## 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:

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

 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

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