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.
Instructions
For this investigation each student will submit a personalized PowerPoint project which contains:
 Civilization information
 Name of civilization, location, and time period.
 What types of structures did they build?
 Did the study of astronomy affect their number system? If so, how.
 About the number system
 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.)
 Did they use zero? If so, for what purpose?
 Did they have a maximum number?
 Using the number system
 Show how to convert 179 to the number system.
 Explain how to add 12 + 28 in the number system.
 Explain how to multiply and divide in the number system.
 If fractions were used, how and why did they use fractions?
 Cite your sources.
 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
Name

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

1036

Maya numerals


Muisca numerals


Aztec numerals

16th Century

Sinhala numerals


Binary number system

17th Century

Hexadecimal number system

1950s

Resources
 Background: https://docs.google.com/presentation/d/1FQQQTK338WXfc1BCCfxHOkSRQbNt1fikrEpnld_fJxE/edit
 http://www.math.wichita.edu/history/Topics/numsys.html
 https://ancientcivilizationsworld.com/numbersystems/
 https://en.wikipedia.org/wiki/List_of_numeral_systems
 https://www.agapebiblestudy.com/documents/The%20Significance%20of%20Numbers%20in%20Scripture.htm
Exit Ticket
CCSS Math Practice
 I can construct viable arguments and critique the reasoning of others.
NGSS Crosscutting Concepts
 Scale, Proportion, and Quantity