Unit #1: Ancient Origins

Lesson 1: Introduction to Ancient Number Systems

Lesson Duration: 45 minutes
Class Level: Year 7 (Ages 11–12)
Class Size: 20 students
NZ Curriculum Area: Mathematics and Statistics
Strand: Number and Algebra
Level: Level 4
Achievement Objective:
Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages. Develop an understanding of the cultural development and application of number systems in real-world and historical contexts.

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WALT (We Are Learning To):

• Understand the purpose and origins of ancient number systems.
• Recognise how different civilisations represented numbers and used them in daily life.
• Make comparisons between ancient and modern numerals.

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Success Criteria:

✔ I can describe why ancient people developed number systems.
✔ I can identify key features of at least two ancient number systems.
✔ I can explain how number systems were used in trade, science, or record-keeping.
✔ I can reflect on how different systems influence how we use numbers today.

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Lesson Overview:

Time	Activity
5 mins	Karakia / Mihi & Set-up
10 mins	Engaging Hook / Discussion
10 mins	Group Activity: Ancient Symbols Detective
10 mins	Class Discussion: What’s the Pattern?
5 mins	Reflection: Number Realisations
5 mins	Wrap-up & Journaling Task

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Detailed Lesson Breakdown:

1. Karakia / Mihi & Set-up (5 mins)

• Begin the class with a short karakia (can be led by kaiako or a student, if appropriate).
• Introduce the unit: “Ancient Number Systems Exploration”
• Connect to tūrangawaewae: “In Aotearoa, our ancestors had systems to measure time, track seasons, and share stories — around the world, people did the same thing in amazing ways.”

Teacher Tip: Use classroom displays to showcase te ao Māori connections to mathematics—such as traditional navigational methods or Maramataka calendars.

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2. Engaging Hook: Time Travel Talk (10 mins)

Resource Suggestion:
Print a “Time Travel Passport” booklet – each child will collect ‘stamps’ as they explore different number systems throughout the unit.

Activity Steps:

• Imagine: You’ve been sent back in time. You’re in a marketplace in ancient Egypt/Mesopotamia/China. You need to buy bread, but no one understands your numbers.
• Prompt questions:
  • What problems might you face?
  • How would you show ‘3’ or ‘20’ if they use different symbols?
  • Why did ancient people need number systems?

Get students to share their thoughts in quick pairs, then open the floor for a few volunteers.

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3. Group Task: Ancient Symbols Detective (10 mins)

Materials Needed:

• Handouts with numeral examples (e.g. Egyptian hieroglyphics, Babylonian cuneiform, Roman numerals, Māori counting in kūmara pits)
• Matching cards (symbol and number equivalents)
• Magnifying glasses or “Detective Glasses” (optional prop)

Group Roles (in 4s):

• Symbol Matcher
• Pattern Spotter
• Culture Connector
• Presenter

Task:
Each group will match ancient numerals with modern equivalents and identify how those symbols represent a number pattern (e.g. place value, tally marks, powers of 10). Circle unusual patterns or features.

Teacher prompts:

• “Why do you think they chose these shapes?”
• "Is there a base system here? Base 10, base 60?"

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4. Whole-Class Discussion: What’s the Pattern? (10 mins)

• Each group presents one thing they discovered about their system.
• Teacher guides a whiteboard mind-map:
  • Differences in base systems
  • Non-symbolic counting methods (e.g. bone tallies)
  • Culturally specific uses (e.g. astronomy, time-keeping, trade)

Key Teaching Point:
Highlight that maths is not neutral — it is shaped by cultural and historical need. Introduce idea that some systems (like Roman numerals) didn't have a zero! Discuss impact.

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5. Reflection: Number Realisations (5 mins)

Ask students:

• "What surprised you about ancient number systems?"
• Pair up and share biggest takeaways.
• Record one reflection in their Time Travel Passport.

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6. Wrap-Up & Journaling Task (5 mins)

Journaling Prompt for Independent Work or Homework:
Draw or describe one symbol from an ancient number system and explain:

• What it represents
• Why it might have been used
• What you like or find strange about it

Collect passports for next lesson.

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Differentiation Strategies:

For Support/ESOL Learners:

• Provide visual exemplars with brief pictorial explanations.
• Use sentence starters (e.g. “I think this symbol means…”)
• Offer key vocabulary cards with illustrations: symbol, trade, pattern, base number.

For Advanced Learners:

• Extension Task: Decode a basic number sentence in Roman or Babylonian numerals.
• Encourage questions like: “How would you multiply using this system?”
• Option to research a lesser-known system (e.g. Mayan, Incan quipu knots)

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Key Te Ao Māori Integration:

• Connect to traditional Māori knowledge systems—mention how the moon phases (Maramataka) are used for time and planning (a non-numerical system).
• Introduce local iwi knowledge if relevant (e.g. students may explore kūmara storage pits or tally-stone usage).

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Materials List:

• A3 number symbol posters (Egyptian, Babylonian, Roman, Hindu-Arabic)
• Time Travel Passport templates
• Matching card sets
• Whiteboard & markers
• Journals or exercise books

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Looking Ahead:

Next Lesson (Lesson 2 of 8):
Explore the Egyptian number system in depth — students will write calculations using hieroglyphics.

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This lesson is intentionally crafted to spark curiosity, centre cultural diversity, and use collaboration to introduce a concept in an age-appropriate and meaningful way. The structure supports teachers to meet NZ curriculum expectations while encouraging students to explore global and historical perspectives on mathematics.