Using the abacus for subtraction and division operations

Hello, today I bring you a Math project I have done along with my peers from the university. This is an abacus’ usage guide for subtraction and division operations for children in Primary education.

Here it is the project, first a written explanation of the abacus’ advantages and disadvantages along with the explanation of the operations done in the video I am also updating, I hope you enjoy our work.

BENEFITS AND DRAWBACKS

– Benefits:

  • Improves mental resilience and concentration.
  • Reinforces space knowledge
  • It provides a visual and manipulative learning
  • Good for blind children

– Drawbacks:

  • It is very big to carry it everywhere
  • It is hard to learn correctly
  • It is only good for simple operations

DETAILED DESCRIPTION OF THE USE OF ABACUS

Subtraction with “carrying”

➢ 33-15

Task 1: the number 33 is represented by putting 3 tens (blue balls) 3 units (purple balls) on the right side.

Task 2: we must subtract 5 units, but as we do not have, we subtract only the 3 units that we have (move the 3 purple balls to the left side).

Task 3: is missing 2 units to get to the 5 that we must subtract, so we removed a ten (move a blue ball to the left side) and add 10 units (move ten purple balls to the right side).

Task 4: of the 10 units that we have now, we subtract the 2 that we need to remove 5 units (move 2 purple balls to the left side).

Task 5: subtracting the ten left to us (move a blue ball on the left).

Task 6: we have on the right side 1 ten (one blue ball) and 8 units (8 purple balls) which is the result of subtraction 33-15 = 18.

➢ 12-8

Task 1: the number 12 is represented by putting 1 tens (blue ball) 2 units (purple balls) on the right side.

Task 2: we must subtract 8 units, but as we do not have, we subtract only the 2 units that we have (move the 2 purple balls to the left side).

Task 3: is missing 6 units to get to the 8 that we must subtract, so we removed a ten (move a blue ball to the left side) and add 10 units (move ten purple balls to the right side).

Task 4: of the 10 units that we have now, we subtract the 6 that we need to remove 8 units (move 6 purple balls to the left side). 6

Task 5: we have on the right side 0 ten (none blue ball) and 4 units (4 purple balls) which is the result of subtraction 12-8 = 4.

➢ 150-22

Task 1: the number 150 is represented by putting 1 hundred (green ball) 5 tens (blue balls) 0 units (none purple balls) on the right side.

Task 2: we must subtract 2 units, but as we do not have, so we removed a ten (move a blue ball to the left side) and add 10 units (move ten purple balls to the right side).

Task 3: of the 10 units we have now, we subtract 2 units (move 2 purple balls to the left side).

Task 4: subtract 2 tens (move 2 blue balls to the left side).

Task 5: we have on the right side 1 hundred (one green ball) 2 ten (2 blue balls) and 8 units (8 purple balls) which is the result of subtraction 150-22 = 128.

Division as a repetitive subtraction

➢ 12:4

Task 1: the dividend (12) is put down (1 blue ball and 2 purple balls) and the divisor (4) is put up (4 red balls).

Task 2: you must subtract to 12 always 4 units, until the units are finished.

Task 3: we must subtract 4 units, but as we do not have, we subtract only the 2 units that we have (move the 2 purple balls to the left side).

Task 4: is missing 2 units to get to the 4 that we must subtract, so we removed a ten (move a blue ball to the left side) and add 10 units (move ten purple balls to the right side).

Task 5: of the 10 units that we have now, we subtract the 2 that we need to remove the first 4 units (move 2 purple balls to the left side). 7

Task 6: subtract 1 unit from the divisor (1st time).

Task 7: we still have 8 units left, so we subtract another 4 units.

Task 8: subtract 1 unit from the divisor (2nd time).

Task 9: we still have 4 units left, so we subtract another 4 units.

Task 10: subtract 1 unit from the divisor (3th time).

Task 11: there are no more units left in the dividend, so the division is over.

Task 12: we have subtracted 3 times 4 units to 12, therefore, 3 is the result of the division 12:4 = 3.

➢ 25:5

Task 1: the dividend (25) is put down (2 blue balls and 5 purple balls) and the divisor (5) is put up (5 red balls).

Task 2: you must subtract to 25 always 5 units, until the units are finished.

Task 3: subtract the first 5 units (move the 5 purple balls to the left side).

Task 4: subtract 1 unit from the divisor (1st time).

Task 5: there is not units to get to the 5 that we must subtract, so we removed a ten (move a blue ball to the left side) and add 10 units (move ten purple balls to the right side).

Task 6: of the 10 units that we have now, we subtract the second 5 units (move 5 purple balls to the left side).

Task 7: subtract 1 unit from the divisor (2nd time).

Task 8: we still have 5 units left, so we subtract another 5 units.

Task 9: subtract 1 unit from the divisor. (3th time).

Task 10: there is not units to get to the 5 that we must subtract, so we removed a ten (move a blue ball to the left side) and add 10 units (move ten purple balls to the right side). 8

Task 11: of the 10 units that we have now, we subtract the second 5 units (move 5 purple balls to the left side).

Task 12: subtract 1 unit from the divisor (4nd time).

Task 13: we still have 5 units left, so we subtract another 5 units.

Task 14: subtract 1 unit from the divisor. (5th time).

Task 15: there are no more units left in the dividend, so the division is over. Task 16: we have subtracted 5 times 5 units to 25, therefore, 5 is the result of the division 25:5 = 5

Remember to visit my peers’ blogs!

www.aprendeaemocionarte.wordpress.com

www.cuentosconnuria.wordpress.com

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