Visualizing the Numbers (Part II)

As discussed earlier, here is the set of patterns I use for numbers from 1 to 10. I use cards for this purpose. The size for the card I use is 3" x 3" for a single dot. On the backside of the card I write the symbols as well as the spelling of the number representing the pattern.

I always keep 55 sets of these cards for my class. And I use them to teach addition, multiplication, subtraction and division. I use these till children in my class can mentally visualize the numbers involved.

When I teach addition, I use different combinations of these cards. I show them that addition is putting the numbers together. Eventually I ask children to take any even number (e.g. eight) and add it to an even number (e.g. two, four, ...etc.) and observe the total. Similarly, I ask them to add an odd number (e.g. one, three, ...etc.) to an even number and observe the total. I carry out the similar exercise for addition of an even number to an odd number and finally, addition of an odd number to an odd number.

This helps children to learn what is summarized in the figure to the left-hand side. . Here the children can observe that 1. when an odd number is added to an even number we get an odd number. 2. when an even number is added to an even number we get an even number and 3. when an odd number is added to an odd number. we get an even number.

Once a child has understood this concept s/he will never accept 55 as an answer for the question, "what is the addition of numbers 27 and 29?" The same is applicable for even larger numbers with three or four digits. With the sets of number patterns we can easily help our children understand that multiplication is only a shortcut for representing repeated addition of a single number. In the previous article we had seen how 8 x 9 (an even number taken odd number of times) could be represented using the number pattern. When dealing with such multiplication, we can ask our children to try an even number any number of times and observe the product.

The observations made by children could be summarized as shown in the figure on right -hand. Children can immediately sense that even shapes appear consistently and they are automatically led to the conclusion that any even number multiplied by any number of times gives an even number.

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