The interactive AL Abacus is available for you to explore. You can work with addition and multiplication using trading and quantity recognition. Place value cards and the math way of counting are also shown. An electronic version from NCTM is available for you to explore.
Introduction
Children dearly love using the AL Abacus. Even very young children can learn mathematics basics. Those learning arithmetic with the abacus have a better understanding of basic concepts and need less time to master arithmetic. They are also eager to solve problems. Although children do enjoy using the abacus, it does not become a crutch. They are proud to be able to do their work without it.
The abacus provides a visual representation and hands-on experience without the problem of little pieces. I asked Stan, age 5, how much is 11 plus 6. When he said 17, I asked him how he knew. He answered, "I have the abacus in my mind."
Before teaching children to enter quantities on the abacus, teach them the quantities 1 to 10 with their fingers. Ask them to use the left hand for quantities 1-5 (because we read from left to right) and the right hand for quantities for the amounts over 5.
Set the abacus flat on a surface with the dot in the upper right hand corner. Clear it by tilting the abacus so the beads fall towards the right. Ask the children to hold up 1 finger and then to enter 1 bead on the top wire by sliding it to the left.
To teach 2, ask the children to show 2 with their fingers and to enter 2 beads by sliding them together as a unit toward the left. The beads are not to be counted. Continue with quantities to 10. It is very important that the children be able to enter and identify any quantity 1-10 without counting.
Simple Adding
To add two quantities, such as 4 apples + 3 apples, first enter 4, place a finger after it, and enter the 3. Remove the finger and add the quantities by pushing them together. The sum is immediately seen as 7 without any counting. Later the children will not need to place a finger between the two quantities.
Tens
Ask the children to enter 1 ten. Then ask them to enter other groups of tens, such as 2-ten, 5-ten or 3-ten. When this is understood, show the place-value card of 30 and explain how we write 3-ten. Point to the 3 while saying "three" and point to the 0 while saying "ten." These cards promote reading in the normal left to right order, in contrast to designating the right column as ones and proceeding left for tens, hundreds, and so forth.
Also ask them to add 2-ten plus 3-ten, 5-ten plus 4-ten, and similar combinations.
Tens and Ones
Ask the children to enter 3-ten and 6. Show them how to form it with the place-value cards by sliding the 6-card over the 0 of the 30-card to form 36.
Continue with other combinations, such as 5-ten 8, 7-ten 3, and so forth. Also show them numbers between 1-100 with the place-value cards and ask them to enter the quantity and to read it. After the children are familiar with 10-ten, tell them it has another name, point to the 1 on the 100 card and say "one" and point to the 0s while saying "hun-dred."
Money
It is very easy to show 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 one-fourth of the beads is a quarter.
Learning the Addition Facts
Children learn the facts best when using strategies. One such strategy is Adding Nines. For example, to add 9 + 6, enter the 9 and the 6 on the top two wires. Move a bead from the 6 to complete a 10. After the children are proficient in finding the sums by moving the beads, challenge them to enter the quantities on the wires and mentally move the beads.
Another interesting strategy is the Two Fives strategy. For example, 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. Ask the children to see it mentally. This strategy works for facts when both addends are 5 or more
Skip Counting and Multiplying
Skip counting is a valuable skill needed for finding factors and multiples and is useful for mastering the multiplication facts. For learning the 2s, ask the children to enter 2, leave a space, and enter another 2. Continue to 20 as shown. Skip counting other numbers from 2-9 also make interesting patterns.
Children easily learn the 5s, which are necessary for counting money and telling time. To demonstrate multiplication, ask the children to enter 6 three times. Explain that the abacus shows 6 taken 3 times, which we write as 6 x 3. Give the children such combinations as 3 x 2, 5 x 5, 10 x 4. Later extend them to 7 x 1, 1 x 9, 8 x 0 and 0 x 6. To calculate 8 x 0, enter 8 zero times.
To find the total for 9 x 3, use the "take and give" method. "Take" a bead from the last row and "give" it to the first row to make a 10. Repeat for the second row by taking another bead from the last row and giving it to the second row. The product is easily seen as 27.
Side 2 of the AL Abacus
On the reverse side of the AL Abacus are labels above the columns indicating 1000s, 100s, 10s, and 1s. This more abstract and traditional use of the abacus stresses "carrying," or "trading." Two wires are used for each denomination, which need to be kept as even as possible for quick recognition. Not used are the third wires from each end. For example, add 8 + 6; the sum is seen immediately because the yellow beads form a 10. However, a trade is necessary. To trade use two hands; the right hand moves down ten 1-beads (5 from each wire) while the left hand moves up one 10-bead. The figures below show 14 before and after trading.
Other Topics
Many young children have learned to add four-place numbers on the abacus and then figured for themselves how to do it on paper. For subtraction, division, and other topics, see Activities for the AL Abacus or the RightStart curriculum by Joan A. Cotter.
The interactive AL Abacus is available for you to explore. You can work with addition and multiplication using trading and quantity recognition. Place value cards and the math way of counting are also shown. An electronic version from NCTM is available for you to explore.
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