# 12. Multiplication and division teaching should determine its position first.

Updated: Dec 11, 2020

The abacus starts from the eighth level (or finishes learning with two digits). If the students have no comment errors and correct fingering, they can enter the multiplication and division unit. The previous question is that students should be required to recite the multiplication table before this, even if they are not yet proficient, they can start learning. With the progress of multiplication and division, students will gradually integrate the multiplication table into their brains to form memories.

Multiplication can be done in two methods: head-to-head or tail-to-tail. Because the calculation starting point is different, the processing method and position on the abacus are also different. In order to facilitate teaching and make students understand the rules of calculation, there are two ways of positioning: pre-positioning and post-positioning. The so-called pre-positioning means that, at the present time of the calculation question, it is determined that the question starts from that level. After the calculation is completed, the answers can be written in order according to the numbers on the abacus; the so-called post-positioning is the opposite. It all start from a fixed level (any three-digit file is selected), and after the calculation, confirm how many digits are written in order.

Regardless of teaching head-to-head or tail-to-tail multiplication, it is recommended to use the positioning method to get started, and teach students to write answers directly according to the numbers shown on the abacus after the calculation. Its advantages are:

(a) Teach students the correct concept of rank, as long as the number of real numbers (multiplicand) and normal number (multiplier) are added, that is, the number of answers. However, if the first two digits multiplied and the answer is less than ten, the number of answers may be one less digit.

(b) As long as it is an integer multiplication problem, the positioning method is the same, remind students to make an inference. In this way, the abacus multiplication positioning from level 8 to level 4 is completed at once.

(C) The first positioning method requires students to confirm the starting position. Although it is easy to understand, but for some young students still find it difficult. We can use fairy tales stories to replace the rank, strengthen memory, make them easy to get started and interesting.

(d) The pre-positioning method can guide students to use the omission technique when calculating to the decimal advance question type, and only calculate the effective answer part, which can be answered without completing the entire question, saving time and efficiency.

(e) If the tail-to-tail multiplication calculation is used, the positioning is increased by one more digit than the front multiplication. Because end multiplication puts the real number (multiplicand) on the abacus first, the last digit is discarded to multiply by the normal (multiplier), and the product number is set at the beginning of the next column. Therefore, its positioning needs to be counted one more digit.

At what stage can post-positioning be used? In the multiplication order, in addition to the integer and decimal question types, the difficulty increases, and the common digits on both sides will gradually increase to what it required. When using pre-positioning method, students must remember the starting position of each multiplier (there are fewer digits multiplied by multiple digits or multiplied by two in the same direction). If there are too many digits, it is inevitable that they will be misplaced or the rank must be remembered, resulting in an increased error rate and students feel frustrated. In order to improve this problem, the post-positioning can be changed. Students fix the multiplier level and write the answer according to the actual positioning after calculation. The disadvantage is that it is not suitable for applications that omission technique calculation, and it is not suitable for basic teaching.

As for the division calculation, because the division of the quotient is consistent with the school mathematics calculation method, and considering the calculation of the decimal and the remainder, it must be positioned first. Division does not have multiplication complications. The basic purpose of abacus learning is to improve students calculation ability and to meet the school mathematics requirements. Having this ability before pursuing higher grades and achievements can gain more recognition from all social circles. Teachers can make appropriate adjustments to different situations to meet the requirements.