Abacus

ABACUS MENTAL ARITMETIC 1st Day

2nd Day

3rd Day

1st DAY

Introduction

Addition

Subtraction

BASIC KNOWLEDGE OF AMA ( 1 HOUR)

Preparation Sitting posture Placing abacus Holding of abacus Holding of pen/pencil

Formula  +/- 5  +/- 10

Various parts of abacus Frame Beam Rod Upper bead Lower bead Clearing device ( if there is a button)

The movement of Fingers Thumb Fore finger Middle finger Example

PARTS OF THE ABACUS Clearing Device

Frame

Dot = Unit Place

Beam

Upper Beads

Rod Lower Beads

5 1

move up 1, move down 1

1) Thumb : move up 1

2) Forefinger : move down 1

move up 2, move down 2

1) Thumb : move up 2

2) Forefinger : move down 2

move up 3, move down 3

1) Thumb : move up 3

2) Forefinger : move down 3

move up 5, move down 5

1) Middle finger : move up 5

2) Middle finger: move down 5

move up 6, move down 6

1) Thumb and middle finger: move up 6 at the same time.

2) Middle finger and forefinger : move down 6 at the same time.

move up 7, move down 7

1) Thumb and middle finger : move up 7 at the same time.

2) Middle finger and forefinger : move down 7 at the same time.

move up 8, move down 8

1) Thumb and middle finger : move up 8 at the same time.

2) Middle finger and forefinger : move down 8 at the same time.

832

9920

3809

Group of 1 to 4 (+/- 5)

(+) +1=+5-4 +2=+5-3 +3=+5-2 +4=+5-1

(-) -1=-5+4 -2=-5+3 -3=-5+2 -4=-5+1

Group of 1 to 9 (+/- 10) (+) +1=-9+10 +2=-8+10 +3=-7+10 +4=-6+10 +5=-5+10 +6=-4+10/+1-5+10 +7=-3+10/+2-5+10 +8=-2+10/+3-5+10 +9=-1+10/+4-5+10

(-) -1=+9-10 -2=+8-10 -3=+7-10 -4=+6-10 -5=+5-10 -6=+4-10/-1+5-10 -7=+3-10/-2+5-10 -8=+2-10/-3+5-10 -9=+1-10/-4+5-10

ADDITION

Practice Example 1 : Move up 1, move up 2. I. “Move up 1, move up 2, how to move?” II. “Ready?” III. “Move up 1” IV. “Move up 2” V. “What is the value on the abacus now?”

Example 2: Move up 3, move up 5. I. “Move up 3, move 5,uphow to move?” Example 2: Move up 3,up move 5. “Move up 3, move up 5, how to II. “Ready?”I. move?” III. “Move up 3” II. “Ready?” “Move up 3” IV. “Move upIII. 5” IV. “Move up 5” “What is theon value on the V. “What is V. the value the abacus now?” abacus now?”

Example 3: Illustrate 2+5=7 I. “2+5, how to do it?” II. “Ready?” III. “First, 2 up 2” IV. “Plus 5, up 5.” V. “Equals 7.” Example 4: Illustrate 6+2=8 I. “6+2, how to do it?” II. “Ready?” III. “First, 6 up 6” IV. “Plus 2, up 2.” V. “Equals 8.”

Example 5: Illustrate 23 + 13 = I. 23 + 13. How do we calculate it? II. Ready; III. First, move up 23. IV. Plus 13, move up 1 at Tens and move up 3 at Ones. V. Equals to 36.

Example 6: Illustrate 14 + 27 = (1) 14 + 27. How do we calculate it ? (2) Ready; (3) First, move up 14. (4) Plus 27, up 2 at Tens and up 7 at Ones, but there are not enough beads at Ones; so down 3 and carry 1. (5) Equals to 41.

(1) 17 + 15 + 18. How do we calculate it ? (2) Ready; (3) First, move up 17. (4) Plus 15, up 1 at Tens and up 5 at Ones, but there are not enough beads at Ones; so down 5 and carry 1. (5) Plus 18, up 1 at Tens and up 8 at Ones, but there are not enough beads at Ones; so down 2 and carry 1. (6) Equals to 50.

