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The Abacus. What is it?. The History. Abacus is a Latin word meaning “sand tray” Pebbles replaced the sand Salamis tablet used as early as 300 B.C. by Babylonians Updated by Greeks - using marble & Romans – using bronze Abax –table or tablet Romans added add’l grooves

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the abacus

The Abacus

What is it?

the history
The History
  • Abacus is a Latin word meaning “sand tray”
  • Pebbles replaced the sand
    • Salamis tablet used as early as 300 B.C. by Babylonians
    • Updated by Greeks - using marble & Romans – using bronze
      • Abax –table or tablet
      • Romans added add’l grooves
        • Corresponded with Roman numerals
the history1
The History
  • Portable devices created
    • Created by Romans
    • Could fit in shirt pocket
    • Used by merchants
  • Introduced to China in early Christian era
    • Chinese abacus, suan pan, born in 11th century
the history2
The History
  • The use of the Suan Pan spread to Korea and Japan in the 15th century
    • Called the Soroban
      • Changed over time with the final (1850) taking away one bead from both the top and bottom
today
Today
  • Abaci are still in use today
    • The blind are able to make calculations by feel
    • Merchants and bankers still depend on their abacus for day-to-day business
      • Asia
      • Middle East
      • Africa
how to use place value
How To Use: Place Value
  • Place Value
    • Each column represents a place value
      • Starting at the farthest right is the 1’s, then 10’s, 100’s, so on.
    • So 236 is represented like:
    • Now you try…
      • 9
      • 12
      • 372
      • 5,065

http://www.mandarintools.com/abacus.html

how to use simple
How To Use: Simple + / -
  • Simple Addition & Subtraction
    • Always work from LEFT to RIGHT
    • Example: 237 + 152
    • Example: 187 - 125

= 389

  • Now You Try!
  • 1 + 3 =
  • 12 + 31 =
  • 123 + 321 =
  • 9 – 6 =
  • 43 – 12 =
  • 263 – 142 =

= 62

how to use complements
Complementary Numbers

In the case of 5:

4 & 1

3 & 2

In the case of 10:

9 & 1

8 & 2

7 & 3

6 & 4

5 & 5

Examples:

4 + 8 = 12

The complementary number for 8 with respect to 10 is 2. Therefore, subtract 2 from 4 and carry 1 to tens

How To Use: Complements
how to use with complements
How To Use: + / - with Complements
  • Adding
    • Subtract the complement
    • Examples:
      • 4+7 =
      • 2+9 =
      • 3+8 =
  • Subtracting
    • Add the complement
    • Examples:
      • 10-7 =
      • 15-8 =
      • 17-9 =
speed combining finger movements
Speed: Combining Finger Movements
  • Using thumb & index finger – pinch beads together (1 “heaven” bead and 3 “earth beads” to create 8)
  • Using thumb & index finger – push beads simultaneously (3 “earth” beads from ones place and 1 “earth” bead to tens place to add 7)
  • Examinations – 10th level (easiest)  1st level (most difficult)
  • Speed ~ What do you think is faster?

http://www.youtube.com/watch?v=yj7XbnYrIk0

crazy but true
Crazy but True…
  • http://www.youtube.com/watch?v=Px_hvzYS3_Y