Visualizing the Numbers (Part I)

Success of the multiplication method described in the previous article depends on two things: 1. Child’s command over the multiplication table for numbers from 1 to 10 and 2. Child’s ability to carry out the required additions accurately.

In this article I would like to focus on helping the child to master the multiplication table for numbers from 1 to 10.

Let us try to recall at this point our own experience. When we are asked, what is 8 x 9; our immediate answer, of course is, 72. Because, we have learned it by heart in our childhood. We are never required to imagine, nine groups, each having eight objects. But, try to recollect the situation when we were trying to drill the multiplication tables in our mind. We used to repeat these mechanically days together without trying to imagine anything.

Therefore, in the initial stages sometimes we used to give any number as an answer that came to our mind for the times-question put forth by our teacher. This is exactly the difficulty our children also face. They have no idea at all to cope with a question like, what is 8 x 9 ?. That is why any random answer like 73 or 63 is possible according to them.

Let us again take this example 8 x 9. We would for example, reject immediately the answer 27 as being too small, or 1,000 as being much too large. We would also reject 73 although it is about the right size. The reason is that the number 8 is even. Hence, our experience accumulated after repeated interaction with many numbers tells us that this as an answer is impossible and the given product could not be an odd number, 73.

The process of rejecting the various numbers as possible answers is actually our ability to visualize numbers.

If children are equipped with this ability to feel the numbers, they manage the simple multiplication as well as other basic arithmetical operations accurately. Their mastery on these operations enhances dramatically.

The method I follow in increasing children’s ability to visualize the numbers is given below.

Children playing with the dice know the pattern .

The moment children see this pattern, they immediately think of number 6. They know that this pattern represents 6 with two rows of three dots. They can directly see that 6 = 2 x 3. Thus the child can feel the number 6.

I ask the children to apply the same logic to represent any number. Thus, number eight in our example above could be represented by :

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