12 + 5 + 11 = 28

21 + 16 +12 = 49

15 + 12 + 21 = 48

21 + 16 + 2 = 39

25 + 12 + 11 = 48

DO THE CALCULATION USING ABACUS

1+1=2 1 +8=9 2+2=4 2+5=7 3+6=9 5+10=15 3+15=18 2+16=18 11+3=14 1+3=4

10+3=13 11+7=18 15+2=17 16+2=18 12+5=17 27+12=39 23+51=74 31+56=87 35+62=97 36+51=87

SUBSTRACTION

Practice. Example 1: Move up 11,move down 6 I. “Move up 11, move down 6, how to do it?” II. “First, move up 11.” III. “Move down 6, not enough beads. How to do it? IV. “Think, who is the big friend of 6? It’s 4.”

Example 2:

37 – 25=

(1) 37 – Example 25. How do we calculate it? 2: Move up 3, move up 5. “Move up 3, move up 5, how to (2) Ready; I.move?” II. “Ready?” (3) First, move up 37. III. “Move up 3” IV. “Move up 5”down 2 at Tens (4) Minus 25, move V. “What is the value on the now?” 5 at Ones. and moveabacus down (5) Equals to 12.

Example 3: Illustrate 15 – 9 = 6 I. “15 - 9, how to do it?” II. “Ready?” III. “First, 15 up 15” IV. “Minus 9, move down 10 and move up 1 at Ones.” V. “Equals 6.”

Example 4: Illustrate 32 – 17 = 15 (1)32 – 17. How do we calculate it? (2) Ready; (3) First, move up 32. (4) Minus 17, down 1 at Tens and down 7 at Ones, but there are not enough beads at Ones; so remove 1 and up 3. (5) Equals to 15.

Example 5: Illustrate 50 - 1 = 49 (1) Move up 50, move down 1. How do we move it? (2) Ready; (3) First, move up 50. (4) Then move down 1, but there are not enough beads at Ones; what do we do ? so remove 1 and up 9. It is 5 at Tens; what do we do? Up 4 and down 5.

Example 6: Illustrate 50 – 3 - 18 = (1) 98 – 21 – 14. How do we calculate it? (2) Ready; (3) First, move up 98. (4) Minus 21, down 2 at Tens and down 1 at Ones. (5) Minus 14, down 1 at Tens and down 4 at Ones. (6) Equals to 63.

Example 7: Illustrate 36-1=35 (1) 36-1=___. How do we calculate it ? (2) Ready; (3) First, move up 36. (4) Minus 1, down 1, (5) Equals to 35.

How about this calculation? 5–3=2 6–1=4 8–4=4 16 – 3 = 13 18 – 4 = 14

5–2=3 7–4=3 15- 3 = 12 15 – 2 = 13 15 – 1 = 14

Exercise 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

5–3 6–2 18 – 4 16 – 3 27 – 14 18 – 4 – 2 28 – 14 – 10 36 – 13 – 23 25 – 22 – 3 17 – 11 – 3

= = = = = = = = = =

1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

15 – 3 – 11 25 – 14 – 10 46 – 13 – 12 38 – 24 – 14 26 – 12 – 11 48 – 34 – 4 57 – 21 – 12 29 – 14 – 13 67 – 32 – 15 55 – 22

= = = = = = = = = =

SUBTRACTION 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

10 – 4 12 – 5 18 – 9 14 – 5 20 – 7 12 – 8 26 – 9 17 – 8 28 – 19 30 – 5

= = = = = = = = = =

1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

34 – 5 16 – 8 25 – 7 31 – 18 26 – 18 45 – 19 – 1 24 – 15 – 3 22 – 18 – 2 41 – 9 – 22 32 – 19 – 9

= = = = = = = = = =

DIRECT ADDITION AND SUBTRACTION 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

2+2+5 = 3+5+1 = 11 + 2 + 1 + 5 = 12 + 1 + 5 = 22 + 1 + 1 = 31 + 11 + 2 = 21 + 11 + 10 = 12 + 20 + 11 = 10 + 31 + 3 = 13 + 11 + 20 =

1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

9–3–1–5 = 8–6–1 = 18 – 12 – 5 = 38 – 21 – 5 = 26 – 15 – 10 = 48 – 21 – 12 – 5 = 17 – 10 – 1 – 5 = 29 – 15 + 10 – 12 = 46 – 21 + 3 + 11 = 12 + 25 – 11 – 15 =

Exercise 1 •

11 + 24 − 13 = 22

•

13 + 22 − 24 = 11

•

24 + 12 − 13 = 23

•

32 + 43 − 12 = 63

•

43 + 24 − 23 = 44