On this element, you can find an abacus. Additionally, the element also has a writing board. Abacus is the oldest “calculator” in the world, and it is used to help with calculating. There are many types of abaci which differ in shape and their usage in calculating. On this element you can find the so-called school abacus, one of the most often used types today. It consists of ten bars, each one with ten differently coloured beads.
The word Abacus is derived from the Greek word “abax” or “abakon”, meaning “tabular form”. Abacus was first created somewhere between 500-300 BC in Asia. It was used by the ancient Sumerans, Egyptians, Greeks, Persians, Romans, Indians, even Europeans, until the 16th century. The modern abacus, suanpan, was invented in China in the 11th century. Suanpan is a frame with a horizontal divider which divides the frame into two parts, the upper one with two beads, and the lower one with five beads.
The so-called school abacus is the most used type today. It consists of ten bars, and each bar has ten differently coloured beads. There are many techniques and ways of calculating with the help of an abacus. It is most often used by representing digits on bars, that is, so that each bar represents a different local value.
Abacus as an element enables younger children to understand the concept of numbers, ones and tens, addition, subtraction, multiplication, and division up to 100. In the following text, we show some examples of how young children can use the abacus.
The concept of numbers and the acquisition of the concept of units and tens: the child demonstrates number 47 on the abacus. He notices that this number has 4 tens and 7 ones. The child first forms 4 rows of 10 beads and 7 more beads in the fifth row.
Addition to 10: if the child must add 4+5, he uses the following process. We move all beads to one side. We separate 4 beads and move them to the right, leave some free space and then add 5 more beads. The child counts all the beads moved to the right.
Addition of single-digit numbers with a transition of tens: if the child must add 7+9, we use the following procedure. We move 7 beads to the right on the first bar, and 9 beads on the second bar. 5 beads (on each bar) are singled out, and the rest of them are moved to the side. There are now two units of 5 beads, which adds up to 10 beads. The child then counts the rest of the beads and gets 6 as a result, meaning that the result is 10+6=16. If both numerators are not larger or equal to 5, the child separates 5 beads from the numerator from which he can, and then he can apply one of the previously introduced procedures to add the rest of the beads and add the resulting sum to the number 5.
Addition of double-digit numbers: If the child must add 37+48, the child first notices that number 37 has 3 tens and 7 ones and marks 10 beds on the first 3 bars and 7 ones on the 4th bar. He repeats the same procedure with the other addend. Finally, the child adds tens and ones (for adding ones, he uses one of the previously introduced procedures).
Subtraction: In subtraction, the child separates the number of beads corresponding to the minuend and gradually separates from it the number of beads corresponding to the subtrahend. If double-digit numbers must be subtracted, you can subtract tens and ones separately. In case that the number of ones of the minuend is smaller than the number of ones of the subtrahend, the child uses one ten (ten ones) of the minuend to determine the number of ones in the result.
Multiplying: If the child calculates the product of numbers 3 and 4, it separates 4 beads on 3 bars and counts the separated beads.
Division of natural numbers without a remainder: If the child wants to divide 35 with 7, he will apply successive subtraction (that is, separation of 7 beads per bar) and will, in the end, count the units consisting of 7 beads.
For older children, each bar represents a different local value, so that the lowest bar represents ones, the following one tens,… With such usage, the abacus becomes the aid for calculations with multi-digit numbers.
- How many beads does each bar have? How many bars are there? How many beads in total does this amount to?
- How many red beads are there? Are there as many blue beads?
- Calculate: 3+6, 7+9, 15-7, 21+43, 37+49, 57-32, 63-28, 67, 7·6, 42:6
- Can you show number 3 on the abacus? What about number 43? And number 323?
- What is the largest number that you can represent on the school abacus? Write it down and read it. 9 999 999 999 (9 billion 999 million 999 thousand and 999)
