Introducing Division (V)

When we think of teaching division it is a good idea to start with measuring interpretation of division. When we divide one quantity into smaller quantities we are measuring. We are asking the question how many times (Latin quot) one quantity is contained in another. So this aspect of division is rightly called measurement or quotation or division.This interprets division not only as inverse multiplication but mainly as repeated subtraction, hence easier to follow.

Before we discuss the actual teaching of division let us learn more about the language of division. Following are the three numbers involved in division:

1. The number to be measured or divided is the most important number and is called the dividend.
2. The number that does the work of division or dividing is called the divisor.
3. The share, portion, ration, measure, or quota that results from division is called the quotient.

These three numbers are identified here in all the four notations:

Advantage of knowing these terms will make further discussion simple and precise.

As a first step we select examples involving smaller numbers, which children find easy to handle. We will select examples having both the dividend and divisor of one digit. Another thing we keep in mind is selecting divisors which will allow for exact sharing, with no remainder. For example: 8 ÷ 4.

When children are solving such types of examples they should say, "How many fours in eight?" or, very briefly, "Fours in eight?" They should not say "Four divided into eight?" which might mean 4 divided into 8 parts! While saying this they can actually find out how many groups of four they can have from eight objects.

While they are finding out how many fours in eight, the teacher can show how to record all the steps in their activity systematically. Look at it here.
Point out that, we have to stop after two sets of four objects are taken away from eight objects. Because that leaves no objects! When we have this situation we find out the total of fours, which is the answer or quotient for our problem. In this case the answer is 2!

In the example discussed here there were only two steps. However, if we set an example: 8 ÷ 2, we will have different ways of solving this example. These are shown here.
Note that the answers are same, that is four. The same example can be solved by following different patterns of subtracting groups of two objects.

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