6-year-old Rahul wasn't able to understand multiplication when it was thrust upon him in school. His mother discussed this problem with some of us. On the basis of suggestions that came up in the discussion she decided to do some activities with him.

First, she brought out Rahul's collection of marbles. Both of them sat down to wrap the marbles in paper packets, each having 4 marbles. Then she placed these packets in a bucket. Next to it she placed an empty bucket. Now she asked Rahul to put one packet of marbles at a time into the empty bucket. After he did this for, say 3 times, she asked him:

Mother : How many packets did you take out?

Rahul : 3. .

Mother : How many marbles in each packet?

Rahul : 4

Mother : So, how many marbles, if you take out 1 packet?"

Rahul : 4.

She wrote down l(4) = 4. Then she asked.him how many in 2 packets, and so on.

Simultaneously, she wrote and said

2 times 4 = 2(4) = 4 + 4 = 8

3 times 4 = 3(4) = 4 + 4 + 4 = 12

4 times 4 = 4(4) = 4 + 4 + 4 + 4 = 16,

and so on, trying to show him a pattern in the language and the process.

She did similar exercises with him with groups of other objects till he realised that multiplication was repeated addition. Soon, when asked, say, how many marbles in 8 packets of 4 each, he would say "8 times 4", add 4 eight times, and come up with the answer.

In the example above, Rahul's mother used brackets to record multiplication. The representation is useful for only some situations. For instance, you wouldn't be able to use it for explaining the 'scale' model to a child. However, the formal symbol (i.e., x) should only be introduced to children once they understand what multiplication is. Similarly, formal terms like product, multiplicand, etc., should be introduced at a later stage, and by exposing children to its use in the context of several practical examples.

One way to gauge whether children have understood multiplication is to ask them to create word problems to represent given multiplication facts like 'seven times six'. If you study the results of such an exercise with children, you may find very interesting information about how much and what they have understood. For instance, you could see which model of multiplication they are most comfortable with. Doing the following exercise will give you a chance to see how effective this method is.

E5) Take some 7-year- olds and 11-year- olds around you. Give them a multiplication fact each (e.g., 6 x 3 = 18) a=d ask them to give you word problems that match them.

See which model of multiplication they tend to use, and if there is any difference in this aspect between the two age groups.

So far we have discussed ways of helping a child learn multiplication. Let us now see how they can learn to multiply efficiently.