You will be surprised to know that most of the people think that both represent the same situation. However, in the grouping interpretation of multiplication, they represent 2 different situations:

The first situation viz. 4 x 3 represents 4 groups with 3 objects in each group, as demonstrated in the diagram below:

The second situation viz. 3 x 4 represents 3 groups with 4 objects in each group, as demonstrated in the diagram below:

At S.A.M, when we teach the concept of multiplication, it is not just about memorization of tables. We ensure that a child is also introduced to concepts of groups and number of objects in a group. These concepts assumes significance particularly in context of word problems.

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Understand "Why" not just "How"

We encourage children to not just focus on "How" to solve a problem but also think "Why" a problem is being solved in a certain way. We will illustrate this with another simple example:

10 - 3y = 1

When we try to solve the above algebric equation, we write it as follows:

10 = 1 + 3y

If you note, "-3y" has been moved from left hand side of the equation to right hand side and it has become "+3y".

We do this step as an algebric rule. Have you ever wondered, why this happens? Why does the sign change when we move it from left to right?

As S.A.M, we explain this concept using the part-whole principle on a bar model.
Let 10 represent the ‘Whole’ as represented by the bar below:

The equation says "10-3y". So, effectively we are taking away 3y from the whole of 10 (yellow portion in the bar below) and post that we are left with "1" (red portion of the bar below)

Hence, "3y" and "1" represents the 2 parts which when combined makes a whole of 10. Thus,

10 = 1 + 3y