Italian version

A few years ago my friend Andrea, an elementary school teacher, invited me to teach a math lesson as part of a school project. He told me that I could freely choose the topic to present to a mixed class of elementary school children, ages 8 to 10. I remember that I enthusiastically welcomed this proposal, and when I thought about the topic to propose, it occurred to me that a few months earlier I had heard about Vedic mathematics, a mathematical formulation that goes back to the Hindu sacred texts, the Vedas. Although I was completely unaware of the subject, I was intrigued by the articles extolling its teaching potential, aimed at developing creativity and mental agility, and it was that curiosity that led me to choose Vedic mathematics as the topic for the lesson.

I searched for information on the web and found the website https://vedicmaths.org/, which is an excellent source for delving into this mathematical system used in India, based on 16 principles (sutras). This system provides not only techniques for fast computation, but alternative and more compact methods for the solution of problems in mathematics, geometry, differential calculus. So I began to look at the first examples, with emphasis on fast calculus techniques, and was amazed to learn that there are different ways of doing the elementary operations we learn as children. For example:

• We normally do column addition from right to left. Actually it can be done from left to right
• Multiplication can also be done from left to right. This method has the advantage that we come more quickly to understand the order of magnitude of the result. If we calculate 37 x 48, we normally find out the number from the units, that is, from the least significant digit. With the “Vedic” method, the number is made up from the most significant digits, and fairly quickly we understand the order of magnitude of the number. In this case, the sequence to arrive at the result would be 1200 -> 1720 -> 1776.
• To divide numbers one can use “straight” division, which was used in a famous Italian TV show by a contestant who bet that he could quickly and accurately roll off the first twenty decimal numbers of the result of 67 divided by 109. In the article Vedic mathematics and the division by 109 I explained this trick.

I was very happy, I had discovered some new things in a world I thought I knew well. Once again, delving into the knowledge of other cultures reveals that one never stops learning, even in contexts such as the mathematics of the four operations where I never thought I would find novelty.

Putting this consideration aside, how could I have approached the problem with elementary school children? A classic frontal lesson, where the teacher talks and the class listens, would have been a flop; I would surely have lost the children’s attention after a few minutes. So I decided that I would do an engaging lesson, where the children should be an active part of the lesson and where I would appeal to their natural curiosity.

So I showed up in the classroom, and told them that they would learn some math tricks with which they could amaze their parents or grandparents. I began by asking for a two-digit number ending in 5. They chose 65, and on the blackboard I wrote quickly:
65 x 65 = 4225
Then they chose 75, and I wrote:
75 x 75 = 5625
Almost all the children were curious about the magic behind that quick calculation. So I explained the rule to them:
65 x 65: first you multiply the tens digit by itself increased by 1, i.e., 6 x (6 +1) = 42, then you queue 25. So the result is 4225.
75 x 75: First you do 7 x (7 +1) = 56, then you queue 25. So the result is 5625.

As a start it was not bad, the children showed curiosity and asked me to continue. Then I asked them to choose a number between 51 and 59. They chose 56, and I wrote on the blackboard:
56 x 56 = 3136
Then they chose 54, and so:
54 x 54 = 2916

At that point a fifth-grade girl raised her hand and said to me candidly:
“I see how you did it!”
54 x 54: first you square the tens digit and add the unit, i.e., 5 x 5 + 4 = 29, and then you queue 4 x 4 = 16 -> 2916
56 x 56: first you square the tens digit and add the unit, i.e., 5 x 5 + 6 = 31, and then you queue 6 x 6 = 36 -> 3136
“That child has the gift of mathematical intuition”, Andrea told me. The lesson continued with several questions from the children, to such an extent that I found myself telling them about some aspects that, in preparing the lesson, I had mistakenly thought did not fit.
That lesson is a fond memory for me, and I like to think that it may have sown interest and curiosity in a subject that is considered difficult. In the next article devoted to mathematics, I will talk about straight division in Vedic mathematics.

You can send your comment to info@esperienzedivalore.it, I will be happy to respond.