Ancient Math Systems

Source: Frank Grießhammer

Type: Investigation

Theme: Historical

Grades: 5, 6, 7, 8, 9, 10

Learning Target: Students will learn how to calculate using Egyptian, Roman, or Mayan mathematics and switching bases. Students will develop their own number system and justify/provide rationale for its use.


For this investigation each student will submit a personalized PowerPoint project which contains:

  1. Civilization information
    1. Name of civilization, location, and time period.
    2. What types of structures did they build?
    3. Did the study of astronomy affect their number system? If so, how.
  2. About the number system
    1. Does the number system have a base? If so, what is it and how did the base come to be? (Common bases were 5, 10, 20, and 60.)
    2. Did they use zero? If so, for what purpose?
    3. Did they have a maximum number?
  3. Using the number system
    1. Show how to convert 179 to the number system.
    2. Explain how to add 12 + 28 in the number system.
    3. Explain how to multiply and divide in the number system.
    4. If fractions were used, how and why did they use fractions?
  4. Cite your sources.
  5. Invent a number system for an alien civilization. How many fingers does the alien creature have? How often does its planet rotate around the star? Why does the alien civilization use numbers?

Examples of Civilizations and their Number Systems

Approx. First Appearance
Babylonian numerals
3,100 BC
Egyptian numerals
3,000 BC
Chinese, Japanese, Korean, Vietnamese numerals
1,600 BC
Aegean numerals
1,500 BC
Roman numerals
1,000 BC
Hebrew numerals
800 BC
Indian numerals
750 – 690 BC
Greek numerals
Chinese rod numerals
1st Century
Khmer numerals
Early 7th Century
Thai numerals
7th Century
Abjad numerals
Eastern Arabic numerals
8th Century
Western Arabic numerals
9th Century
Cyrillic numerals
10th Century
Tangut numerals
Maya numerals
Muisca numerals
Aztec numerals
16th Century
Sinhala numerals
Binary number system
17th Century
Hexadecimal number system


Exit Ticket
CCSS Math Practice
  • I can construct viable arguments and critique the reasoning of others.
NGSS Crosscutting Concepts
  • Scale, Proportion, and Quantity