Addition Fluency 1

Importance of adding 2 numbers, each <=10

Addition of any two numbers can be ultimately reduced to a series of additions of 2 numbers, each <=9. (In any “place”, whether it is hundredth or millionth place the number would be from 0 to 9). Hence the fundamental unit of any addition is the addition fact of 2 numbers, each <=9.

Later we will also see techniques for adding bigger numbers using fingers.

Two Strategies for Addition

All addition strategies can be reduced to two - “Counting All” or “Counting On” .

1. Counting All – This idea come from the “put together” metaphor. To find 2 + 3, we put 2 tokens first and then 3 tokens next. The total number of tokens of counted again. This is a good beginning strategy for children as it is very easy to understand. But very soon, children will realize that it is tedious for bigger numbers. Hence a second strategy has evolved.

2. Counting On – This idea comes from the “more than” metaphor. We know the individual count of at least one of the numbers. I.e in 3 + 5, we know the count (3 or 5) of at least one of the quantities. So we “count on” from this number, using fingers to keep track of the count.

   1. This method is very useful when one of the numbers is big and the other small. So, if we want to find 45 + 8, then we know 45 (we remember this number) and count on 8 steps from 46.

   2. The count for the 2ndnumber can be kept with our fingers.

So, we see that “counting on” is a more powerful strategy.

Addition facts can be classified in several ways depending on how they can be represented using the fingers. We will see some of them in subsequent chapters.