Mathematical treasures
Sheela Iyer
Multiplication is one of the most important functions in mathematics. But, it has received a bad name because children are forced to memorize the multiplication tables. What if I tell you that memorizing the multiplication tables is no longer necessary?
The array method is an innovative way of learning multiplication, gradually leading to constructing the entire multiplication table. This method is simple to learn and makes the multiplication process visual and easy to understand.
Constructing tables for multiplying any one digit number by another one digit number with the help of the array method is very easy. All you need are 10 to 20 small sticks like those from a broomstick, which can easily be carried in the school bag.
An “array” is built by arranging the sticks in a vertical direction with another set crossing them horizontally.
To find 2×5, students have to arrange two sticks vertically with equal spacing and then place another five sticks horizontally across the two sticks so that a criss-cross pattern is formed. The array can be referred to as a 2X5 array.
One can get the product of 2 and 5 by counting the number of junctions where the sticks cross each other. In the 2X5 array there will be 10 such junctions. This means 2X5=10!
Looking at this array from a perpendicular direction, we can see that it is also a 5X2 array!
The students will get a visual confirmation that 2X5=5X2. They will learn later that this is called the commutative property of multiplication.
Once the idea is understood, students can easily get products of numbers from 1 to 9 with numbers from 1 to 20. i.e. from 1X1 to 9X20.
These products can be arranged in a single table which wil be a 10X10 array and called a “one-page multiplication table.”
By studying the numerous patterns in this one-page multiplication table, most of the multiplication tables can be remembered.
The same idea or arrays can be extended to the multiplication of a two-digit number by another two-digit number.
This method also illustrates the logic behind the standard algorithm when numbers greater than 10 are multiplied together.
The array method of multiplication is one of several methods that I picked up from the rich mine of mathematical treasures that PKS sir had.
The author teaches primary math at Reliance Foundation School, Jamnagar.
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