Addition Fluency 2

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We will now see techniques for learning addition facts, involving 2 single digit numbers, visually until they can be practiced, recalled and used fluently.

This is the simplest case. Each number can be represented with fingers on each of the hands and the total counted. Over a period of time, the visual understanding strengthens and the number can be &ldquo;recognized&rdquo; by just seeing the finger pattern.
 * 1)  Adding 2 numbers, each &lt;=5 (Counting All) 

The 2 numbers can also be added by &ldquo;counting on&rdquo;. One of the numbers can be &ldquo;remembered&rdquo; and the 2ndnumber represented by folded fingers. As the &ldquo;counting on&rdquo; progresses, the fingers can be straightened one by one until the all the fingers are straightened.
 * 1)  Adding 2 numbers, each &lt;=5 (Counting On) 

Many teachers may feel that using &ldquo;counting on&rdquo; with small numbers is superfluous. But doing &ldquo;counting on&rdquo; with small numbers gives children practice of &ldquo;counting on&rdquo;. It also enables the answer to be checked with both the above methods.

One of the numbers (preferably the bigger) can be remembered. The second number can be represented by extending fingers of both palms. As the &ldquo;counting on&rdquo; progresses, the fingers can be straightened one by one until the all the fingers are straightened.
 * 1)  Adding 2 numbers, both &gt;=5 &amp; &lt;= 9 (Counting On) 

(Please read Chapter 7.3 for revising Segment representation)
 * 1)  Adding 2 numbers, both &gt;=5 &amp; &lt;=9 (Counting All) (Segment Representation) 

One of the numbers (preferably the bigger) can be remembered. The second number can be represented on one of the hands using Segment representation. As the &ldquo;counting on&rdquo; progresses, the thumb can touch each of the segments until the 2ndnumber is counted out.

Each of the numbers is represented on one of the palms using the Modulo5 representation. Both the palms are brought together and the total number of extended fingers is found out. The answer is got by adding ten to it. The following example will clarify the technique.
 * 1)  Adding 2 numbers, both &gt;=5 &amp; &lt;=9 (Counting All) (Modulo5 Representation) 

Take 9 + 7. If 9 is represented on the left hand, it would have 4 fingers extended. Similarly representing 7 on the right hand would have 2 fingers extended. So the total extended fingers would be 6. The total is 16. Hence 9 + 7 is 16.

This works because in this representation, 5 is hidden in each hand. On one hand to represent 7, we extend 2 fingers (hiding 5) and I on the other hand to represent 9, we extend 4 fingers (hiding 5). Hence a total of 10 is hidden in this process. Hence the answer 6 extended fingers becomes 16.

Adding 2 numbers at least one of which is &lt;=9 (Counting On)

The bigger number should be remembered. The 2ndnumber can be represented with folded fingers, with one or 2 hands. As the &ldquo;counting on&rdquo; progresses, the fingers can be straightened one by one until the all the fingers are straightened.

Example 56 + 4 will proceed as 57 -&gt; 58 -&gt; 59 -&gt; 60, with one finger being straightened at each step.

Strengthening Number Sense

We are using a variety of techniques to represent numbers on fingers, because these will strengthen number sense.

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