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 numerationWrite 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 ZeroTimeline

A

B CDE

FG

A. African B. Egyptian C. Babylonian D. GreekE. 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’sAdditive systemDisadvantages

Examples241241240

Write the following numbers:67242,320345

567,922

Rhind Papyrus, c. 1650 BC

Moscow Papyrus, c. 1850 BC

Ciphered numeration system3000 B.C.Disadvantages

Examples241241240

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 subtractionPositionalDisadvantages

Examples241241240

Write the following numbers:

672241098

777 479 1776 Your birth year

Convert to our present system:

XL MDCXII MCMLXIV

A

B CDE

FG

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

Maximum Extent of the Babylonian Empire, c. 1750 BC

Maximum Extent of the Egyptian Empire, c. 1500 BC

Maximum Extent of the Roman Empire, c. 15 AD

Homeland & Colonies of Greek Civilization, c. 700 BC

Maximum Extent of the Roman Empire, c. 100 AD

3000 - 200 B.C.Positional systemPlace ValuesBase of 60 No place holder Disadvantages

Examples Write the following numbers:24 48124 6721240 3702

Convert to our number system

<

V

Bablyonian Tablets, c. 1800 BC

Bablyonian Tablets, c. 1800 BC

300 – 900 A.D.Place value systemBase 20Introduced zero

Mayan Codices

800 A.D.10 symbolsGrouping by “tens”Place valueAdditive 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 numberzero subtracted from a number is the numberzero multiplied by a number is zerozero divided by a number is zeroa number divided by zero is ……Zero divide by zero is ….

3000 BC – Egyptian Numerals2000 BC – Babylonian (Iran/Iraq)400 BC – Greek Ciphered Numerals100 BC – 500 AD Roman Empire300 BC – Mayan (Central America)500 AD – Hindu Numerals800 AD – Arabs adopt Hindu Numerals500 – 1100 Dark Ages in Europe1202 – 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?