Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease. For instance, suppose we divide 417 by 3, we first divide the 4 hundreds by 3 to get 1 hundred in the quotient, with a remainder of 1 hundred. This remainder can then be converted into tens, to get 10 tens. We also have 1 ten from before. So now we divide the 11 tens by 3, to get 3 tens in the quotient with 2 remaining. This remainder is then converted into 20 ones. So we have a total of 27 ones. Dividing this by 3 we get 9 ones in the quotient and no remainder. So, the answer is 139.
Now, lets try dividing from the ones first and see what happens. We would first divide 7 by 3 to get 2 ones in the quotient, and 1 one remaining. Next, we would consider the 1 ten To divide this, we would need to convert it into 10 ones. Also we had 1 one remaining from before. So we divided the 11 ones by 3 to get 3 ones in the quotient, and 2 ones remaining. Now go to the 4 in the hundreds place. Dividing this by 3 we get 1 hundred in the quotient, and 1 hundred remaining that is, 10 tens remains. Dividing this by 3 we get 3 tens, and 1 ten remaining. We already have 2 ones remaining, don't forget! So, now we have (10+2) ones remaining. Giving this by 3 we get 4 ones. So, in this back and forth way, we have done the division to get the same answer, of course, but in double the time, and with having to keep track of several quotients.
How does a child construct for herself the understanding of the step-by-step process? How help her to see how and why the algorithm works? Let us consider what Zarina has 4: Zarina has been teaching upper primary school children for some time.