Addition Fluency 3

We will now see more addition strategies which use finger representation strategies based on the “number line” & “place value” concepts.

Using the Ruler as a calculator

Two rulers, each with cm markings up to 30, can be used by students as a calculator. For larger numbers the meter scale with markings up to 100 can be used

Let us add 23 and 17. Keep the rulers parallel, one above and numbers increasing from left to right. Keep the scales such that the 0 of the upper scale coincides with 23 of the lower scale. The total would be the reading on the lower scale which coincides with 17 of the upper scale.

This method should be used initially in addition problems where the total would be less than 100. Initially this method can be practiced on foot rules with markings up to 30 and using smaller numbers.

This method is a good introduction to the concept of the number line – a line where numbers can be arranged serially. and using it for addition

Adding 2-digit numbers using the “place value” concept -1

This is possible in cases where one of the numbers can be represented with fingers of both hands, such that the fingers of one of the hands represent the “tens” and the other represents “ones”. For example, 45 can be represented with 4 fingers of the right hand and 5 fingers of the left hand.

The other number is remembered. The addition is done by “counting on” the tens (left hand fingers) and then the “ones (right hand fingers).

45 + 24 will proceed like this 45 -> 55 (1st finger from left hand) ->65 (2ndfinger from left hand) -> 66 (1stfinger from right hand) -> 67 (2ndfinger) -> 68 (3rdfinger) -> 69 (4thfinger)

Adding 2 digit numbers using the “place value” concept -2

As students become fluent with this idea, it can be used to add any two 2-digit numbers.

Let us again take 67 + 89.

Remember 89.

Extend 7 fingers using both hands representing the unit’s place value. Count on and get the total as 96. Remember 96.

Extend 8 fingers using both hands representing the ten’s place value. Count on from 96 in tens. 96 -> 106 -> 116 ->126 ->136 -> 146 ->156 ->166 ->176.

Answer is 176.

Using the Number Line Concept

The number line can be used as a tool for addition as well as subtraction.

It can be used for addition using the concept of "adding on". The number line has to be marked with a number range, suitable for the problem at hand.

Imagine adding 83 & 42. Start with 83 on the number line. Count ahead in steps of ten 4 times (which is adding 40) and reach 123. Then count ahead 2 steps and reach 125.

Using the Blank Number line Concept"

Here the number line is not actually drawn and marked with numbers. The student imagines the number line and shows the "adding on" concept by drawing short curves which start from one number & jumps to the result desired.

Again taking 83 + 42. the student marks 83 on paper. Then makes 4 jumps signifying 40. Where each jump lands, she marks 93, 103, 113 & 123 respectively. Then she makes another jump signifying 2 and ending at 125.

This exercise prepares students for doing the addition mentally visualising the blank number line in her mind.