Learning Resources Horizontal ABACUS User Manual

Simple Adding

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

Note 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 Strategy

To add 9 + 6, enter 9 and 6 on the first two wires. Next, 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. Note 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).

A

A

A

Fig. 1: entering the 4.

Fig. 2: entering the 3.

4 + 3

4

4 + 3 = 7

Fig. 3: adding them together.

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

A

A

A

A

A

HORIZONTALABACUS

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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.

Next, 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. ([e-mail])

Cotter, Joan A. Activities for the AL Abacus: A Hands-on Approach to Arithmetic.
2nd Ed. Hutchinson, MN: Activities for Learning, 2000.

ll0l00l000 ll0l00l000

ll0l00l000 ll0l00l000

ll0l00l000

ll0l00l000

5248

+ 1937

5248

+ 1937

5248

+ 1937

5

5248

+ 1937

85

5248

+ 1937

185

5248

+ 1937

7185

5248

+ 1937

85

ll0l00l000

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Fig. 11

Fig. 12

Fig. 13

Fig. 14

1

1

Fig. 15

Fig. 16

1

11

1

1

Fig. 17