2. Demonstrate an understanding of the evolution of our numeration system by connecting concepts such as, counting, grouping and place values from the past to the present
Recognize early systems of numeration
Write numbers in Roman, Babylonian, Greek and Egyptian

3. The Very Beginning
Ancient Egypt
Ancient Greece
Roman Empire
Babylonian Numeration
The Mayans
Hindu-Arabic Numerals
Brief History of Zero
Timeline

4. E C B G F A D A. African B. Egyptian C. Babylonian D. Greek
E. Roman F. Mayan G. Hindu-Arabic

5. First known form of counting
Used “grouping”
Ishango Bone c. 18,000 BC

6. Ishango Region

7. Developed in 3400 B.C. Grouping by 10’s Additive system Disadvantages
Examples 24
124
1240

8. Write the following numbers:
672
42,320
345
567,922

9. Rhind Papyrus, c BC

10. Moscow Papyrus, c BC

11. Ciphered numeration system 3000 B.C. Disadvantages Examples24
124
1240

12. Write the following numbers:
672
188
345
949
888
Convert to our number system:


13. Zenon Papyri, c. 200 AD

14. 500 B.C. – 100 A.D. Grouping , additivity and subtraction Positional
Disadvantages
Examples 24
124
1240

15. Write the following
numbers:
672 24
1098
777
479
1776
Your birth year

16. Convert to our present
system: XL
MDCXII
MCMLXIV

18. E C B G F A D A. African B. Egyptian C. Babylonian D. Greek
E. Roman F. Mayan G. Hindu-Arabic

19. Maximum Extent of the Babylonian Empire, c. 1750 BC
Maximum Extent of the Egyptian Empire, c BC
Homeland & Colonies of Greek Civilization, c. 700 BC
Maximum Extent of the Roman Empire, c. 100 AD
Maximum Extent of the Roman Empire, c. 15 AD

20. Examples Write the following numbers:
B.C.
Positional system
Place Values
Base of 60
No place holder
Disadvantages
Examples Write the following numbers:
Convert to our number system V
<

21. Bablyonian Tablets, c. 1800 BC

22. Bablyonian Tablets, c. 1800 BC

23. 300 – 900 A.D.
Place value system
Base 20
Introduced zero

25. Mayan Codices

26. 800 A.D.
10 symbols
Grouping by “tens”
Place value
Additive and multiplicative

28. Who discovered it? Why?
Place holder (space, “ , θ )
A number itself (7th century India)
the sum of zero and a number is the number
zero subtracted from a number is the number
zero multiplied by a number is zero
zero divided by a number is zero
a number divided by zero is ……
Zero divide by zero is ….

29. 3000 BC – Egyptian Numerals
2000 BC – Babylonian (Iran/Iraq)
400 BC – Greek Ciphered Numerals
100 BC – 500 AD Roman Empire
300 BC – Mayan (Central America)
500 AD – Hindu Numerals
800 AD – Arabs adopt Hindu Numerals
500 – 1100 Dark Ages in Europe
1202 – Fibonacci publishes Liber Abaci

30. Which numeration system do you think works best? Why?
How important is zero in our Hindu Arabic System?
Do you think our numeration system will continue to evolve?