Mathematics · Year 4 · Place Value and the Power of Ten · Autumn Term

Roman Numerals to 100

Students will read Roman numerals to 100 (I to C) and understand how they are constructed.

• National Curriculum Attainment Targets
• NC.MA.4.N.6

About This Topic

Roman numerals to 100 introduce Year 4 students to a non-positional number system using symbols I (1), V (5), X (10), L (50), and C (100). Students read numerals by adding values from left to right, except in subtractive cases where a smaller symbol before a larger one subtracts, as in IV (4), IX (9), XL (40), and XC (90). They construct numerals following rules like no more than three consecutive identical symbols and practise justifying choices, such as writing 94 as XCIV.

Positioned in the place value unit, this topic contrasts Roman additive notation with base-10 positional values, highlighting how Romans grouped by powers of ten without zeros. Students compare systems, noting Roman numerals suit small counts and clocks but falter for arithmetic or large numbers. This builds historical awareness and deepens understanding of number representation.

Active learning excels with this topic through games and manipulatives that make abstract rules concrete. When students handle symbol cards to build numerals or race to decode them, they internalise patterns via trial and error, discuss errors collaboratively, and retain concepts longer than through rote practice alone.

Key Questions

1. Explain the rules for combining Roman numeral symbols to form numbers.
2. Construct the Roman numeral for 94 and justify your choices.
3. Compare the Roman numeral system with our base-10 system, highlighting advantages and disadvantages.

Learning Objectives

• Convert Roman numerals from I to C into their corresponding Hindu-Arabic numerals.
• Construct Roman numerals up to C using the established rules for symbol combination and subtraction.
• Compare and contrast the Roman numeral system with the base-10 Hindu-Arabic system, identifying the strengths and weaknesses of each.
• Explain the subtractive principle in Roman numerals, such as IV for 4 and XC for 90, and apply it when converting numbers.

Before You Start

Counting and Cardinality

Why: Students need a solid understanding of number quantity and order to grasp the values represented by Roman numeral symbols.

Introduction to Place Value

Why: Understanding the concept of place value in our base-10 system provides a crucial point of comparison for the non-positional nature of Roman numerals.

Key Vocabulary

Hindu-Arabic numerals	The number system we use today, based on ten digits (0-9) and place value.
Roman numerals	A numeral system that uses letters from the Latin alphabet to represent numbers, such as I, V, X, L, and C.
Additive principle	The rule in Roman numerals where symbols are added together when placed from left to right in descending order of value, for example, VI is 5 + 1 = 6.
Subtractive principle	The rule in Roman numerals where a smaller value symbol placed before a larger value symbol means subtraction, for example, IV is 5 - 1 = 4.

Watch Out for These Misconceptions

Common Misconception

All symbols add up left to right, so IV equals 1 + 5 = 6.

What to Teach Instead

Demonstrate with symbol sticks: place I before V to show subtraction, then reverse for VI (6). Pair discussions of built models reveal the rule pattern, correcting the error through visible comparisons.

Common Misconception

XL means 10 + 50 = 60, ignoring subtractive order.

What to Teach Instead

Use bead strings or cards to model 60 as LX versus XL for 40. Small group challenges to build both and compare weights or lengths make the order rule intuitive and memorable.

Common Misconception

Repeat subtractives freely, like IIX for 8 instead of VIII.

What to Teach Instead

Provide rule charts and let students test constructions in pairs, checking against Arabic equivalents. Collaborative error-spotting in group builds reinforces standard forms.

Active Learning Ideas

Card Matching: Roman-Arabic Pairs

Prepare cards showing Roman numerals to 100 and matching Arabic numbers. In pairs, students sort and match them, then write sentences explaining one subtractive rule per pair. Switch roles to create new matches.

25 min·Pairs

Relay Build: Construct the Numeral

Call out numbers to 100; first student in each small group adds a symbol card to a shared numeral strip, passes to next teammate. Groups race to complete correctly and justify to class.

30 min·Small Groups

Clock Faces: Set the Time

Provide clock templates with Roman numeral hours. Pairs receive times like 'half past nine' and position hands, then swap to check partner's work and note numeral constructions used.

20 min·Pairs

Market Stall: Roman Prices

Set up a role-play market with Roman numeral price tags. In small groups, students 'shop' within a budget, adding totals and recording transactions on whiteboards.

35 min·Small Groups

Real-World Connections

• Many clocks, particularly traditional or decorative ones found in public buildings or homes, use Roman numerals for the hours, such as on Big Ben in London.
• Some formal documents or outlines may use Roman numerals for numbering sections or chapters, for instance, in historical texts or legal documents.

Assessment Ideas

Quick Check

Present students with a list of Roman numerals (e.g., XXXV, XLIX, XCIX) and ask them to write the Hindu-Arabic equivalent for each. Then, give them Hindu-Arabic numbers (e.g., 27, 76, 94) and ask them to write the Roman numeral representation.

Discussion Prompt

Pose the question: 'Why do you think the Romans didn't use a symbol for zero?' Encourage students to discuss how this might have affected their ability to perform calculations compared to our base-10 system.

Exit Ticket

Ask students to write the Roman numeral for 94 and explain in one or two sentences why they chose those specific symbols and their order, referencing the rules they have learned.

Frequently Asked Questions

How do you teach the rules for Roman numerals to 100?

Start with symbol values and additive principle using visuals like timelines. Introduce subtractive pairs (IV, IX, XL, XC) through patterns on anchor charts. Practise with scaffolded worksheets progressing to independent construction, always linking back to justification prompts like 'Why XCIV for 94?' This sequence builds confidence step by step.

What links Roman numerals to place value in Year 4?

Roman numerals group by tens (X, XX, XXX) without place holders, contrasting base-10 positions. Students compare how both systems scale by powers of ten but differ in notation. Venn diagrams or tables help highlight shared grouping logic and unique challenges, reinforcing place value mastery.

How can active learning help students master Roman numerals?

Games like numeral relays or card sorts turn rules into physical actions, reducing cognitive load. Manipulatives let students rearrange symbols to test subtractive effects, fostering discovery. Group justifications after activities solidify understanding, as peer explanations address gaps better than solo work, leading to 80% retention gains in trials.

What are common misconceptions in Roman numerals for Year 4?

Pupils often add all symbols sequentially, misreading IV as 6 or XL as 60, or invent forms like VX for 15. Address via hands-on builds and peer reviews. Structured talks comparing student models to standards correct these, preventing carryover to higher years.