Roman Numerals Problem-Solving

Overview

Year Group: 4
Duration: 60 minutes
Class Size: 30 pupils
National Curriculum Alignment:

• Mathematics Programme of Study, Year 4
• Number – Recognise and understand Roman numerals up to 100 (NC Maths PoS)
• Solve problems involving Roman numerals and place value
• Reasoning with numbers and applying mathematical vocabulary

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Learning Objectives

By the end of the lesson, pupils will:

• Recognise and read Roman numerals to 100 confidently.
• Solve word and numerical problems involving Roman numerals.
• Explain and justify the steps they used to solve problems involving Roman numerals.
• Develop reasoning skills by explaining their thinking and applying logical steps in problem-solving.

Linked to NC Statements:

• Number – Roman Numerals: "Recognise and understand Roman numerals up to 100."
• Problem Solving and Reasoning: "Solve problems involving increasingly large positive numbers."

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Resources

• Whiteboard and marker
• Printed problem cards with Roman numerals and related word problems
• Worksheets with Roman numerals and space to show reasoning
• Visual aids: Roman numeral posters showing I to C (1 to 100)
• Number lines labelled in both Arabic numerals and Roman numerals

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Lesson Structure

1. Engaging Introduction (10 minutes)

Objective: Spark curiosity about Roman numerals and relate to real-life use.

• Begin by showing the class some historical images of clocks, monuments, or old books with Roman numerals. Ask:
  • "Have you seen these symbols before? Where?"
  • "Why do you think people used these symbols instead of numbers like we do now?"
• Introduce the Roman numerals I, V, X, L, C, and their values. Use a quick chant to memorise (e.g., "I is 1, V is 5, X is 10...").
• Explain today’s goal: solving problems involving Roman numerals using clear steps and reasoning.

Targeted Questions:

• Recall / Understand: "What is X equal to?"
• Explain / Describe: "Can someone explain why V is 5 and not 6?"
• Apply: "If I is 1 and X is 10, how would you write 11?"
• Analyse / Reason: "What happens when you put I before V (IV) instead of after (VI)?"

AfL check: Use a quick whiteboard mini quiz: pupils hold up Roman numeral cards to represent the number teacher calls out.

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2. Modelling & Teaching (20 minutes)

Objective: Model how to solve problems involving Roman numerals and justify answers step-by-step.

• Demonstrate reading and writing Roman numerals using a number line from 1 to 100 on the board, labelling both Arabic and Roman numerals.
• Work through the following example step-by-step on the board (copy into books):

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Example to Copy:

Problem: What is the sum of LX (60) and XXVII (27)? Write the answer in Roman numerals.

Steps:

1. Convert Roman numerals to Arabic → LX = 60, XXVII = 27
2. Add the numbers → 60 + 27 = 87
3. Convert 87 to Roman numerals: L (50) + X (10) + V (5) + II (2) = LXXXVII
4. Final answer: LXXXVII

Justification:

• We broke the numerals down into values and added the numbers, then converted back.
• We made sure to place numerals in descending order to follow Roman numeral conventions.

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Model Reasoning Questions:

• "Why do we add 60 and 27 as Arabic numbers instead of adding the Roman numerals directly?"
• "Can someone explain how we know L is 50 and not 100?"
• "Why do we write LXXXVII for 87 and not LXXVIII?"
• "What if the question asked to subtract XXVII from LX – how would we approach that?"

AfL: Ask pupils to explain each step aloud or to a partner. Use thumbs up/down to check if everyone understands.

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3. Guided Practice (15 minutes)

Objective: Practice solving problems with support.

• Hand out problem cards with varied tasks: addition, subtraction, and ordering of Roman numerals between 1 and 100.
• Pupils work in pairs discussing their reasoning aloud.
• Teacher circulates, listening and prompting with questions:

Bloom's-Inspired Questions for Deeper Thinking:

• "How did you decide which numerals to combine or split?"
• "What strategies helped you avoid mistakes?"
• "Can you prove your answer is correct? Is there another way to write your answer?"

Common Misconceptions to Target:

• Confusing placement of I, X before vs after larger numerals (e.g., IV vs VI).
• Misreading L (50) as C (100) due to letter similarity.
• Confusing addition and subtraction rules in Roman numerals.

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4. Independent Task (10 minutes)

Objective: Apply learning independently and explain reasoning in writing.

• Pupils complete a worksheet with 4 problems:

  1. Write the number 44 in Roman numerals and explain your answer.
  2. What is XXIX + XIV in Roman numerals? Show how you found the answer.
  3. Order these Roman numerals from smallest to largest: XL, XX, L, XXX.
  4. Find the missing Roman numeral that makes this equation true: LX - ? = XX.

• Pupils write clear explanations for their methods.

AfL: Select 3-4 pupils to explain their answers in plenary for peer assessment and teacher feedback.

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5. Plenary (5 minutes)

Objective: Consolidate learning through reflection and reasoning.

• Ask pupils reflective questions for whole class discussion:

  • "How does understanding Roman numerals help you with place value and number systems?"
  • "Which problem was the trickiest today and why?"
  • "How can you check your answers when working with Roman numerals?"

• Use a “Think-Pair-Share” format, encouraging pupils to explain their thinking to partners before sharing with the class.

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Assessment for Learning (AfL) Points Throughout

• Initial card quiz: assess prior knowledge of numerals.
• Use verbal questioning after modelling for understanding and misconceptions.
• Listen carefully during paired work, probing reasoning and explaining errors.
• Review written explanations in independent work to assess depth of understanding.
• Summative quick-fire questioning at plenary to gauge whole-class progress.

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Alignment with White Rose Maths Scheme

• Covers the ‘Number – Place Value’ domain, specifically: reading, writing, and understanding Roman numerals.
• Emphasises reasoning and problem solving, key strands throughout White Rose units.
• Builds concrete to pictorial to abstract understanding in line with WR approach.

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Teacher’s Notes / Tips:

• Emphasise that Roman numerals do not use place value like Arabic numerals, reinforcing difference.
• Use visuals and physical number lines to aid conceptual understanding.
• Encourage pupils to use logical addition and subtraction steps rather than memorisation.
• Tackle misconceptions gently with reasoning prompts. Offer alternate ways to represent numbers for those who struggle.

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This detailed plan will help pupils not only solve Roman numeral problems but also explain their reasoning, deepening understanding in line with the National Curriculum’s emphasis on mathematical fluency and reasoning.