Visualizing the Numbers (Part V)

In the last article we saw how division can be taught with the help of the patterns. One thing we have to remember about division is that, it is a difficult operation to learn compared to the other operations we have seen so for.

The reason is that in the case of division children have to attend to two outcomes simultaneously. The first outcome of the process of division is the quotient and the other is the remainder. Thus when we are generalizing our results we have to bring to the notice of the children these two outcomes.

I usually ask children to find out both the outcomes for numbers from 1 to 10 when these are divided by 1, 3, 5,… 9 one by one. I ask them to put their observations as shown in the figure below



Similarly, I ask them to find out both the outcomes for numbers from 1 to 10 when these are divided by 2, 4, 6,…. 10 one by one. I ask them to put these observations as shown in the figure to the right-hand side
.

Once they have noted down their observations, I ask them to focus their attention on the remainder. I ask them “How does the remainder compare in size to the divisor i.e. the number with which we are dividing?” While answering this question it becomes clear to them when to stop the subtraction. If this concept is not digested properly the answer to the question “What is the result of 56 divided by 8?” could be “6 with remainder 8”. Therefore, children should be given thorough understanding of the remainders obtained through various divisions. Another benefit of observing the patterns in the remainders will be clear when we will discuss divisibility in detail.

Children should also observe how the quotients change when the same divider divides the subsequently higher order numbers.

After trying different divisions with the help of patterns and watching out both the outcomes repeatedly, I can summarize their observations in the following form.

Summarization in the case of the division operation is a bit tedious because of the two outcomes. However, our earlier summaries related to subtraction and multiplication are very useful.

To start with, in the figure below


I have shown summary for a division of an even number with an even number .

When an even number is divided by an even number we are likely to get either an even quotient or an odd quotient. Whatever is the quotient, we always subtract an even number from an even number. Hence, the remainder is always even or zero. Here we can ask the children to recall our earlier summary of observations with respect to subtraction.

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