Japanese Visual Multiplication
I believe that different cultures have different ways in teaching and I find it really interesting when learning about other fascinating ways to do maths. I came across an interesting method to visualize multiplication that reduces it to simple counting. Let’s watch the video below and get to some examples.
First, suppose we want to multiply 12 by 23. Draw 1 lines slanted upward to the right and then move downward to the right a short distance and draw another 2 lines upward to the right. Then draw 2 lines slanted downward to the right, and then move upward to the right a short distance and draw another 3 lines slanted downward to the right (see the Fig. 1 below).
Now count up the number of intersection points in each corner of the figure. The number of intersection points at left will be the first digit of the answer. The middle digit of the answer will be the sum of the intersection points at the top and bottom of the rectangle. The number of intersection points at right will be the last digit of the answer.
The math behind the fact is applying the Distributive Property of Multiplication over Addition. The method works because the number of parallel lines are like placeholders at the power of 10 and the number of dots at each intersection is a product of the number of lines. Then we are summing up all the products that are coefficients of the same power of 10. Therefore, in the example,
23 x 12 = (2 x 10 +3)(1 x 10 +2) = 2x10x1x10 + (2x10x2 + 3x1x10) + 3x2 = 276
The diagram display actually this multiplication visually. The method can be generalized to products of 3-digit numbers using more sets of parallel lines.
For example,
We notice that when the sum of the products is 10 or more, we carry the first digit of that sum and add it to the next sum on the left.
Another good example.
Overall, I think this visual method is very valuable to teach the basis of multiplication to children. However, it isn’t very useful when handling large numbers.
No comments:
Post a Comment