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

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

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

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

Ishango Region

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

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

Rhind Papyrus, c. 1650 BC

Moscow Papyrus, c. 1850 BC

Ciphered numeration system 3000 B.C. Disadvantages Examples 24 124 1240

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

Zenon Papyri, c. 200 AD

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

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

Convert to our present system: XL MDCXII MCMLXIV

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

Maximum Extent of the Babylonian Empire, c. 1750 BC Maximum Extent of the Egyptian Empire, c. 1500 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

Examples Write the following numbers: 3000 - 200 B.C. Positional system Place Values Base of 60 No place holder Disadvantages Examples Write the following numbers: 24 48 124 672 1240 3702 Convert to our number system V <

Bablyonian Tablets, c. 1800 BC

Bablyonian Tablets, c. 1800 BC

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

Mayan Codices

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

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 ….

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

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?