Mathematics · Year 4

Active learning ideas

Roman Numerals to 100

Active learning helps students grasp Roman numerals because the non-positional system requires physical manipulation of symbols to internalize rules like subtractive notation. When students build numerals with cards or beads, they see why order matters in a way that worksheets alone cannot show.

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

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Concept Mapping
• 25 min · Pairs

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.

Explain the rules for combining Roman numeral symbols to form numbers.

Facilitation Tip

During Card Matching, circulate and ask pairs to explain how they paired IV with 4, listening for references to symbol order rather than just matching shapes.

What to look for

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.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 02

• Concept Mapping
• 30 min · Small Groups

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.

Construct the Roman numeral for 94 and justify your choices.

Facilitation Tip

In Relay Build, time the rotations so partners cannot rely on prior guesses, forcing them to apply rules each step.

What to look for

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.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 03

• Concept Mapping
• 20 min · Pairs

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.

Compare the Roman numeral system with our base-10 system, highlighting advantages and disadvantages.

Facilitation Tip

For Clock Faces, provide mini-whiteboards so students can sketch numeral placements before placing clock hands, reinforcing visual planning.

What to look for

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.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 04

• Concept Mapping
• 35 min · Small Groups

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.

Explain the rules for combining Roman numeral symbols to form numbers.

Facilitation Tip

At Market Stall, give price tags in mixed formats so students must convert between numeral and pence to complete purchases.

What to look for

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.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

A few notes on teaching this unit

Teach this topic by modeling the contrast between additive and subtractive cases using concrete materials like bead strings or base-ten blocks. Avoid rushing to abstract rules; let students discover patterns through guided error analysis. Research suggests that kinesthetic engagement with numeral construction improves retention more than rote memorization of symbol values.

Students will confidently read and write Roman numerals up to 100, justifying their constructions with accurate rule references. They will explain patterns such as subtractive pairs and symbol repetition limits without prompting.

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Watch Out for These Misconceptions

• During Card Matching, watch for students who pair IV with 6, treating symbols as purely additive.

  Have students physically place I and V on the table, then flip I to the right side to form VI. Ask them to compare the visual difference and re-evaluate their pairings.

• During Relay Build, watch for teams that build XL as LX by ignoring subtractive order.

  Give each team two bead strings, one labeled LX and one XL, and ask them to weigh each string on a balance scale to see which matches the Arabic 40 more closely.

• During Market Stall, watch for students who write 8 as IIX instead of VIII.

  Provide a rule chart at the stall and ask students to test both versions by calculating total costs for items priced at 8 pence, comparing which total is easier to read and add.

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Methods used in this brief

• Concept Mapping