1. Evolution of Numbers Setsuko Mori

2. Overview California Mathematics Content Standards. An essential Question & a unit question. A map of ancient civilization. 1.Egypt 2.Babylonia 3.Maya 4.China 5.Roma Computers Works Cited

3. California Mathematics Content Standards: Grade Seven, Number Sense 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms: 2.0 Students use exponents, powers, and roots and use exponents in working with fractions:

4. Unit Question (2): How has a method of counting evolved over time from ancient civilization to today? Essential Question: Why are numbers important in your life?

5. Imagine thousands of years ago… what did ancient people count? How did they count? Why did they count?

6. Ancient Civilization 123 4 5 Current Decimal System

7. Five thousand years ago, 1. Egyptian Civilization: 3000-1600 BC Counting Geese , The ancient Egyptians built pyramids as tombs for the pharaohs and their queens. How did they built them? How did they calculate? Did they take an inventory of Pharaoh’s possessions?

8. Egyptian Numeration System : 3400 BCE How many symbols/numerals are there? How many digits are there? What is the base for this system? How does this system differ from the current decimal system?

9. What are they in decimal system? 200 70 70 6 4000600 20 2

10. 2. Babylonia, Mesopotamia: 1750 BC How many symbols are there? How do these numerals differ from Egyptians’? Babylonian numerals on a clay tablet.

11. Babylonian Numerals Two numerals: Ĭ = 1 < = 10

12. How to decipher this number? How to decipher this number? How many place values are there? Is there a place holder? How does base 60 work?

13. Sexagesimal System (base 60) 60 2 1 3 0 21600 X 1 x57 3600 X 5760 X 461 X 40= 42,400 +++

14. Sexagesimal System Base 60 for Today 1 hour = 60 minutes 1 minute = 60 seconds 01:59:5902:00:00

15. 3. Mayan Civilization C.E. 300 and C.E. 900 The Pyramid of Kukulkan at Chichén Itzá The pyramid was used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.

16. Mayan Numerals

17. What is the number in blue? How many symbols are there? Base 20?

18. Why Base 20? Mayan Civil Calendar: 20 days x 18months + one 5 day month. Mayan Ritual Calendar: 20 days x 13 months. Ten fingers and ten toes? Mayans cerebrate K'atun, a ceremony that was conducted every 20 years.

19. 4. Chinese Numerals １０ 100,000,000 10,000 100 1,000 1,000,000,000,000 一億三千六百二十九 (equals 100,003,629)

20. 5. Roman Numeration system 500 B.C.E. and C.E. 100 1 I1IV4 V5IX9 X10XL40 L50XC90 C100CD400 D500CM900 M1000 CCLXXXI (equals 281) MCVIII (equals 1108)

21. Computer Language Two symbols: 0 and 1 Binary numeral system On or off on a circuit board 0 01 10 11 100 101012345 110 111 1000 1001 1010 101167891011

22. Egyptian 7 symbols Base 10 Babylonian 2 symbols Place valued Place holder Base 60 Mayan 2 symbols Zero Place valued Base 20 Roman 7 symbols Base 10 Chinese 16 symbols Base 10 Hindu-Arabic (ours) Decimal System Base 10 Computer 2 symbols Base 2

23. References http://www.ancientegypt.co.uk/menu.html http://www.ancientegypt.co.uk/menu.html The British Museum (Egyptology) http://www.ancientegypt.co.uk/menu.html Http://webexhibits.org/calendars/calendar- mayan.htmlHttp://webexhibits.org/calendars/calendar- mayan.html (Mayan Calendar) http://www-groups.dcs.st- and.ac.uk/~history/index.html http://www-groups.dcs.st- and.ac.uk/~history/index.html (History of Mathematics Archive) http://www.historyworld.net/ http://www.historyworld.net/ (History of World)