X, never 'double subtract' like this. 8 is written VIII (5 + 1 + 1 + 1), and 9 (not 8) is the one written with a subtractive pair, IX.
Independent practice worksheets
Set the matching ChalkBee Roman numeral worksheets for independent practice. The answer keys are computed in code from the same conversion rules taught in this unit, so they are never wrong. Start a class at the grade below their own if the addition and subtractive rules are still shaky, since the value range grows fast, up to 39 in Grade 3 and up to 3999 by Grade 6.
Differentiation
- Keep a symbol-value reference chart (I=1, V=5, X=10, L=50, C=100, D=500, M=1000) visible during independent work; this is a recall-and-apply skill, not a mental-maths one.
- Limit practice to numbers under 40 until the addition rule and the first three subtractive pairs (IV, IX, XL) are secure, matching the Grade 3 worksheet range.
- Model the addition case and the subtraction case in two different colours on the board, so students can see at a glance which rule a symbol pair is using.
- Break larger numbers into place-value chunks (thousands, hundreds, tens, ones) for the student before asking them to convert each chunk, rather than handing over the whole number at once.
- Move into the Grade 5 and 6 worksheet ranges (numbers to 1000 and 3999), where every subtractive pair and multiple thousands digits are needed.
- Ask students to find a real Roman numeral in the world around them, a clock, a book, a film, a building, and explain what it means and why that context uses it.
- Pose a 'spot the error' challenge: give a handful of incorrectly written Roman numerals (IIII, IC, VL) and ask students to find and explain each mistake.
- Introduce Roman numeral years, such as the current year or a student's own birth year, as a real-world application of the four-chunk method.
Assessment: exit ticket
A short exit ticket sampling recall of symbol values, the addition rule, the subtractive rule, and a combined conversion.
1. What number does XV represent?
Answer: 15. X is 10, V is 5, both written largest to smallest, so add: 10 + 5 = 15.
2. Write 40 as a Roman numeral.
Answer: XL. 40 is 10 less than 50, and X is allowed to subtract from L, so it is the subtractive pair XL.
3. What number does XIX represent?
Answer: 19. X is 10 (addition), then IX is the subtractive pair for 9 (10 - 1), so 10 + 9 = 19.
4. Write 1776 as a Roman numeral.
Answer: MDCCLXXVI. Break it into chunks: 1000 (M) + 500 (D) + 200 (CC) + 50 (L) + 20 (XX) + 6 (VI).
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 the seven symbols plus the addition rule (sections 1 to 2), Lesson 2 the subtractive pairs (section 3), Lesson 3 combining both rules plus real-world reading and the exit ticket (sections 4 to 5 and assessment).
- Language to keep saying: 'largest to smallest, add' for the addition rule, and 'small-then-big, subtract' for the subtractive rule. These two phrases resolve most of the unit's misconceptions on their own.
- Curriculum note: Common Core (US) and the Australian Curriculum v9 (ACARA) have no dedicated Roman-numeral content descriptor, so this unit does not force-fit an unrelated base-ten code. England's statutory National Curriculum explicitly covers Roman numerals on clocks in Year 3, reading to 100 in Year 4, and reading to 1000 plus recognising years in Year 5; those three genuine requirements are cited in the curriculum anchor.
- The worksheet value range grows quickly by grade (up to 39 in Grade 3, 100 in Grade 4, 1000 in Grade 5, and 3999 in Grade 6), so match the independent practice set to how much of the subtractive-pair list a class has secured, not just their grade number.
- Use Student view to project this lesson. Print saves the full teacher unit, including answers and teacher notes; use the linked independent-practice worksheets for student handouts.