Learning Resources Horizontal ABACUS Manuale utente

Simple Adding

To add, for example, 4 apples and 3 apples: First enter 4 (Fig. 1).

ext, place a finger after the 4 and enter 3 more (Fig. 2). Remove the

finger and add the quantities by pushing them together (Fig. 3). The

sum of 7 is immediately obvious without any counting. The finger as

separator is needed only for the first few additions.

ote that the problem is written horizontally, in the equation form.

Addition Strategies

An addition strategy is an efficient technique for recalling an

addition fact. Counting is slow and often inaccurate. Rote memory is

high maintenance, requiring frequent review. It also hampers

integrating new concepts and applying knowledge.

A visual strategy for 4 + 3 is to take one from the 3 and give it to the

4, making 5 and 2, which the child learned previously with fingers

(Fig. 4). Later, ask the child to do this mentally.

10 Strateg

To add 9 + 6, enter 9 and 6 on the first two wires. ext, move a bead

from the 6 to the 9 to change the 9 into 10 (9 + 6 = 10 + 5 = 15).

After the child works on the abacus, ask him to practice this strategy

mentally (Fig. 5). This strategy is also effective for adding 8.

Two-fives strategy

To add 6 + 7, enter 6 and 7 on two wires. The two 5s make 10, while

the remaining 1 and 2 make 3, giving the sum of 13. This strategy

works for facts where both addends are 5 or more (Fig. 6).

U.S. Money

It is very easy to represent

money on the abacus; there

are 100 beads to represent a

dollar. A single bead is a

penny, a group of five is a

nickel, a whole row is a dime,

and each of the four groups

shown at the right is a

quarter (Fig. 7).

Multiplication

To demonstrate multiplication, ask the child to enter 6 four times.

Explain that the abacus shows 6 taken four times, which we write as

6 x 4. Let the child find the product, 24 (Fig. 8).

6 x 4 = 24

(6 taken 4

times)

The purpose of this exercise is to help the child understand

multiplication, not memorize the facts.

Bead Trading

To understand the pattern of trading—that 10 ones is 1 ten, 10 tens

is 1 hundred, and 10 hundreds is 1 thousand—children must work

with numbers beyond 99.

On the reverse side of the abacus is a label indicating 1000, 100, 10,

and 1. This more abstract though traditional use of the abacus

stresses “trading,” or carrying. ote that two wires are used for each

denomination. Keeping the two columns as even as possible makes

trading easier.

For example, in adding 8 + 6 = 14, we cannot have more than 9 ones.

To trade, move down ten 1-beads (five from each wire) and move up

one 10-bead. Use your right hand for the ones and your left hand for

the ten. Ask the child to read the sum before and after trading,

shown below (Fig. 9 and 10).

Fig. 1: entering the 4.

Fig. 2: entering the 3.

4 + 3

4+3=7

Fig. 3: adding them together.

Fig. 9: 8+6 Before trading Fig. 10: 8+6 After trading

HORIZONTAL ABACUS

ll0l00l000 ll0l00l000

4+3=7

9 + 6 = 15

6 + 7 = 13

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Adding Four-Digit Numbers

Example: 5248 + 1937. First, enter from left to right the number 5248

(Fig. 11).

Start the addition of the second number by adding the 7 ones, which

gives 15 ones (Fig. 12). Trade as shown below (Fig. 13). It is very

important to record the results of each step; write 5 ones and an

extra ten.

ext, add the 3 tens and record that result, 8 tens, as shown (Fig. 14).

Then, add the 9 hundreds; another trade is necessary. Again, record

the results, the 1 hundred and the extra 1 thousand (Fig. 15 and 16).

Finally, add the thousands; no trade is necessary. The solution is 7185

(Fig. 17). After 6–10 problems adding four-digit numbers, most

children can do these additions on paper without further instruction.

References

Cotter, Joan A. “Using Language and Visualization to Teach Place Value.” Teaching

Children Mathematics 7 (October, 2000): 108–114. ([email protected])

Cotter, Joan A. Activities for the AL Abacus: A Hands-on Approach to Arithmetic.

2nd Ed. Hutchinson, M : Activities for Learning, 2000.

ll0l00l000 ll0l00l000

ll0l00l000

5248

+ 1937

5248

+ 1937

5248

+ 1937

5248

+ 1937

5248

+ 1937

185

5248

+ 1937

7185

5248

+ 1937

ll0l00l000

For a dealer near you, call:

(847) 573-8400 (U.S. & Int’l)

(800) 222-3909 (U.S. & Canada)

+44 (0)1553 762276 (U.K. & Europe)

Learning Resources Ltd., King’s Lynn, Norfolk (U.K.)

lease retain our address for future reference.

Made in China. LRM4335-TG

Visit our web site at:

LER 4335

Joan A. Cotter

Fig. 11

Fig. 12 Fig. 13

Fig. 14

Fig. 15 Fig. 16 1

Fig. 17

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