A workshop on ‘Primary Maths' was held at our school for two days. The organizers began with a question on Subtraction.
"How do we subtract two numbers by borrowing (regrouping)?"
This seemed an easy question to answer; or so we thought. I was eager to tell the steps and did so - "If the top number is smaller than the lower number, we just borrow 1 from the tens place and subtract with the new bigger number so formed." For example, if we have to subtract 82 - 35, then at ones place we have 2 - 5 which is not possible. So, 1 is borrowed from 8 and 2 becomes 12. Now we can easily subtract 5 from 12 which gives 7. In the tens place, we are left with 7 as the top number instead of 8. So 7 - 3 is 4. Hence, 82-35 is 47.
"Excellent!" said the facilitator. Everybody clapped and I was beaming with pride like a Grade 2 child. Appreciation never fails in lifting up the spirits.
"What do we mean by borrowing?" was the next question.
"When we have something less, we borrow. Like if we need to give 4 pencils to our child for his test in the school the next day, but we have only 1 pencil at home, then we might borrow from our neighbors," came a quick reply from my colleague.
"That's correct! But what does borrowing in subtraction means?" We were wondering why was the facilitator asking the same question again, and what exactly she wanted to know. Borrowing means borrowing, taking something that we have less, from someone who has it. What else can it mean?
Facilitator smiled. She knew very well that conventional schooling had only taught us the algorithm (procedure) of subtraction without understanding the proper meaning of borrowing.
"Let me tell you a story," she started, "the story of a girl who sold apples."
"Shyama is a little girl who sells apples. She has created baskets of tens. She has also kept aside some single apples in case somebody asks for less than ten. So, on a particular day, she had 6 baskets of ten apples in each and 4 single apples. A man comes and asks for 7 apples." The facilitator paused for a moment and then continued."Do you think Shyama has enough apples? Can she give 7 apples to the man?"
"Yes, she can! She has so many baskets full of apples. Why can't she give 7 apples to somebody?" was our unanimous reply.
"But she has only 4 single apples. How can she give 7 out of 4?"
The simplicity of the problem seemed annoying. ‘Isn't it obvious,' I thought in my mind but answered politely - "Of course she will open one of the baskets of 10 apples and give from that."
"Brilliant! Shyama will open 1 basket of 10 apples, and combine those ten apples with the 4 single apples that she had. Now she has 14 single apples. Out of these 14 apples, she gives 7 apples easily to the man." The facilitator spoke in a soft voice.
"We do this exactly in subtraction by borrowing. We open the neighboring group of tens, if at ones place, objects are less and we have to subtract (give away) a bigger number. Since we open the groups and rearrange, it is called regrouping. When we borrow, we do not borrow one, but one whole group of tens. That's why in the tens place we decrease the number by 1 tens. We follow the same procedure for the hundreds place, thousands place and for all the other bigger places.
Since children are small, we use terms like borrowing to attract their attention. But it's very important to give them a hands on experience. Use groups of concrete objects like pencils, marbles, sketch pens, garlands of flowers, chalk pieces and so on to create similar scenes like in the story of Shyama. Play the game of shopkeeper and customer, and ask them to open up the neighboring group in order to subtract."
This workshop was an eye opener for me. Even after learning Maths for so many years, I did not know the simple procedure of subtraction by borrowing. Probably, I was good at memorizing the algorithm. But some children find it difficult to do so. A proper hands on, visual experience helps them grasp the concept better. We, as parents, can also learn the basics of different operations, at least now if we did not get the chance to do so in our childhood. Only if we understand the basics well, will we be able to pass it on to our young ones correctly.
Click on the link http://bit.ly/Appystore__subraction to watch Video on Subtraction with Borrowing.
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